Physics education researchers have developed rigorous empirical methods to evaluate what students learn about physics concepts under various modes of instruction, including the traditional one (i.e. lecturing without active student engagement), and the most important finding to emerge from this field is that the traditional approach to physics instruction is not effective. This often goes unnoticed, because the methods that are traditionally used to assess whether or not students have achieved the goals, namely having students solve quantitative problems by the manipulation of formulae, do not evaluate functional understanding and scientific reasoning ability; and thus the students’ lack thereof is not observed. The failure is not that of the students or the instructor, but of the method of instruction. This project has as its goal to mitigate this failure in a sustainable way, by making a complete transformation of the way a set of courses is taught. Faculty members who have not taught these courses will be able to do so effectively, without compromising their ability to accomplish our other missions of research and advanced physics education. The development of a common set of teaching materials (based on interactive engagement) for all instructors to use, with mentoring and faculty development, will make high-quality introductory physics teaching sustainable in the long term.
The introductory physics classes at UNC-CH are typical of large universities in many ways. There are two sequences (of two semesters each), with essentially no crossover of students between the two. Each of the four courses is taught in multiple sections in both the fall and spring semesters (and in a single section in summer school). The average number of students enrolled in the four courses in a given semester (fall or spring) is 640. The courses assume no advance knowledge of physics, though many students who take them have had a physics course in high school.
The algebra-based sequence (P24/25) has average enrollments of 500/370 students per year (plus 55/45 in summer school), taught in lecture sections that range in size from 30 – 150 students. The students also meet in laboratory sections of 16 every two weeks, taught by graduate teaching assistants. The syllabus includes mechanics and thermal physics in P24 and E&M, optics, and modern physics in P25. The students are predominantly life science majors who are required to take the course. Many are planning careers in health affairs and therefore intend to take the MCAT. Essentially none of these students will take an additional physics course.
The calculus-based sequence (P26/27) is the foundation of the physics majors’ sequence, and requires a semester of calculus as a prerequisite (the second and third semesters of calculus are to be taken as co-requisites). It has average enrollments of 235/175 students per year (plus 35/33 in summer school), taught in lecture sections that range in size from 20 – 110 students. (There is also a separate Honors section that enrolls 24 students or fewer.) These enrollments are smaller than those at most other public research universities of comparable size, due to the absence of an engineering school at UNC-CH. The students also meet once per week in recitation sections of 30 – 50 students and laboratory sections of 12 students, taught by graduate teaching assistants. The recitation sections focus on problem-solving skills, often oriented toward the end-of-chapter problems assigned for homework. Attendance is often low. In recent years some faculty have experimented in a minor way with the use of Tutorials in Introductory Physics by the Univ. of Washington Physics Education Research Group. The syllabus includes mechanics in P26 and E&M and optics in P27. (Thermal physics and modern physics are taught in separate courses.) The students are typically physical science majors who are required to take the course. On average, approximately 15% are physics or applied science majors (who will take additional physics courses), 15% are computer science majors, and 30% are chemistry majors. The latter two groups, and the students pursuing other majors who make up the rest of the class, are unlikely to take an additional physics course. It is worth noting that approximately 15% of the students have not declared a major by the time they take the sequence (in their first or second year).
In the past five years, in the fall and spring semesters a total of 88 lecture sections of these courses have been taught by 24 faculty members. The lecturers ranged from award-winning teachers with 30+ years of experience in teaching introductory physics to postdocs or other persons outside of the permanent faculty who were hired to teach a single course. Each section is considered an independent class, although some coordination among the lecture sections in a given semester is made necessary by the fact that students from different sections enroll in the same recitation and laboratory sections. (This coordination is more important among sections of P26 or P27, which have recitations, than it is for those of P24 or P25, which do not.) Homework assignments (in the form of end-of-chapter problems) may be assigned in all courses, though in P24/25 they often are not graded. Some sections have used the Web-based homework system WebAssign. Each lecturer adopts her or his own style and method of presentation, and the sharing of “best practices” takes place only under the occasional impetus of the individual faculty member.
Traditional physics instruction, as practiced in most physics departments today, involves the presentation of the course material in a standard lecture, with the concepts organized as fully-formulated generalizations that are applied to a few special cases. The students act as passive absorbers of the material and are not required during the lecture to engage intellectually with the ideas being presented. This traditional method is sometimes called the “transmissionist” or “broadcast” mode of teaching.
For the past 25 years or so, the field of physics education research has taken as its subject the learning and teaching of physics. In research carried out by physicists in university physics departments, rigorous empirical methods have been developed to evaluate what students learn about physics concepts under various modes of instruction, including the traditional one.1 The most important finding to emerge from the field of physics education research is that the traditional approach to physics instructionis not effective in achieving the learning goals we have for our students. The methods that are traditionally used to assess whether or not students have achieved the goals, namely scores on homework assignments and exams in which students solve quantitative problems by the manipulation of formulae, do not evaluate functional understanding and scientific reasoning ability. The fact that traditional instruction has ultimately been effective for a small number of students, namely those who later become professional physicists, does not mean that it is effective for the vast majority of introductory physics students.
A more specific set of findings was summarized by McDermott2, one of the founders of the physics education research field.
These findings of physics education research are extremely robust, in that they have been demonstrated in thousands of students in many types of institutions (from high school to elite universities) and with many different instructors (from marginally-qualified beginners to award-winning experts). The failure is not that of the students or the instructors, but of the method of instruction.
It is fair to say that of the many physics teachers who teach in the traditional way, very few do so because we have made a thorough evaluation of the efficacy of other pedagogical methods and have concluded that standard lecturing is best. Very few teachers have ever had the opportunity to make such a study, even if we had been motivated to do so. Most teachers of physics at the university level have very little teaching experience when we begin our professorial careers, with that experience being limited to leading laboratory and recitation sections for a few years during our graduate training. Teaching methods and the literature of physics education research do not form part of the graduate training of the vast majority of physicists, and the relatively brief postdoctoral period before the first faculty appointment is typically devoted entirely to research. The realities of university life, especially at research universities, offer neither opportunities nor incentives for enhancing or transforming our approach to teaching. The reasons why we continue to lecture in the traditional way despite the available evidence that it is ineffective can be summarized as follows3:
These barriers to change are all entirely understandable, and impugn neither the skills nor the dedication of university physics teachers. They can be overcome, however, with an appropriate group effort within a department.
Physicists generally agree on a set of overall goals for introductory physics courses, independent of the specific content of the course. These goals include an understanding of fundamental physics concepts and the ability to apply them to specific situations, the ability to make use of multiple representations (equations, graphs) in analyzing a situation, and the ability to design and carry out a scientific experiment. Bloom’s taxonomy of the cognitive domain4 provides a way of organizing these goals.
Other fields that require their students to take introductory physics courses typically have similar goals. For example, a small group of UNC-CH Biology faculty emphasized the importance of basic physics concepts, and hoped that their students would come away from the introductory physics course with an awareness that these concepts have important applications in living things. They would like students to understand what a model is, and how models of varying degrees of sophistication can be used to analyze a physical situation. They are especially concerned that students gain a facility with dimensional analysis and scaling as well as knowledge of basic mechanics and electric circuits5 . UNC-CH Mathematics majors pursuing the BS degree are also required to take a year of introductory physics, with the goal of seeing the physical motivation for the development of the calculus by examining the relationships among rates of change of physical quantities6 . The UNC-CH Environmental Science program also requires their students to take introductory physics, with the overall goal that “students should be able to examine a physical situation, abstract it to a mathematical representation, and use that representation to predict the behavior of the system,” and “students should have experience with analyzing and manipulating real physical situations, not just artificially simplified ones in the laboratory.”7 That program also has specific content goals, not all of which are covered in the two-semester introductory sequence. Geology faculty agree with the biologists that it is important for students to understand about modeling physical systems, and to realize that physics and mathematics concepts have applications in other contexts. The use of geology examples (which they are happy to supply) could help students see the connections. It would be especially useful for geology students to have some acquaintance with continuum mechanics, or at least to be aware that phenomena such as ductility and deformation exist. Some knowledge of fluid flow is also important for students in the field. If possible, the geologists would like students to gain some experience with numerical modeling (perhaps in simple calculations with Excel spreadsheets).8
As all teachers know, we signal what we want students to learn by how we assess them, i.e. by what kind of questions we ask on homework assignments and exams. It is notable, therefore, that although the goals we identify for our courses include higher-level thinking (including analysis, synthesis, and evaluation), the questions wepose to our students on homework assignments and exams typically only require knowledge, comprehension and application (and often can be solved by the use of rote memorization or undirected equation-picking).
It is clear from the findings of physics education research that traditional instruction in introductory physics, in which the student is expected to absorb passively the information presented in a standard lecture, is not effective at achieving our learning goals regardless of the skill with which the lecture is presented. However, it has been abundantly demonstrated that pedagogical methods that promote conceptual understanding through interactive engagement of students in “minds-on” (and perhaps “hands-on”) activities that yield immediate feedback through discussion with peers and/or instructors are far more effective at achieving those goals. These methods are especially effective when they are structured in ways that address the preconceptions that students bring to the classroom. Based on these findings, it is here proposed that the UNC-CH Physics and Astronomy Department take specific action:
To bring introductory physics instruction at UNC-CH closer to achieving our goals, the instructors assigned to teach the introductory courses should adopt interactive engagement methods of teaching throughout all segments of the courses.
Many such methods (discussed in detail in Section III below) have been developed by physics instructors for use in lecture settings, in recitations, in laboratory exercises, and in individual homework assignments. In transforming our teaching of introductory physics, it is therefore possible to select from a “menu” of methods based on their measured effectiveness, the resources (human and technological) required to implement them, and our own preferences and teaching style. However, a significant benefit can be gained if a group of instructors at an institution agrees upon a common set of methods to be employed by all those who teach the introductory courses. This allows the assembly of a set of teaching materials that can be shared by all instructors, thereby obviating the need for each instructor to “re-invent the wheel” (or, as is sometimes said of traditional instruction, to “re-invent the flat tire”) upon being assigned to teach the course for the first time or after a long absence from it. This can produce a significant saving of faculty time and effort (particularly for junior faculty, for whom the task of course development is new and thus even more time-consuming). Where technology-dependent methods are selected, the adoption of the same methods in all courses makes the most efficient use of the investment in the necessary hardware and software. The use of common techniques in all courses also assures that the students, who are unfamiliar with (and often suspicious of) methods that require them to learn in this way (see Section II.A.3 below), are able in the second semester to build on their experience in the first rather than having to adjust to a new set of pedagogical methodsii. (Note that the resistance of students to new learning methods can be overcome to some degree by explaining their purpose, and noting that their efficacy is supported by abundant evidence rather than being a mere notion of the instructor.). Finally, having the same methods used in all courses, and especially in multiple sections of the same course, allows the instructors assigned to teach different sections of the same course in the same semester to combine forces as a team to share the tasks of teaching the class in creative ways that may reduce redundant effort.
Evaluation of the effectiveness of these different pedagogical methods has been accomplished in many cases by use of standardized evaluation tools. The most widely-used of these is the Force Concept Inventory9 (FCI), a set of 30 multiple-choice questions that test understanding of basic Newtonian concepts. The incorrect answers (“distracters”) embody common preconceptions about force and motion (e.g. the impetus concept described in Section II.A.1). The questions are worded in everyday language rather than the more formal wording typically used in physics problems. Before taking a university introductory physics course, typical scores on this test are in the 25-70% range (where a score of ~60% represents the threshold of Newtonian thought and ~87% can be defined as “mastery” of the Newtonian view). Fewer than 1/3 of the students who have taken a high school physics course have reached the Newtonian threshold, which probably explains why success in a college physics class is not well correlated with having had a high school class. Another such instrument is the Mechanics Baseline Test10 (MBT), which tests the students’ ability to interpret graphical representations and vectors and to do a modest amount of calculation. It is worth noting that although random guessing would produce an average score of 20% on these tests (because the answer to each question is selected from among five possibilities), committed non-Newtonian thinkers tend to score below 20% because they consistently choose the distracters that reflect their preconceptions.
Many articles have been published in which these instruments have been used to evaluate the effectiveness of a specific pedagogical technique developed by the authors of the article. However, a more broadly useful survey11 presents an overview of such data, involving > 6500 students in 62 introductory physics courses that used a variety of pedagogical methods (some traditional, some involving interactive engagement). In this study, the gain in understanding of basic mechanics resulting from the course (measured by comparing pre- and post-instruction scores on the FCI and MBT) was more than twice as large for courses that used interactive engagement than for courses that used traditional instruction. This was true independent of the initial knowledge state of the students and the type of institution. The difference in knowledge gained between the interactive engagement courses and the traditional courses is similar to the difference seen when comparing instruction given one-on-one with that delivered to large groups.12 This demonstrates that the key to more effective physics instruction is interactive engagement rather than a particular means to achieving it. This conclusion is supported by the findings of cognitive science research into teaching and learning (See Section II.A.1 below).
There exists also an instrument for measuring students’ conceptual understanding of electricity and magnetism, the Conceptual Survey of Electricity and Magnetism (CSEM).13 This test has been less widely used than the mechanics tests, in part because it was developed more recently. It also faces the challenge of surveying a much broader conceptual area than Newtonian mechanics, one that relies on understanding of concepts from mechanics such as force, motion, and energy. Unlike mechanics, most students lack familiarity with both the phenomena and the language and concepts involved in electricity and magnetism, which makes the development of an instrument to measure changes in students’ understanding more difficult. There has also been less physics education research about students’ preconceptions in this area, making it more difficult to construct appropriate “distracters.” Nevertheless, the results obtained so far (from more than 5000 students at 30 institutions) indicate that after traditional instruction, scores averaged around 50%, but that classes that employed an interactive engagement approach achieved post-instruction scores of about 70% (comparable to the scores of physics graduate students).
Because interactive engagement methods tend to emphasize conceptual understanding, the concern is often raised that students’ problem-solving skills will suffer if they are taught by these methods. However, a sound understanding of basic physics concepts is necessary for expert problem-solving (see Section II.A.4 below), and thus the ability to select the right principle is strongly correlated with the ability to solve physics problems.14 Further, where performance on an identical task (a set of standard final exam problems) has been compared for students taught by interactive engagement methods and by traditional instruction, the problem-solving performance of the students taught with interactive engagement is found to be no worse, and often significantly better, than that of the traditionally-taught students.15 Finally, specific methods designed to enhance students’ problem-solving skills can be incorporated into courses that use interactive engagement (see for example section III.D.2.d).
Making a significant change in the way a core mission is carried out is always difficult for a university department. This is especially true in regard to changes in teaching in a research university, where the reward structure for faculty is strongly biased toward excellence in research. In such an environment, the very significant commitment of time and effort that is required to effect educational change may be difficult to achieve without disadvantaging the faculty who take part. The inherent conservatism of an educational institution is also a factor. In some ways, both teachers and students are like farmers: we tend to do things the way we always have, because the loss of one season’s “crop” (i.e. a semester or academic year) due to a failed innovation is unrecoverable—those students will not have an opportunity to take that course again. But as research scientists, it is incumbent upon us to pay attention to findings reported in the literature and to build upon them by modifying our procedures accordingly when our current methods have been demonstrated to be ineffective. It would not be to our credit if we continued to base our experiments on the existence of the ether after the Michelson-Morley experiment had demonstrated that it does not exist; no more is it wise to persist in teaching our students in ways that have been shown to be less effective than they could be.
The changes here proposed will bring our introductory physics students closer to the educational goals we have for them. If we are sincere about those goals, we are obliged to do whatever we can, within the constraints of the research university environment, to achieve them. The constraints we operate under are significant: clearly we cannot approach the ideal of teaching our students one-on-one, nor is it even likely to be practical to teach 640 students per semester in an inquiry-based studio setting as is done in Workshop Physics16, effective though that might be. It will only be practical to change our way of teaching if in the steady state the operating costs (in expenditures of faculty time as well as money) are similar to those we sustain currently. If we can teach our students more effectively for a similar amount of effort, clearly we and our students will benefit. If this can be accomplished with a one-time expenditure of time and effort that is within our capabilities, and that does not have a significant negative effect on our research mission while it is undertaken, then the long-term benefits will outweigh the temporary costs.
Besides the goal of more effective teaching, we must also consider the long-term sustainability of our teaching. Of the 24 instructors who taught lecture sections of introductory courses in the fall and spring semesters of the last five years, seven are now retired or near retirement and four were temporary instructors hired to teach a single course. The count is even more striking for P24/25, for which five of the 12 instructors of the last five years are retired or near retirement and three were temporary. Clearly we need a system whereby faculty members who have not taught these courses can begin to do so, without compromising our ability to accomplish our other missions of research and advanced physics education.
Teaching large classes of introductory physics is difficult. Besides the inherent difficulty of introducing students to a subject that is largely unfamiliar to them (and is perceived to be “hard”), there are other many other aspects that require significant effort on the part of the teacher. The classes are typically large, so it is difficult to develop the kinds of personal knowledge of and relationships with the students that facilitate teaching and learning. In a class of 20 or so students (such as a typical upper-division undergraduate physics class), it is possible to establish a dialog whereby the students feel free to ask questions and to engage with the instructor in the material and the process of learning. In a lecture class of 50 students or more, this is all but impossible. The sheer logistics of keeping track of as many as 150 students, monitoring their performance, grading their tests, and even making sure who is enrolled and who is not makes for a daunting task.
To add to the difficulty, the “audience” for introductory physics teaching is quite different from the one we encounter in our other classes. 95% of the students who take these classes do so because they are majoring in a subject (other than physics) for which the classes are a requirement. They are not there by choice, and they are unlikely to take another physics course once they complete the introductory sequence. Their motivation to learn physics is therefore often limited to a motivation to “do well enough” to achieve their ambitions in their own fields. They generally do not see physics as being relevant to their fields of study or their future careers. They also typically find the subject to be daunting (even before they have begun to study it), due to the widespread belief that “physics is hard.” While some students enter the class with a genuine curiosity about physics, or develop one during the semester, the participation of most of the students in the class is driven more by external factors than by their internal motivation. It is also true that the level of relevant skill they bring (in scientific reasoning and mathematical manipulation) is significantly less than most instructors would desire.
For the relatively few students who either are intending to major in physics or could be enticed to do so, it is important that their first experience of the subject in college be a favorable one. The health of our department is dependent upon a steady (and, we hope, increasing) number of undergraduate majors. Within the College of Arts & Sciences, which has undergraduate education as one of its primary missions, the allocation of resources such as faculty positions to a department is influenced by the number of students who choose to major in the subject. The future of our discipline also depends upon a steady flow of bright, talented, and motivated young physicists. It is therefore crucial that potential future physicists not be “turned off” by their experience in the introductory courses. It has been well documented, in an extensive study of college students who had both the intention and the background to be successful science majors,17 that one of the primary reasons they give for switching to a non-science major is “bad teaching.” If we want to maintain or increase the number of physics majors, we must provide good teaching in the “gateway courses” (P26/27) that introduce the students to our discipline.
Because of the significant effort that is inherent in teaching large introductory courses, we would like to have a large pool of potential instructors so that a small group of faculty are not “stuck” teaching them every semester. Generally, faculty members who demonstrate significant skill at teaching introductory courses also have talents and knowledge that could be put to excellent use in other courses at the advanced undergraduate or graduate level. They, and the students, would benefit from the intellectual refreshment that comes from teaching a different course. For long-term sustainability, it is also vital that we bring our younger colleagues into the pool of introductory physics teachers. However, the task of “reinventing the wheel,” or beginning to teach such a course “from scratch” for the first time, is one that requires a very significant expenditure of time and effort. A young assistant professor, who must do everything that is necessary to achieve tenure within six years, has the difficult dilemma of either devoting an enormous amount of time to developing an effective course (and thereby possibly neglecting the tasks that will influence her tenure decision), or else doing what is necessary to “get by” in the class (which typically means teaching as she was taught). Even the latter choice is very time-consuming, especially the first time she teaches the course. For this reason, our department has often been reluctant to assign these courses to our youngest colleagues. Yet these new faculty members have much to offer our introductory students: they are typically lively and filled with an infectious excitement about physics, and they put a youthful face on a subject that is often seen as dry and dull. If we are to bring our younger colleagues into the “pool” of potential instructors of introductory physics, we must make it possible for them to become effective teachers without “heroic” effort. The development of a common set of teaching materials (based on interactive engagement) for new instructors to use, coupled with an appropriate program of mentoring and faculty development, can make high-quality introductory physics teaching sustainable in the long term.
In the last thirty or forty years, the field of cognitive science has undergone a revolution in the development of powerful research tools to investigate the processes of thinking and learning and the development of competence18. Of particular relevance to physics teaching is the improved understanding of the nature of competent performance and the principles of knowledge organization that underlie people’s abilities to solve problems in science. Research on learning and transfer has also uncovered important principles for structuring learning experiences that enable people to use what they have learned in new settings. This basic research is now available to be put into educational practice.
The picture of the learning process that has emerged from this research is generally referred to as constructivism. It has its roots in the ideas of Jean Piaget19, and it takes the view that individuals actively construct the knowledge we possess. This construction requires serious mental engagement by the learner, and is affected by knowledge we already have. If new knowledge conflicts with previously-constructed knowledge, it will not make sense to us and may not be constructed in a way that is useful for long-term recall or applicability in a variety of situations20. Three key findings of cognitive science that are supported by a solid research base and that are especially relevant for physics teaching can be summarized as follows21:
The implications of these principles for physics teaching are profound20.
The first of these principles, that the student is not an empty vessel into which knowledge can be poured, is especially important for physics teaching. By the time students arrive in the university classroom, they have spent almost two decades constructing knowledge to organize their experiences and observations in ways that make sense and can be used to make predictions. This body of understanding is usually fragmented, incomplete, and full of incorrect beliefs about the meaning and application of concepts within scientific settings. A classic example is the widely-held view that if an object is thrown straight up in the air it experiences during its flight a “force from the hand” that gradually diminishes as the object ascends until it is “used up” and the ball comes momentarily to rest at the top up the flight. Gravity then “takes over” and the object acquires increasing amounts of gravitational force as it falls, causing it to pick up speed until it arrives at its starting point. (Additional preconceptions are discussed in section II.B below.) This view would have been familiar to a medieval scholar, who would have referred to the “force of the hand” as impetus. It contradicts the Newtonian view (and Newton’s development of mechanics was hampered by it), but it is a logical (albeit incorrect) construction based on experience with moving objects. Because such views have been constructed over a long period of time with considerable effort, they are tenacious and difficult to uproot without explicit mental engagement to confront and reconstruct this knowledge. Standard methods of testing that probe only factual knowledge or do not force students to apply concepts in a wide range of situations can give a false sense of the “understanding” students have after instruction. Students may also respond in the classroom as they have been taught while maintaining their original views (see the story from Eric Mazur in the next section).
The second principle emerges from studies that compare expert and novice approaches to problem-solving (these differences are discussed more fully in Section II.A.4 below). One of the pronounced differences between experts and novices is that experts’ command of concepts shapes their understanding of new information, allowing them to see patterns and relationships that are not apparent to novices. Where a physicist sees orbital motion as a simple application of conservation of energy and angular momentum, an introductory physics student sees it as a disconnected topic to be learned separately from previous concepts. Without a well-organized hierarchical knowledge structure, the student cannot transfer what she has learned to a new situation.
The third principle also arises out of comparative studies of experts and novices. When asked to verbalize their thought processes while solving a problem, experts reveal that they monitor their own understanding as they work, noting when additional information is needed or whether new information was consistent with what they already knew, what analogies might advance their understanding, and what limiting cases are relevant. These metacognitive strategies can be taught, with the result that physics learning is enhanced22.
The constructivist view of learning has been developed in recent decades on the basis of cognitive science research on teaching, learning, and problem solving. However, as noted above, few teachers of physics in universities have had the opportunity to acquaint ourselves with the findings of this research or to consider deeply the question of how students learn. We rarely articulate or examine any aspects of our model of student learning, and it is therefore not as well-formed and consistent as the constructivist model. Based on observation of typical teaching practice, we can infer some elements of the “transmissionist” model held by most physics teachers.23
The first of these elements is vital, since the preconceptions that students bring to the classroom based on their ~20 years of experience in the world are very strongly held and will persist unless specifically confronted and overcome. Eric Mazur (Harvard) gives a telling example in his story24 of one of his students who was given a series of conceptual questions involving Newton’s laws (the FCI 9). The student, faced with questions such as whether the light car or the heavy truck exerts the greater force upon the other in a collision between the two, inquired, “Professor Mazur, how should I answer these questions? According to what you taught us, or by the way I think about these things?”
The second element is particularly important in regard to our assessment methods. If students’ knowledge of physics principles is heavily dependent on context (“since this is Chapter 7, I must need to use the work-energy theorem to solve this problem”), homework and exam questions that provide abundant contextual clues do not probe whether or not the student can recognize independently the contexts in which the principle is relevant. Yet it is this recognition that is at the heart of the understanding of fundamental physics principles such as energy conservation.
The final three elements of the “transmissionist” model arise from our own experience as students (or at least our memories of that experience). People who are university physics teachers today received essentially all of our physics education via the “transmissionist” method. This worked for us because we were motivated to spend long hours learning on our own (i.e. we had a large “time on task”), and as a result we were prepared to learn effectively from a good lecture.25 Since we are successful at what we do, and we have developed a deep understanding of fundamental physics principles (an understanding that we would like to pass on to our students as efficiently and effectively as possible), it is clear that this method of teaching “worked” for us. However, students who resemble us constitute a tiny fraction of the students to whom we teach introductory physics. At UNC-CH, less than 5% of the students in our introductory physics classes indicate a desire to major in physics. Of those, perhaps 1/3 will ultimately complete the major. Approximately 65% of those will go on to graduate school (some in fields other than physics). Thus of the ~ 735 students who begin one of the introductory physics sequences at UNC-CH, less than 1% are “like us” in having the interest, motivation, and skills to succeed in physics at the Ph.D. level. It is incumbent upon us to teach in ways that are effective for the other 99%.
At UNC-CH, as at many universities, the vast majority of the introductory physics students are in the traditional 18-22 year old age group. They are therefore nearly all at approximately the same stage of intellectual development in their approach to learning physics. W.G. Perry categorized the various stages of development seen among college students into four stages26, which can be observed among physics students.
The first of these stages is Dualism, in which all questions have a single right answer and the authorities (the physics teacher) will tell you what the answer is. Students in this stage consider knowledge to be discrete, factual, and quantitative, and that their role is to take the information given them and memorize it. They are passive learners, and are capable of giving simple explanations of terms and concepts but find it challenging to interpret what they have learned. Most students begin their study of physics in this stage, and traditional instruction typically does little to help them move beyond it. To gain a real understanding of physics principles, students must advance to higher levels of development in their thinking about physics.
The second stage is Multiplicity, in which many questions have no right answer so that all opinions about them are considered equally valid. The student expect the teacher to show her “the way to think” so that the she can follow it. She finds it challenging to make use of evidence to understand the differences among multiple perspectives. With appropriate instruction and modeling of expert methods of approach to problem-solving, introductory physics students can move into this stage.
The third stage is Relativism, in which it is recognized that not all approaches to a problem are of equal validity in all situations, that knowledge is contextual. The student in this stage is learning to analyze, synthesize, and evaluate (see Bloom’s taxonomy in Section I.B.3), and expects the instructor to provide guidance. She is able to use evidence to analyze and support a position and to generate new relationships, but still finds it challenging to sort out evidence and decide among equally good alternatives. Bringing students to this stage is a reasonable goal for an introductory physics course.
The fourth and final stage is Commitment, in which choices are made after the reasoned exploration of the Relativist phase. In this stage the student takes the best of what is offered and incorporates it into her own learning. She is able to learn independently and collaboratively and can relate designated learning tasks to her own issues and values. She still finds in-depth scholarship to be challenging, but is willing to take on the challenge. Students typically do not reach this stage after only a year of physics study, but the introductory course can lay the foundation for achieving this stage in more advanced study.
It is worth noting that individuals can exhibit multiple stages in Perry’s scheme simultaneously, in different areas of thought. For example, a student may be at the relativist stage in her understanding of political theory and its historical implications, yet be a dualist in regard to a new and different subject such as physics.
The specific attitudes that students have regarding the learning of physics are of special relevance. A series of studies of students’ expectations about the nature of physics, what they are supposed to do, and what kinds of materials they are supposed to learn27 has shown that students’ beliefs about how physics is to be learned are often counterproductive to helping them develop a strong understanding of physics or expert problem-solving skills. For example, before beginning a college physics course, typically more than 40% of the students surveyed believed that they should take what is given by authorities without evaluation, that physics consists of separate facts or “pieces,” that they should focus on memorizing and using formulae, that ideas learned in physics are unrelated to experiences outside the classroom, that physics and mathematics have no strong relationship to one another, and that it would not be necessary for them to modify their thinking as they learn physics. In contrast, physics instructors expect our students to learn independently by evaluating and understanding the information presented, believe that physics is a connected and consistent framework, that it is important for students to understand the underlying concepts, that ideas learned in physics are useful in real-world contexts, that mathematics is a convenient way of representing physical phenomena, and that students should make an effort to use available information to modify and correct their thinking.28 The truly depressing finding of these surveys is that the tendency of the students to agree with the instructors on these points declined in almost every case after traditional instruction. At the end of a traditional course, 50% to 60% of the students surveyed held attitudes that interfered with their success.29
Cognitive research has revealed the significant differences in the ways that an expert, (i.e. a physicist) approaches a physics problem and the ways that a novice (i.e. an introductory physics student) approaches it.30 The physicist’s ability to solve problems depends on a rich body of knowledge about physics, but this knowledge is not a set of disconnected facts. Rather, it is connected and organized around concepts (e.g. Newton’s laws or conservation laws), it is conditionalized to specify the contexts in which it applies, and it supports transfer to new contexts. This body of knowledge allows the physicist to sort problems into classes that can be solved with a particular approach (e.g. by applying conservation of momentum), and to solve the problems using general principles applicable to each class.31 On the other hand, the physics student’s knowledge tends to consist of an unconnected collection of facts without underlying principles.
The physicist’s command of physics concepts shapes her understanding of new information—it allows her to see patterns, relationships or discrepancies that are not apparent to the physics student. This makes it easier to learn new material, as has been illustrated in a wide range of fields including electronics,32 chess,33 and computer programming.34 In the electronics experiment, expert and novice electronics technicians were shown a complex circuit diagram for a short time and then asked to reproduce as much of the diagram as they could. The experts could reproduce large portions of the diagram accurately even after exposures of only seconds, whereas novices could not. The experts achieved this facility by organizing what they saw into clusters of related elements (referred to as “chunks”) governed by underlying principles or concepts, such as a group of transistors and resistors that formed an amplifier. They were then able to use what they knew about the structure and function of a typical amplifier to reproduce the “amplifier chunk.” When both experts and novices were shown diagrams in which circuit elements were arranged randomly, so that “chunking” was impossible, both groups were equally poor in their recall. An expert knows more than a novice because she has more conceptual “chunks” in her memory, she knows more relationships and features that define each chunk, she understands more of the interrelationships among the “chunks,” and she has effective methods for retrieving related “chunks.”
Expert and novice solvers of physics problems also differ in the way that they use the knowledge that they possess. When a physicist is presented with a physics problem, she draws a diagram and identifies the major principles that apply to the situation (e.g. conservation of mechanical energy, impulse-momentum theorem). She may recall useful analogies (“this is similar to the ballistic pendulum”) and identify limiting cases (“if there were no friction, the energy would remain the same”) before deciding on a procedure by which the relevant concepts can be applied. Only then does she write down the relevant equations and proceed to a quantitative solution, which she then checks for “reasonableness” by comparing it to the qualitative analysis she first performed. Experts will use this approach even in solving a problem for which their well-developed physical intuition is not helpful,35 so that they are not able to predict the solution approximately in advance. The key element to the expert strategy is that it begins with the “deep structure” of the underlying physics principles and the contexts in which they apply.36
The introductory physics student pays attention primarily to the “surface features” of the problem (e.g. that it contains an inclined plane or a spring) and begins by finding and manipulating equations that contain the quantities given in the problem until she isolates the quantity that is desired. She will typically substitute numerical values into the equations as soon as possible, and will not check to see whether the result is dimensionally correct or has a reasonable magnitude. Students persist in using this method (often called “plug and chug”) because it often yields correct answers to the kind of problems they are asked to solve, particularly if they can narrow down the set of possibly-useful equations by knowing which chapter it comes from and matching the variables in the equation to the quantities given in the problem statement.
As noted above, students enter the introductory physics classroom with a variety of preconceptions about the physical world that they have constructed over their lifetimes to date. These preconceptions, unless explicitly confronted and modified, tend to interfere with learning the correct concepts. There is a large literature produced by physics education researchers in which these preconceptions are articulated. A comprehensive bibliography of publications prior to 1999 is available,37 which also includes works about the design of effective instruction. Brief summaries of a few of the findings are given in the following sections.
In kinematics, students display significant confusion among position, velocity, and acceleration, all of which tend to be subsumed under a vague concept of “motion.” Two objects moving in parallel are taken to have the same speed when they have the same location, e.g. a car that is passing another car in an adjacent lane is said to have the same speed when the cars are side by side.38 Even students who are able to state the definition of velocity are frequently unable to relate their idea of speed to the ratio of the distance traveled to the elapsed time or to the idea of instantaneous velocity. This confusion extends to graphical representation of motion, so that students tend to draw identical position-time and velocity-time graphs for motion that they observe.39 In general, students display significant difficulty in connecting graphical representations with real motion and with physics concepts.40 Similarly, students tend to believe that two objects have the same acceleration when they have the same velocity.41 This inability to distinguish between a quantity and the change in that quantity manifests itself in other concepts, such as electric or gravitational potential difference. Finally, since acceleration is associated in the students’ mind with motion in general, an object with zero velocity (e.g. a projectile at the top of a vertical flight) is believed to have zero acceleration.42
As students move beyond one-dimensional kinematics, their understanding of vectors and how to manipulate them becomes important. Yet a significant number of students display serious conceptual confusion about basic vector concepts, such as two-dimensional vector addition and subtraction.43 Lack of facility with these simple procedures (despite having been introduced to them in earlier mathematics classes) seriously inhibits their ability to understand the concept of net force.
Among the most pervasive difficulties that students have in understanding elementary dynamics arises from their preconception that a force requires an active agent. This inhibits their ability to recognize the presence of passive forces such as the normal force exerted by a surface or the tension in a string that adjusts itself to an applied force.44 Students also tend to equate force with motion, concluding that an object in motion must experience a force in the direction of motion, and that constant force produces constant velocity.42 Motion is also widely believed to continue in a curvilinear path once constraints are removed,45 as if the object “remembers” the curve in which it had been traveling.
Difficulties with Newton’s 3 rd law are also extremely pervasive. Confusion between the concepts of force and momentum, and between force and mass, frequently lead students to conclude that two interacting objects can exert forces of different magnitude upon one another.46
There has been much less investigation of student preconceptions about electricity and magnetism than about mechanics. In addition, students have less experience with electromagnetic phenomena than they do with forces and motion, so their preconceptions tend to be less focused. On the other hand, persistent preconceptions from mechanics (e.g. the association of constant force and constant velocity, and lack of application of Newton’s 3 rd law) can inhibit the learning of concepts in electromagnetism.47
Much of the investigation into students’ understanding of electricity has involved DC circuits.48 In this context it becomes clear that students do not reliably distinguish among current, voltage, energy, and power. Many preconceptions can be elucidated from student responses to questions about simple series and parallel circuits involving only light bulbs, batteries, and switches. Even the simple idea that the two terminals of a light bulb must be connected externally to different terminals of a battery and internally to one another through the filament is mysterious to many students.49 Students tend to believe that current is “used up” as it flows in a circuit, so that for example two identical bulbs connected in series across a battery would have different brightnesses. They also frequently display the belief that a battery produces a constant current regardless of the load across it. The inability to distinguish between a quantity and the difference in that quantity leads students to associate the brightness of a bulb with the magnitude of the potential at one of its terminals rather than with the potential difference between its terminals.
Students enter the elementary physics classroom with extensive experience of light and shadow and of using mirrors and lenses in their everyday lives. However, research into their conceptual understanding reveals that they hold preconceptions that are at odds with readily-observable phenomena. Although students are aware that light propagates in straight lines (in situations where diffraction and refraction are irrelevant), they display an inability to apply this concept properly to a simple situation involving a light source and a mask, as well as a failure to recognize that a line source can be treated as a series of point sources.50 Students also had difficulty locating the image in a plane mirror, believing that it lies behind the mirror along the line of sight between the viewer and the object51 (this is of course true only if the line of sight is perpendicular to the mirror). They also believed that when presented with a small mirror in which they could see only their heads, they would be able to see more of themselves if they stepped backwards. Despite the fact that this belief contradicts their own experience with small wall-mounted mirrors such as those found in bathrooms, it is very widespread.
Students also have a variety of preconceptions about the behavior of lenses that are contrary to phenomena that they must surely have observed. For example, when a group of students was shown a converging lens producing an image of an object (the filament of an unfrosted light bulb) on a translucent screen and they asked what would happen if the lens were removed, almost none of them recognized that without the lens there would be no image.52 This preconception is persistent, despite the fact that in their daily lives students have not observed light bulbs forming images in the absence of a lens.
Further confusion about image formation was illustrated in the same study when students were presented with the same apparatus and asked what would happen if half of the lens were covered with an opaque barrier. A majority of the students predicted that half of the image would disappear rather than that the image would become dimmer but otherwise remain the same. They also believed that if the lens remained uncovered but the screen were moved toward or away from the lens that the image would change in size but would persist (as if the presence of the screen caused the image to be formed rather than simply making it visible).
The fact that students enter introductory physics with preconceptions about physical phenomena would not be problematic if what they learn in the course were sufficient to remove those preconceptions and replace them with the correct ideas. However, physics education research has demonstrated over and over again that these preconceptions persist even after traditional instruction, and are found to persist in students who have successfully completed a standard university physics course. The fact that this comes as a surprise to many instructors results from our use of quantitative exam problems as our primary means of assessment. Students are able to solve these problems correctly by following memorized procedures without making use of the concepts, or by separating the “physics class concepts” in their minds from their own beliefs about the way the world works.
For example, 60-70% of students who had completed an introductory physics course continued to confuse velocity and acceleration, believing that two objects with the same velocity at a given moment must also have the same acceleration.41 In an extensive study of students’ understanding of Atwood’s machine,53 a group of students was presented with two modified Atwood’s machines: one consisting of a block suspended vertically from a string that passes over a pulley and is then attached to a wall, and the other in which the string passed over a second pulley and terminated in a second (identical) mass. The students were asked to compare the tensions in the strings in the two machines. Despite having studied Newton’s laws, analyzed textbook problems involving massless strings, performed a standard Atwood’s machine experiment and completed a homework problem involving a virtually identical situation, only about half the students were able to answer correctly that the tension in the two strings would be equal.
The lack of effectiveness of traditional instruction can also be illustrated for more sophisticated mechanics concepts such as work, energy, and momentum. In one study,54 students were asked to compare the kinetic energy and momentum of two pucks of different mass acted upon by equal forces over equal distances. Of a group of students who had earned above-average grades in the honors section of a calculus-based introductory physics class, only 50% were able to explain why the change in kinetic energy is the same for both pucks, and only 25% were able to explain why the more massive puck has the larger change in momentum. Of students who had completed the algebra-based course with above-average grades, essentially none were able to answer the questions correctly. Even physics majors enrolled in junior-level intermediate mechanics courses often show the same kinds of confusion between velocity and acceleration and lack of understanding of the vector nature of Newton’s 2 nd law that are displayed by students in the introductory course.55
In studies of understanding of simple DC circuits in which students are asked on a final exam to rank the brightness of identical bulbs connected in series and in parallel to an ideal battery, only 10% of students in algebra-based courses and 15% of those in calculus-based courses were able to give the correct answer.48 Many of these students were able to solve correctly more complicated circuit problems involving Ohm’s law and Kirchhoff’s rules.
Physical optics is a topic that most students know very little about before beginning a physics course. One might reasonably expect, therefore, that traditional instruction about light as an electromagnetic wave and the concepts and formal representations that are used to predict and explain diffraction, interference, and polarization would suffice to induce in students a correct understanding. However, students who had completed a calculus-based introductory course and earned above-average grades showed serious difficulty with the concepts they had been taught. For example, only 20% of such students (drawn from different classes with different instructors) were able to reason correctly that if the width of a slit is narrowed, the diffraction minima will move farther from the center of the pattern.56 This was despite the fact that they had completed all standard lecture and laboratory instruction on single-slit diffraction. (Even more distressing is the fact that only 60% of physics graduate teaching assistants were able to answer the question with the correct reasoning, which suggests that more advanced instruction does not alleviate fundamental misconceptions.) Many students simultaneously apply reasoning from geometrical and physical optics to account for diffraction, using geometrical optics for light passing through the center of the slit and physical optics for light at the edges. In other cases students show a tendency to memorize algebraic formulae without an understanding of the derivations (despite these having been carefully presented in the lecture and the textbook), for example in a two-slit interference case using the formula derived for the location of an interference maximum when asked to locate an interference minimum.
Many more examples of the persistence of mistaken ideas despite traditional instruction could be cited (for a compendium of such publications, see Reference 37; many more of these ideas are discussed topic-by-topic in recent books about physics teaching57 ). It is clear that the fact that most physics instructors have not observed this phenomenon is related more to the fact that we have not looked for it than to the fact that our students do not display it. The constructivist view that the learner will not properly grasp new concepts unless her previous understanding is explicitly addressed is borne out by the body of physics education research involving tens of thousands of students at scores of institutions.
Although traditional instruction has been shown to be ineffective in many cases at replacing mistaken concepts with correct ones, there are pedagogical methods that research has demonstrated to be more effective. As early as the work of Piaget, the use of conceptual conflict to bring about conceptual change has formed the basis of many effective pedagogical methods. In such methods, the tendency to make a particular error is deliberately exposed by asking the student to predict the outcome of an experiment, or to answer questions about the detailed behavior of a particular system. The error is then confronted by showing that it leads to a prediction contrary to reality (by performing the experiment, or through a Socratic dialog or other series of directed questions). The student is then guided to a resolution of the conflict by substitution of the correct concept for the mistaken one. This approach can be used in many contexts (lecture, recitation, homework, laboratory), and is the basis for some of the pedagogical methods and materials discussed below in Sections III.B – III.E. Probably the most extensive and explicit embodiment of this approach is in the set of tutorials developed by the Univ. of Washington Group58 (discussed in Section III.C.2.a), which is intended to be used in recitation sections of large classes. The use of lecture demonstrations in which students are required to predict the outcome and discuss reasons for their predictions (and why those predictions were incorrect) is another way of providing conceptual conflict. The Oregon/Tuftsgroup has developed a set of experiments and worksheets for use in large lecture classes, this material is discussed in Section III.B.2.c below. In the laboratory, the Socratic Dialog Inducing exercises discussed in Section III.E.2.b are intended to guide the students through the confrontation of specific errors.
In the absence of specific evidence demonstrating that students who have successfully completed UNC-CH introductory physics classes display the same absence of a coherent conceptual framework; persistence of conceptual difficulties; inability to reason scientifically; and lack of understanding of the connections among concepts, formal representations, and the real world that have been documented over decades of physics education research, it is tempting to argue that our students are not like those students, and that our traditional-style teaching is much more effective than the teaching that those students received. And yet, this is no more reasonable than it would be to argue that the ether exists in our laboratories, even if none was found in experiments in 1887 at the Case School of Applied Science. The studies that make up the body of the physics education research literature have been conducted at all types of institutions, including major public research universities that enroll the best students in their respective states (e.g. the Universities of Washington, Maryland, Colorado, Indiana, Minnesota, and California-Berkeley), large institutions with a focus on engineering and technology that enroll students with above-average standardized test scores (e.g. Iowa State, New Mexico State, Arizona State), and elite private institutions (Harvard, Carnegie-Mellon) as well as scores of other institutions large and small, selective and inclusive. The instructors for the classes measured had widely-varying teaching styles and levels of experience. Yet the same conclusion is reached over and over again: after successfully completing a standard introductory physics course, most students have not achieved the learning goals we have for them, even though they have learned to solve standard quantitative problems in certain contexts.
Once we have recognized that we need to change the way we teach introductory physics, the next question we must address is what new methods we should employ instead. This task is much easier today than it would have been in past decades, because many different pedagogical methods have been developed and tested by physicists. In most cases the specific materials (problems, exercises, software, instruction schemes) required to implement the method are available either freely or for purchase (by the institution or by the students) at modest cost. The task before us is not therefore to develop new teaching methods and the materials needed to implement them, but to select the methods we find most effective and most suitable and to adapt them to our own local circumstances and teaching skills. We must make sure that we institutionalize the changes through faculty development and mentoring and TA training programs so that the longevity of the changes does not depend on the particular faculty members involved, and we must evaluate the results of the changes and continue over time to make modifications and improvements in the way we teach. What we do not have to do is engage in physics education research to create and assess new teaching methods and materials for introductory physics. Our task is one of adaptation and implementation, not invention. However, in doing so we are not merely following national trends. It is all but unknown for a major research university physics department to totally transform its introductory teaching without the catalyst of either an indigenous physics education research group or a major external threat to its resources.iii Smaller, primarily undergraduate departments have found such changes to be easier to make, both because teaching is a larger part of their mission (and thus commands a larger fraction of faculty time and effort) and because the smaller numbers of students make it possible for one or two faculty members to effect the necessary modifications in the courses. (Even in such cases the longevity of the transformation is not assured without some form of institutionalization that extends beyond the individual faculty member.) In performing the transformation here proposed, the UNC-CH Physics & Astronomy Department will serve as a model to physics departments at other research universities, and also to other departments and schools within our own institution.
In order to determine what teaching methods are most likely to achieve the learning goals we have for our students, it is necessary to identify those goals. Each course will have a set of specific content goals that are tied to the syllabus. For example, a student in P24 or P26 should, by the end of the course, be able to state Newton’s 3 rd law, apply it to a qualitative question (“in a collision between a small car and a large truck, which exerts the greater force on the other?”), and use it in a quantitative calculation of the net force on a body. However, it is also possible to identify a set of more generic learning goals that we hope that students in all introductory physics courses will achieve. The list of goals given below summarizes the ideas of faculty in our department who teach the introductory courses. As indicated, each goal can be identified with one of the elements of Bloom’s taxonomy of educational goals (see Section I.B.3).
By the end of an introductory physics course, students should be able to:
This list of goals is certainly daunting, and we should not despair if not all of our students achieve them even after we have transformed our teaching to use more effective methods. Upon extensive reflection, we may even choose to limit the number of these goals that we attempt to accomplish in our introductory courses. However, if we are sincere about our introductory teaching mission, and if we are committed to accomplishing it at a level that is commensurate with the quality of our institution (and with the quality of the scientific research in which members of our department engage), we must do the best we can using the best techniques available.
Certain of the learning goals we have for the introductory courses can most effectively be addressed in lectures. These are:
Others can be addressed in both lecture and in smaller-group settings such as recitations and Supplemental Instruction settings. These are:
One technique that is becoming more widely used in large lectures to engage students actively in the learning process goes by many names, but is most often referred to as “peer instruction” after Eric Mazur’s book of that name, 24 or else more generally as “interactive lecturing.”59 An instructor using this method intersperses her lecture with multiple-choice questions posed to the students (the question may be displayed as a PowerPoint slide, projected on a transparency, or simply written on the board). These questions are qualitative in nature (e.g. “will the brightness of the bulb in this circuit increase, decrease, or stay the same if the switch is opened?”) or involve a simple one-step calculation that the students can do in their heads. The distracters are chosen to embody specific errors of reasoning that students are likely to make. The students are all asked to respond (in an anonymous or semi-anonymous fashion), and the instructor can then gauge the degree to which the students understand the concept involved. If the concept appears to be well understood, she proceeds to the next topic in the lecture. If a significant number of students choose the wrong answer, she asks all the students to discuss the reasons for their choices in pairs or small groups for a few minutes before calling for another set of responses. In many cases those who have chosen the correct answer convince their neighbors who have chosen incorrectly, and the majority of the students now grasp the concept. If not, the instructor explains it further (perhaps asking a few students to tell the class why they chose the answers they did), paying particular attention to the specific preconceptions or misunderstandings that the most common wrong answers indicate. She may modify the question or supply a similar one and ask for another round of responses and discussions. Only when she perceives that most of the students have come to understand the concept and are convinced of the right answers to her questions does she proceed to the next topic. Variations on the technique involve having the students respond as small groups that must reach consensus before answering, or having one of the questions serve as a quiz for which the students receive credit for getting the right answer.
This method has a number of positive features. It allows the instructor to gauge the understanding of the students as she goes along, so that they do not fail to understand a later concept due to their lack of comprehension of an earlier one. It forces the students to be intellectually active during the lecture rather than passively recording what the instructor writes on the board. It engages the students in continual application and assessment of their own understanding of the concepts presented. It makes use of the students’ ability to explain things to one another in their own words, which are often easier for their peers to understand than the more formal discourse of the instructor. And, most importantly, it has been shown to be more effective than traditional lecturing. In many cases the students are aware of the difference, and attendance is better than for traditional lectures.60
Like all methods, it also has its disadvantages. The instructor is much less in control of the rhythm and pacing of the class than she is in a traditional lecture, and she must be “fast on her feet” to adapt to the responses of the students. She may not be able to cover the same amount of material that she otherwise would in a lecture (on the other hand, the students are likely to learn more of what she does cover). It can be distressing for her to see that her carefully-crafted explanation of a concept has not moved the students from their preconceived ideas.iv She (and her colleagues in nearby rooms) must be able to tolerate and manage a noisy classroom in which students are discussing the questions with one another.
Implementing this method requires some method of observing the students’ responses. In the simplest case, students can hold up flashcards with letters or numbers printed on them (corresponding to the various multiple-choice answers). This is inexpensive and requires no sophisticated technology whatsoever, but has some disadvantages. The responses are not totally anonymous (since students can see each other’s cards without too much difficulty), which may inhibit students who are unsure of their answers. It is impossible to record who has responded, so the instructor cannot give any course credit for participation. This reduces the students’ incentive to engage in the process. It can be difficult to see all the responses in a very large lecture hall (though this has not proved to be a problem in Phillips 215). Finally, some students resist using the cards because they consider them to be “dorky.”
A more sophisticated way of receiving student responses is to use an electronic response system. Such a system may be hard-wired or operate by infrared or rf signals (including via a wireless intranet). Each remote signaling unit (now almost universally referred to as a “clicker”) has a unique ID, as does the student using it. The students press the appropriate buttons to send their responses, and the instructor sees a display of a histogram of the responses of the entire class (which may also be shown to the students). Depending on the system, the responses may be totally anonymous, or the instructor may have a record that a particular student has responded (and thus can be given credit for participation), or the specific response each student gave may be recorded. Besides these advantages, students often consider the signaling units to be “cool” and are therefore more willing to use them. However, as with all electronic devices, there are expenses and maintenance issues associated with their installation and use. Either the department or the students may purchase the remote signaling units (some publishers now bundle units with their textbooks), with the latter option more made more attractive if multiple classes (perhaps in different departments) use the same system. See the following section for a description of systems currently available.
It is also possible to employ a more limited implementation of this method, in which a response system is not required. In this case, students are asked to write their responses to the questions in a workbook or on a worksheet (typically one in which the questions are pre-printed). To the degree that the students actually do the exercise, they gain the benefit of interactive engagement. However, without the reinforcement of “polling,” the students are much less likely to participate.v The instructor also does not have a way of knowing if the majority of students have grasped the concept being presented, and thus does not know if further explanation is necessary.
The other resource needed to implement interactive lecturing is a supply of appropriate questions upon which the instructor can draw. Eric Mazur’s book24 contains 149 questions on mechanics, 56 on E&M, 27 on optics, and 11 on modern physics. Many more (including some on other introductory physics topics, as well as other science and mathematics subjects) have been contributed to the Project Galileo web site (http://galileo.harvard.edu) maintained at Harvard. Many others are available as part of the “warm-ups” used in the Just-in-Time Teaching technique (see Section III.B.2.d below). Once the instructor understands the specific conceptual difficulties students are likely to have with a particular topic, it is also not difficult to write additional questions. The books on physics teaching in Reference lvii can be helpful in that regard.
Electronic response systems for use in interactive lecturing have been used for decades, and studies have found that they can enhance conceptual understanding if they are part of a constructivist-oriented classroom.61 However, it is clear that the benefits accrue from the pedagogical methods of interactive engagement, not simply from the use of electronic technology. A number of electronic response systems are currently available for purchase, and others are expected to come to market in the near future. There are several aspects to be considered in the selection of a system, and the evaluation of these aspects can change rapidly as the technology and the business models change. Thus any detailed description of the available systems quickly becomes outdated, and fresh information should be sought immediately before a decision to purchase is made.
The first consideration is the type of transmission system. The available systems use either IR or RF transmission. IR transmission requires line-of-sight access to a receiver, and thus several receivers in a large classroom. However, the transmitters and receivers are relatively inexpensive (since they are similar to those used in TV remote controls). RF signalers require fewer receivers (usually only one per classroom) and are less easily “confused,” but are more expensive to produce. Some systems use the wireless interface of standard laptops, which is RF (this obviously requires that students bring their laptops with them to class).
The second consideration is the user interface. It is important that the students have a means of determining whether or not their responses have been received and recorded by the system. This can be done by two-way signaling (so that, e.g., an LED on the student’s transmitter illuminates when the response has been received), or by displaying a grid that shows all the responses received by transmitter code number. The former is more expensive than the latter, but easier to use (since the students do not need to search the grid for their code). The software that the instructor uses is also important. It should be easy to learn and to use, and should be compatible with whatever other software (e.g. PowerPoint) will be used during the lecture. It should be easy to enter the questions to which the students are to respond, either before the lecture or “on the fly.” The responses of the individual students should be recorded in a format that is easy to use (e.g. importable to Excel). It is desirable that the histogram of responses be displayed to the instructor in real time (rather than at the end of a preset time interval or upon a mouse click) so that she can terminate the response collection early if it becomes obvious that almost all of the students are answering correctly.
The final consideration is the business model. The transmitters can be purchased by the department and checked out to the students (either on a daily or a semester basis), purchased by the students for a nominal fee and then registered (for an additional fee) to activate them, or purchased by the students at a higher cost but with the option of sell-back at the end of the semester. Some publishers now bundle the transmitters with their textbooks, and provide questions from a data bank for use in the classroom. This reduces the cost to the students for purchase of a new textbook, but causes difficulty when students purchase them used. It also limits the instructors’ choice of textbooks. The availability and cost of replacement transmitters must also be considered, since it is inevitable that some students will lose or damage theirs during the semester. Some cost savings can be realized if students use the transmitters in multiple classes (either in the same semester or in successive semesters), so coordination of system selection with other departments would be wise. It is desirable in that case that students not have to register their transmitters multiple times (and thus pay multiple registration fees).
One system currently available is called H-ITT,62 and is an IR system with two-way communication. One receiver for every 50 seats in the classroom is needed, to be connected in a daisy chain to the computer via a COM or USB port. Responses are recorded in .csv or .xml format, and a program to associate transmitter ID numbers with student names is included. Receivers are $200 each, and transmitters (if bought individually) are $25 each. They can also be bought bundled with textbooks published by Pearson Publishing (which includes Addison Wesley, Prentice Hall, Allyn & Bacon, and Benjamin Cummings). In that case the department obtains one receiver for every 50 textbooks purchased and the students get a $25 rebate on the transmitter when bought with the textbook, effectively making it free (if the textbook is purchased new).
The PRS (Personal Response System) sold by GTCO63 also uses IR transmission. The transmission is one-way, so students must find their ID numbers (or other identifiers) on a grid to ascertain if their responses have been received. The transmitter cost is in the $30 range, but sell-back is possible.
The CPS system marketed by eInstruction64 also operates on IR transmission, but an RF version is expected out soon. Receiver units (one per 90 students) are $250 and include a software site license. The students purchase the transmitters for $3 and then pay a $15 activation fee per semester (regardless of the number of courses in which the transmitter will be used). The transmitters are now bundled with some McGraw-Hill textbooks.
Faculty members at UIUC have developed an RF-based system that they expect to be available for purchase in 2005. The communication is two-way, and the software allows the response screen to be present as a floating window that does not interfere with other programs that are running on the instructor’s computer. The response histogram is visible to the instructor in real time, and the responses are recorded in a .txt or .csv file.
The Silicon Chalk65 system is a client-based software package that is installed on the computers of the instructors and the students. It does not require a server, and the communication between instructor and students occurs via the campus wireless network. This software performs many functions, including sending screen shots from the instructor’s to the students’ computers, but the feature most relevant to interactive lecturing is the polling function. The students send their responses from their computers and the results are available in a histogram in the usual way. This system is unlikely to be cost-effective unless full use is made of the many other features the software contains, and a large classroom may overload the wireless network. Students would have to bring their laptops to class, which can be awkward in large lecture halls with small desk tablets (e.g. Phillips 215). The awkwardness would be compounded by the students’ need to take notes on paper as well as operate their laptops. Although Silicon Chalk allows the students to annotate the screen shots they are sent, much of what students might wish to note down in a physics class would be in the form of equations, drawings or graphs that are difficult to produce quickly via keyboard. Other possible concerns about the use of laptops in class (namely that the students may be distracted by other computer activities such as Web-surfing, games or Instant Messaging) are obviated by the ability of the instructor to use the Silicon Chalk software to control the applications that run concurrently on the students’ computers. The system is purchased in the form of a site license at $15 per machine per year for the first 500, $10 each thereafter.
Lecture demonstrations have traditionally been an important part of introductory physics lectures. They are widely regarded as useful for convincing students that physics concepts relate to the real world, for helping students visualize the concepts and deepen their understanding, and for keeping students engaged and alert in class. In the traditional lecture, the instructor normally explains the demonstration, performs it, and then perhaps gives more explanation. The students observe the demonstration passively (though they may clap and cheer if the instructor has a flair for showmanship). Though lecture demonstrations are very popular among students,66 their role in achieving learning goals is less often assessed. It has recently been established that students who have observed a demonstration passively understand the underlying concepts no better than do students who did not see the demonstration.67 However, if students are actively engaged in the demonstration by recording a prediction of its outcome and discussing it with one another before hearing the instructor’s explanation, their understanding of the underlying concept can thereby be increased.68 This is the basis of the technique of “interactive lecture demonstrations.”
An instructor using this method begins by describing the demonstration to be performed and asking the students to predict the outcome of the demonstration. This prediction may be in qualitative form (higher/lower, yes/no) or in the form of a sketch of a graph. It is important that the students specify their predictions (either by writing them down on a “prediction sheet” or by using an electronic response system such as those described in the preceding section) so that they engage fully in the process. Recording their participation (by collecting the prediction sheets or by using the electronic response system) and rewarding it with course credit provides further incentive. The instructor then has the students discuss their predictions with one another and modify their predictions if they find their neighbors’ logic to be convincing (the modified predictions are also recorded in writing or electronically). She asks a few students to give their predictions orally and to explain their reasoning, thereby eliciting the most common predictions (and setting the stage for conceptual conflict as described in Section II.B.3). She then performs the demonstration. If the demonstration has been well chosen to confront a common preconception or misunderstanding, a significant number of the students will have made an incorrect prediction and will therefore be faced with a conflict. The instructor focuses the students’ attention on the conflict by asking them to describe and discuss what they observed. This can be done by asking a few students to share their ideas orally, by having all students discuss the outcome with their neighbors as was done before the demonstration, or by having the students write down their observations and explanations on a “results sheet” that they will take with them. The instructor then discusses and explains the demonstration and the ways in which it embodies the relevant physics concept, and also describes other physical situations where the same concept applies but that appear different on the surface.
This method can be used with a great many of the demonstrations that are typically done in physics lectures, with only a modest increase in the lecture time that must be allocated to them. If the department has available microcomputer-based laboratory (MBL) tools such as electronic force and motion sensors, these can be used in the demonstration and the students can be asked to predict the graphs that the sensor readout software will produce before being shown those graphs as part of the demonstration. This allows the demonstrations to be more quantitative, and helps the students connect the motion with its graphical representation. A set of materials consisting of prediction and results sheets (for the students to record their responses), presentation notes and teacher’s guide, and software for the MBL tools is available commercially.69 The demonstrations cover mechanics (including fluids and waves), E&M, optics, and thermal physics.
The advantages of this method are that it allows the instructor to elicit and confront conceptual difficulties that the students have. It engages the students in the process of understanding, and it makes it more likely that they will see in the demonstration what they are meant to see. Although it requires somewhat more class time to be allotted to the demonstration, it makes that time more effective in guiding the students to a better understanding of the concepts. Although it may reduce somewhat the entertainment value of the demonstration (since the students are required to expend effort rather than merely watch the instructor work), it increases the educational value.
Just-in-Time-Teaching (JiTT)70 is a pedagogical strategy developed to allow instructors to adapt their lectures to specific student learning difficulties, to provide individual interactions among students and instructors, to give students immediate feedback on their learning, and to allow the use of information technology to enhance learning. It has many facets, but the heart of it is the Warm-up.
The Warm-up is an exercise that students perform before each lecture, after they have read the assigned section in the textbook. It consists of ~ 4 questions presented via a Web page. It is intended to help the students consider their everyday understanding and experiences, realize that their current mental constructs are incomplete, and come prepared to deal with them in the classroom where they will be guided by the instructor. By giving the students a small amount of course credit for completing the assignment (but not necessarily answering the questions correctly), the students can be motivated to prepare for each class.
While advance preparation on the part of the students is certainly valuable, the key advantage to JiTT is the feedback it gives the instructor about the students’ understanding of the concepts to be covered in the lecture. The due date and time for the Warm-up is set to allow the instructor a few hours before the lecture to read the student responses and adjust the day’s lesson according to the students’ demonstrated knowledge. If the majority of the students have answered a conceptual question correctly, that topic need not be emphasized because the students already understand it.. If a large number of students display confusion about a topic, the instructor can devote more time to it in the lecture. This feedback allows the instructor to tailor the lectures to the needs of the specific students in the classroom.
A typical Warm-up includes at least one question to which the students are asked to give a written response. By reading these responses before the lecture, the instructor can gain insight into the students’ thinking and identify preconceptions that may be hindering their correct understanding. Some particularly characteristic answers can be used (anonymously) in the lecture, which helps the students become engaged in the classroom as they recognize their own wording. To confront a pervasive preconception, the instructor might say, “Many of you wrote something like this…” and read out a typical response, which catches the students’ attention. The instructor can then explain why the answer is incorrect (or engage the students in a discussion that brings out the incorrect reasoning). This answer can be compared to a correct one (also read anonymously). The student with the correct answer will recognize her own wording and feel rewarded for her effort. Other students will relate to and understand better the wording of a peer, which will typically not be the same as the formal language used in the textbook.
While it may appear that reading through the responses from as many as 150 students shortly before the lecture requires a large investment of instructor time, the cost is not so high as it first appears. The students’ answers tend to fall into a small number of predictable categories, following a universal set of preconceptions and misunderstandings. It is therefore not necessary to read all of the responses, but only a selection. An experienced instructor can anticipate the kinds of responses that she will receive, and needs only to find a particularly telling example among them. Examples of Warm-up questions requiring written responses include the following:
Warm-ups also typically include a question in which students are asked to estimate a physical quantity. This forces the students to apply their physics knowledge to the real world, and gives them an understanding of the magnitude of the quantities they learn about. It also introduces them to the “back of the envelope” thinking that is a characteristic part of physics reasoning. Quantities they can be asked to estimate include the time for a free-fall drop from the top of a three-story building, the tangential velocity of an object in Chapel Hill due to the rotation of the Earth, the amount of thermal energy necessary to raise a person’s body temperature by 1 °F, the resistance of a typical lightbulb, the force of the Earth’s magnetic field on a 10-cm segment of a typical wire in the home, and the time it takes light to do one lap in a swimming pool (underwater). To answer these questions, students must make appropriate approximations, consult reference sources (e.g. to find the latitude of Chapel Hill), and apply their conceptual knowledge without specific clues to what equations might be appropriate. They must engage actively in the kind of learning that is most valuable to them in their study of physics. They also come to appreciate that the ideas they are considering in the classroom do in fact have consequences in the world they live in. This can help to address the students’ tendency to believe that physics tells them nothing about the real world.
The final questions in a typical Warm-up are multiple-choice conceptual questions. These are of the same sort that would be used in interactive lecturing (see Section III.B.2.a). They can ask about the direction of a vector, whether a quantity increases or decreases under stated conditions, which of several quantities is larger, which of several quantities is conserved in an interaction, and the like. They can also include questions about definitions and the meanings of “physics words” that are often confused with their common English usage. More difficult questions can be used as a basis for class discussion.
The Warm-up Web page also provides a medium for communication between the students and the instructor. By including a text box in which students are invited to give a response of their choice, the instructor can further identify what aspects of the material students are having difficulty with. Often a student will ask a question by this means that she would not feel comfortable asking in class. Students may also continue their engagement with the concepts covered in the Warm-up by asking additional questions because they do not understand how to answer the problems posed. These can be used to tailor the lecture to meet the students’ needs.
Another tool used in JiTT is the Puzzle, which is used to close out the treatment of a particular topic. It is a question (delivered via a Web page, and possibly including images or simulations) that usually involves a real-world scenario, and can be used as the basis for a discussion in lecture or recitation. It involves the integration of multiple ideas, and can include a quantitative component. Giving students credit for solving the Puzzle provides an incentive for them to extend their understanding of the topic at hand, as well as a challenge for the better students that might help maintain their interest. Examples of Puzzles include:
The Warm-up and the Puzzle are two JiTT tools that can be used separately as well as together. They engage the students in active learning, and provide feedback to the instructor about the state of the students’ understanding. Implementing them requires an efficient way to collect the student responses delivered via a Web page, and therefore some assistance from IT experts. However, the ubiquity of Web access at Carolina means that there is no fundamental barrier to the use of either of these tools. There exists a large pool of questions suitable for use in Warm-ups and Puzzles, both in printed form24,70 and on the Web71. Physlets (see below) can be incorporated into both types of exercises, to good effect.
Many physics instructors by now have encountered the Java applets for physics known as “physlets.”72 These controllable animations can be used in lectures, recitations, homework, JiTT exercises, or laboratories. They use simple graphics and animations to deal with one facet of a phenomenon, and are designed to engage the student with its conceptual and quantitative aspects. The instructor or the student manipulates the animation to explore the phenomenon and reach conclusions about it. For example, a physlet on projectile motion could allow the launch angle, initial speed, and projectile mass to be changed and the consequences of those changes to be observed qualitatively and quantitatively. In this case, the simulation would substitute for a lecture demonstration, which would take more time than the animation and would be more difficult to measure quantitatively. Physlets can also be used to visualize invisible quantities such as electric and magnetic fields and observe their changes as charges and currents are manipulated. The animations can be powerful tools to supplement the static pictures shown in textbooks. They help students make connections among physical quantities, their graphical representation, and the equations governing them. They also help the students build mental models of physical systems. Many physlets are available for use, either on CD72 or on the Web.73 The scripting language is also available for constructing new physlets.
Although many good pedagogical techniques have been developed elsewhere, we should not overlook those that our own faculty have invented and incorporated into their teaching, often through long experience with what is effective at engaging the students in the learning process. Because each faculty member teaches independently, these methods are rarely shared with our colleagues and therefore do not reach the majority of our students. The transformation process outlined here provides an opportunity for these best practices to be identified and disseminated among the faculty who teach introductory physics, by incorporating them into the template for all of the courses. In this way we will give all our students the benefit that has previously accrued only to the few who happened to be taught by a particular instructor.
Certain of the learning goals we have for our introductory physics courses can be addressed effectively in recitations or Supplemental Instruction settings. These are:
The University of Washington Physics Education Group has developed a set of exercises for use in the recitation sections of large-enrollment courses, known as “tutorials.” These tutorials can be used in conjunction with any type of lectures, and are published74 and available for purchase by the students (they can be bundled with a textbook from the same publisher, at a reduced price). The exercises are designed to be done in groups of three to five students working together as they fill in the answers in their workbooks. Developed from and extensive base of physics education research, the questions are structured to guide the students through the process of surfacing and confronting their preconceptions and resolving the conflict to enhance understanding. Some of the tutorials involve simple manipulation of simple apparatus (rolling objects, batteries and bulbs, etc.). While the students work on the exercises, the instructors (typically graduate or undergraduate student TAs) circulate throughout the room and ask leading questions to help students when they encounter difficulties. These tutorials have been used on a trial basis in the P26/27 sequence in 2004-05.
As implemented at the Univ. of Washington, the tutorials follow a two-week cycle. The students attend lectures on the topic (e.g. Newton’s 2 nd and 3 rd laws) during the first week. They then take a 10-minute pretest on the material, either during the weekend via the Web or at the beginning of the Monday lecture. The pretest consists of conceptual questions for which the students are asked to explain their answers. The answers are compiled and discussed at a Monday morning meeting of the lead TAs and faculty instructors (at Washington this meeting also serves as a session of the graduate class on college physics teaching). It is typical for the distribution of student responses to be statistically indistinguishable from those give by students who have not yet heard the material presented in lecture.
On Monday afternoon all of the instructors who will be teaching the tutorial sessions attend a meeting during which they work in groups to answer the tutorial questions that will be presented to the students. As they work, the lead TA assigned to the group highlights the difficulties and preconceptions the students are likely to have, and all group members discuss strategies for addressing these difficulties through appropriate Socratic interchange. The TAs are then shown the responses to the pretest that the students in their sections gave, and discuss the common themes in the explanations for the answers. Although the answers and explanations show little difference from section to section and year to year, this helps convince all the instructors that these difficulties are in fact shared by virtually all students (none of the students are “special”).
The tutorial sessions meet throughout the week. The typical class size is 24 (six tables of four), with two instructors. One instructor is more experienced, and is expected to model the proper Socratic teaching techniques for the less-experienced TA (who may be an undergraduate). During the 50-minute class, most of the groups finish the entire tutorial (though this is less true for the first course in the three-course sequence). Each tutorial also has an associated homework assignment that reinforces the tutorial. The students complete these exercises and hand them in at the following week’s tutorial. The less-experienced TA for the section (who typically is assigned to fewer sections than are the more experienced instructors) looks over all the homework answers and assigns a numerical score to one selected problem. They are also assigned to grade the tutorial-style problem that appears on every examination.
A similar system developed at the Univ. of Maryland75 makes use of computer-aided data acquisition in the tutorial session. The authors of the system assume that conceptual learning is integrated throughout the course, so that the tutorials are not the sole source of conceptual development and thus can include a significant focus on quantitative problem-solving as well. To use the Maryland system, known as Activity-Based Physics (ABP) tutorials, the recitation sections must be provided with a computer and a data-acquisition interface for every three or four students (note that at UNC-CH the computers could presumably be the students’ CCI laptops). The data acquisition equipment (hardware and software) required is of the sort typically used in introductory laboratories to produce, detect and record motion, force, etc. In the tutorials, the computers are used for simulations as well as for data acquisition and analysis. As with the Univ. of Washington tutorials, students work in groups and proceed through a series of exercises designed to advance their conceptual understanding step by step. However, the exercises also include graphical and mathematical analysis using both analytical methods and the data-acquisition software.
Cooperative Group Problem Solving (CGPS) is a mode of “cognitive apprenticeship” developed at the University of Minnesota.76 It is intended to draw students into engaging in expert practice by the use of problems and tasks chosen to illustrate the power of certain problem-solving methods, to give students practice in applying those methods in diverse settings, and to help them develop self-monitoring and correction skills and integrate the skills they need to advance toward expertise. In recitation, students are given problems to solve in small groups. In their work, they are expected to follow a problem-solving strategy that has been explained and modeled for them in lecture and that is continually reinforced throughout the course. The strategy consists of focusing on what is happening in the problem, describing the physics, planning a solution, executing the plan, and evaluating the solution. They are graded not only on their solution, but also on the degree to which they have followed the strategy. In this regard, it resembles the “strategy writing” technique described in Section III.D.2.d.
The problems the students solve during recitations under the CGPS method are designed to force students to use expert rather than novice strategies. Since students will use novice strategies as long as they continue to be effective, it is necessary for the CGPS problems to be too complex to be solved using “equation picking” or “plug and chug” methods. Groups are able to solve problems that are too complex for individual students to solve, and by talking with one another students often can reveal and resolve their misconceptions. Appropriate complexity can be attained by the use of context-rich problems, which involve real objects and plausible situations, excess or missing information, and multiple sets of principles that could be applied. The unknown variable of the problem is not explicitly stated nor are diagrams or pictures given. To solve the problem, the students must visualize the situation using their own experiences, apply fundamental principles, and make appropriate idealizations (e.g. that a “very light” object is massless). Because the problems are written in the form of a “short story” in which the student (“you”) is the principal figure and is given a plausible motivation for doing a calculation, students find the problems more interesting than the typical context-free problems found at the back of a textbook chapter.
As implemented at the Univ. of Minnesota, students in recitation solve the problems in groups of three that are assigned by the instructor. The groups are mixed in ability (based on test performance), each group including one student from each third of the class (top, middle, bottom). As much as possible, groups are single-gender or else include two women and one man. (This is the result of a finding that mixed-gender groups in which males are the majority do not work well, because the men tend to ignore the woman even if she is the highest-ability student in the group.) The groups are changed every few weeks to allow students to realize that success can be achieved in any group. Each student in the group is assigned a role: Manager (who designs plans of action), Checker/Recorder (who organizes and writes down what has been done up to that point), and the Skeptic (who questions premises and plans). If the group has four students (because the number of students in the class is not divisible by three), a fourth role of Engergizer/Summarizer (who energizes the group when motivation is low and keeps track of decisions and reasons for different actions) is added. The students rotate through the roles from week to week. A single group product, i.e. a solution to the problem, is signed by all members of the group and turned in at the end of class. One member of each group is also asked to present the group’s solution at the board, and these are used as a basis for class discussion. A solution to the problem is handed out to the students at the end of the session. From time to time there is also a discussion about group functioning, focusing on difficulties the groups have encountered and ways in which they could interact better.
Exercises incorporating physlets can be used in recitations as well as in lectures. In manipulating the animations, students are engaged in hands-on, active learning as they explore phenomena. For example, students can work in small groups to explore the effect that changing the length, mass, release angle or initial velocity of a pendulum has on its kinetic and potential energy as a function of time. As they work, they can answer questions about total energy, work, periodic motion, and the like. They can also explore forcing and damping in ways that are difficult to do in the laboratory or in static exercises. The same kind of advantages that are present for physlets used in lecture (see Section III.B.2.e) are present in recitation, and the students are even more actively engaged because they are doing the manipulations themselves. In addition to exercises available on the Web73, there is also a published book with CD77 containing illustrations, guided explorations and problems for students to use either in recitation or as homework.
Some of the learning goals can be most effectively addressed in homework assignments that students perform individually outside of class. These are:
In recent years the grading of end-of-chapter problems has been automated by the use of information technology and Web interfaces. This has a number of advantages. Because assignments are delivered electronically, they can be given due dates that do not coincide with class meetings, which can encourage students to keep up with the material and can enhance their time-on-task. Feedback can be delivered quickly (immediately or after a due date), and students can make multiple submissions to correct minor mistakes. Each student can receive problems containing different numerical values, which reduces cheating. Most importantly, the instructor does not have to spend time hand-grading the assignments, so the grading can be more complete (all problems rather than a selection) and instructor time can be spent on other aspects of the course. At least one study78 has found the increase in student performance on exams associated with Web-delivered homework compared to traditional paper-and-pencil assignments to be significant.
These systems also have their disadvantages. Automated grading makes it difficult to include problems with solutions that require graphs, explanations, proofs, or other narrative or pictorial input. The required format for the numerical answers may be somewhat rigid (especially in regard to significant figures), which can be frustrating for the students and may not give an accurate assessment of their understanding. Creating a problem in the proper coding is difficult, so instructors are usually limited to problems already present in the system (generally end-of-chapter problems from one or more textbooks). There is a cost (to the institution, the students, or both) associated with the use of the systems. Like all Web-based instructional systems, it is dependent upon the availability of a working network (both at the local institution and at the service provider), and thus is subject to breakdown at times of critical need.
The system most familiar to UNC-CH faculty is WebAssign,79 developed at NCSU. It has available end-of-chapter problems from a wide range of textbooks. The cost is $250 per instructor in the first year, $150 thereafter. A site license for three or more faculty in a single department is available at $150 per instructor. The student fee is $6.50 per semester ($9.95 on line), which can be paid by the student or by the department.
A similar system that also delivers end-of-chapter problems from multiple textbooks is CAPA,80 developed at Michigan State Univ. It is intended to allow sharing of resources among different institutions, and so emphasizes user-designed problems. Use of the system is free, but problem libraries bear a cost.
A third university-based system is Tycho, developed at UIUC. This system includes both end-of-chapter problems81 and interactive examples.82 The interactive examples are multistep problems that lead the students through the solution of a problem, providing hints along the way upon request. The students must provide both conceptual/strategy answers and quantitative answers at various points in the problem solution.
Mastering Physics83 is a Web-based homework system developed at MIT and available through the textbook publisher Addison Wesley. The available problems are limited to textbooks from that publisher, and access can be bundled with textbook purchase (for a new textbook). The system offers self-tutoring multistep problems with individualized wrong-answer feedback.
As noted in Sections III.B.2.e and III.C.2.c above, the use of animations (physlets) can be very effective in enhancing student learning. In exercises using these simulations the students manipulate the variable controlling the phenomenon under consideration and note the results both qualitatively and quantitatively. These exercises can be even more effective as individual homework than they are in group settings such as lecture and recitation, since the student is free to explore according to her own understanding and interest without a set time limit. The animations allow the exploration of more sophisticated questions than is possible with a static problem. A collection of homework problems and their accompanying physlets is available for student purchase.77 The student responses can be collected on paper or via a Web site.
Another means of using simulations in homework exercises has been published under the name Interactive Physics.84 This workbook/CD contains 40 mechanics exercises covering many of the usual introductory mechanics topics, including 1-D kinematics, projectile motion, friction, energy, collisions, rolling, and simple harmonic motion. Each exercise begins with a brief review of the relevant physics topics. The student then answers a series of questions using the simulation. She is asked to predict the result before running the simulation with a given set of values (masses, initial velocities, elastic vs. inelastic, etc.), and to change the values and explore the results. She is to sketch graphs and record results of the simulation in the workbook. Each exercise ends with a self-test consisting of qualitative questions about the situation depicted in the simulation (e.g. “True or false: The initial kinetic energy of the projectile depends on the launch angle.”). The answers to the self-tests are given at the back of the book. The workbook is designed to be used as a supplement to standard instruction, for the students to use during their own study time. It is particularly well suited to help students understand the relationships among the physics concepts, motion, and mathematical and graphical representations of motion. If a primary textbook from the same publisher is used, students can buy the workbook bundled with the text, at some savings in cost.
The Interactive Physics environment is also suitable for use in recitations or lectures. Small groups of students could use the simulations in structured recitation exercises (either those published in the workbook or ones devised by the instructors). Since they can run from a CD loaded on a laptop, no special equipment is necessary to use them in this way. The simulations can also be used in interactive lecturing, similar to interactive demonstrations. Students can be asked to predict the outcome of the simulation as the values are changed, and to confront the preconceptions that lead to incorrect predictions. The Interactive Physics environment can also be used to construct new simulations for use in class. The graphical user interface requires no explicit coding, so simulations are easy to construct and manipulate. The available “objects” are limited to those relevant to mechanics, however.
As described in Section II.A.4 above, the problem-solving strategies employed by introductory physics students (novices) differ significantly from those employed by their instructors (experts). Students generally begin by manipulating equations to isolate the desired variable, and tend to focus on the surface features of a problem rather than the underlying principle that can be used to solve it. They tend to view problem solving in physics as memorizing, recalling, and manipulating equations to get answers. However, it is possible to guide students in the utilization of expert methods if those are modeled by the instructor, and if the students are given incentives to solve problems in this way. 31,85 One such method is called “strategy writing.” For each problem, the student is asked to identify in writing the major physics principle(s) and concept(s) to be used in solving the problem, to articulate the rationale for using a particular principle, and to describe how the principle will be applied to construct the solution. A strategy must therefore include a principle, a justification, and a procedure—a “what,” a “why,” and a “how.” What a strategy does not include is equations and their manipulation to obtain a quantitative result—that is considered to be a separate process, (i.e. the solution to the problem) that follows the articulation of the strategy. A strategy is successful if a student who has previously made no progress on a problem would be able, upon being provided with the written strategy, to solve (or at least make significant progress toward solving) the problem.
In order for students to understand the use of strategies, it is important that instructors model them when solving problems. In a typical lecture, a good instructor will always be careful to state verbally the principle that is to be applied to solve a particular problem, and to explain why that principle is applicable to the situation at hand. However, she often writes down only the equations by which the principle is instantiated. Students taking notes in lecture typically copy only what is written down, not any (or very little) of what is said. They observe that it is the manipulation of equations that leads to solutions, and this reinforces their preconception that principles have little relevance to the solving of problems. Solutions provided to homework problems tend similarly to include only equations with a few words of explanation. Common grading practices on exams and homework assignments also serve to reinforce the impression that problem solving consists of finding the right equations and manipulating them.86
To implement strategy writing in a large lecture class, the instructor should work out sample problems (perhaps one per lecture) by first presenting the strategy with a discussion of the concepts involved. Only after the strategy has been articulated (and written down, at least in abbreviated form) should the solution be presented. This highlights the physics that is being applied in a way that simply talking about it while solving the problem cannot. Students should then be required to write out strategies to problems on exams and in homework assignments (and should be graded on them), and the correct answers that are provided to them afterward should include both the strategy and the solution for every problem. To save time (both the students’ and the graders’) the students might be required to write out strategies for only one or two problems on an exam or assignment, or to provide only a strategy but not a solution to some problems. Grading of the strategies is important so that the instructor can gauge how well students are grasping the concepts presented, and so students can obtain feedback aimed at helping them internalize the features of a good strategy and therefore the elements of an expert-like problem-solving technique. The incentive provided by a grade is also important to persuade students to perform a task that they typically find to be difficult.
When this method of teaching was employed in one lecture section of a large calculus-based introductory physics class, it was found that students who were required to write strategies performed significantly better than the traditionally-taught students from the other sections on tasks in which they were asked to identify the principle that should be used to solve a particular problem.85 Although the students had initially resisted performing the task, at the end of the course they reported that the method had helped them and urged that it be used in future.
The role of the laboratory exercises in introductory physics classes is one about which opinions abound among physics teachers. In order to design laboratory experiences that are maximally effective in achieving the learning goals we have for our students, it is necessary to agree upon those goals. Purposes that have been proposed for including mandatory laboratory exercises in these classes include:
Given the finite time allocated to an introductory physics laboratory meeting and to students’ independent work before and after the meeting, it is apparent that it is not possible to fulfill all of these purposes with the same laboratory exercises. For example, some physics departments (notably UIUC) have decided to abandon the goal of teaching introductory physics students to write laboratory reports, with the expectation that the skills of scientific communication that such reports are expected to foster will be taught elsewhere in the curriculum. (This decision was also influenced by the realization that the feedback that the students receive on their lab reports comes too late to be of much use, and is routinely ignored.) It is therefore necessary for the faculty responsible for the course to identify which of these purposes are most important for the specific student population for which the course is intended. Different courses may have different sets of purposes, and thus the laboratory exercises assigned in the courses may differ in format and in content. However, if the exercises are to fulfill the agreed-upon purposes, they must be explicitly designed with appropriate learning goals in mind.
Of the list of learning goals for introductory physics classes given in Section III.A, several are most appropriately addressed in laboratory exercises. These are:
RealTime Physics87 is a set of laboratory activities intended to help students understand fundamental physics concepts; give them direct experience with the physical world through computer-assisted data collection, display, and analysis; enhance traditional laboratory skills, and reinforce topics covered in lectures and readings through a combination of conceptual activities and quantitative experiments. The activities invite students to construct their own models of physical phenomena based on observations and experiments and help them confront and resolve their misconceptions.
For each laboratory exercise, students read the instructions and answer the questions on a pre-laboratory preparation sheet that they hand in at the beginning of the session. These questions concern the uses of pieces of apparatus specified in the laboratory description, and predictions of what will happen under certain circumstances. During the session they make measurements using computer-based data acquisition tools (e.g. motion and force sensors) and the graphing and statistics functions incorporated into the software. They answer questions that require explanations, and test the predictions they made before the laboratory sessionbegan. The measurements are organized into “investigations” associated with a particular set of concepts (e.g. Newton’s 3 rd law), and each investigation involves several sets of measurements. There are several investigations per laboratory session, and each investigation has extensions for students who finish early. The laboratory reports are prepared as the students go along (by filling in the answers to the questions in the laboratory textbook and including records of what was measured) and handed in at the end of the laboratory session. Graphs produced by the software are either sketched onto axes in the laboratory textbook or printed out and stapled to the textbook sheets (which are perforated for easy tearing). Each laboratory also has a homework exercise that is handed in at the beginning of the next period.
The laboratory textbook is published and available for student purchase. It is divided into Mechanics, Heat and Thermodynamics, Electric Circuits, and Light & Optics volumes that can be purchased separately. A Teachers’ Guide is available on-line.88 The equipment used is common in university instructional laboratories.
Socratic Dialogue Inducing (SDI) labs89 are intended to introduce Socratic pedagogy into laboratory exercises. They emphasize hands-on experience with simple mechanics experiments and facilitate interactive engagement. They are structured to introduce conceptual conflict, and make use of kinesthetic involvement and extensive verbal, written, pictorial, diagrammatic, graphical, and mathematical analysis of concrete Newtonian experiments. By repeated exposure to experiments at increasing levels of sophistication, peer discussion, and Socratic dialogue with instructors, students construct a coherent conceptual understanding of Newtonian mechanics.
In SDI labs as normally implemented, students work in groups of four, with six groups and two instructors (preferably one experienced and one “apprentice”) per class. The students work through the laboratory manual, performing concrete experiments which exemplify Newton’s laws. They construct time-sequential force-motion-vector diagrams (using colors to distinguish force vectors from motion vectors) and write down answers to laboratory-manual questions. They are often asked to predict the outcome of an experiment before performing it. They collaborate within their groups and are asked to justify the answers they give to the laboratory-manual questions. Often the questions probe for conceptual understanding through the students’ reconciliation of their force-motion-vector diagrams with kinematic principles and Newton’s laws. Other questions introduce students to strategies for scientific thinking and problem-solving and stress the physical interpretation of formulae. As the students work, the instructors (called “Socratic dialogists”) move among the tables to respond to questions and monitor student progress. The instructors question the students in such a way that the students are led to express their ideas and figure things out for themselves. At the end of the session the students hand in the laboratory manuals, which are annotated but not graded. The laboratory grade is determined by several written laboratory exams containing questions that demand a good conceptual understanding of experiments similar to those performed in the laboratory.
The equipment involved in the labs is simple, and is generally available in a typical physics department. The laboratory manuals and teachers’ guide are available electronically.89 The laboratory exercises are confined to mechanics, none exist for other topics.
The Cooperative Group Problem Solving method developed at the Univ. of Minnesota (see Section III.C.2.b) has also been extended to laboratory exercises.76 These exercises are intended for students to learn physics through the solving of problems, and to confront some of the misconceptions that students bring with them. The exercises are posed as context-rich problems that the students solve in part by making measurements. Before they come to the laboratory session, the students prepare by reviewing designated sections of the textbook and assuring that they have mastered certain skills (e.g. using trigonometric functions, drawing force diagrams, etc.). They also make a prediction for the results of the measurements they will make (based on a description of the apparatus and kind of measurements). The prediction is mathematical (involving an equation) and quantitative, and may involve a graph. They also answer “method questions” about procedures in advance of the laboratory session. These questions either help the students think about how to analyze their data and display their results, or guide them through a method for predicting the relationships among the variables. The answers to the questions are written in a “laboratory journal” and checked by the instructor at the beginning of the session. In the laboratory they first explore the range of reliability of the apparatus, and develop a plan for their measurements (the plan is recorded in the journal). Then they follow their plan and make their measurements, analyze their data, and arrive at their conclusions, all of which is recorded in the journal. The conclusions are stated in terms of the context-rich question with which the students were initially presented.
The laboratory exercises devoted to a specific topic (e.g. “Forces”) may extend over more than one laboratory session, and each session may involve the solving of more than one problem. When a topic is completed, the students are assigned to prepare a report of one of the problems. The reports are graded on the usual criteria of organization, clarity, logic, quality of comparison between theory and experiment, analysis of uncertainty, and correct physics. (It is worth noting that incorrect grammar or spelling in the report reduces the maximum possible score to 70%!)
A perennial source of complaint for introductory physics students in large-enrollment classes is the discrepancy (of either sign) between when a concept is introduced in lecture and when that concept is explored in the laboratory. This discrepancy is inevitable when the class is structured as a large lecture with many smaller laboratory sessions, because the limitations of resources (space, equipment, and instructional personnel) require that the laboratory sessions on a given topic take place over a one- or two-week period. If the laboratory exercises are of the traditional sort, in which students confirm the correctness of various relationships among physical quantities by quantitative experiments, confusion is understandable if the students have not yet been introduced to those quantities and relationships and must rely on the abbreviated discussion in the laboratory manual and the short “mini-lecture” by the teaching assistant at the beginning of the session. If the labs are designed to explore the relationships and enhance conceptual understanding, it will generally matter less to the students whether the laboratory or the lecture comes first. Awareness on the part of the lecture instructor of how the laboratory schedule meshes with the lecture schedule is also important, so that references to the laboratory exercises can be introduced into the lecture to reinforce the relationship between the two.
For courses that are taught in multiple sections (either because the number of students exceeds the capacity of the lecture hall or because smaller class size or increased flexibility of scheduling for students is desired), more than one faculty member will typically participate in the teaching of the course. As introductory physics is currently taught at UNC, the two or three faculty members assigned to a course conduct their classes more or less independently. Each faculty member prepares her lectures independently, perhaps coordinating with her colleague(s) regarding the topics to be taught in a given week. (Such coordination is more important in classes where the lecture sections have recitation sections in common.) She also prepares her exams independently, though she may ask her colleague to critique a draft. Homework assignments may or may not be shared among sections, at the discretion of the faculty members. This method maximizes faculty autonomy, but at the cost of significant duplication of effort.
At some other institutions, notably the Univ. of Illinois at Urbana-Champaign, the department has chosen a different division of labor. In large-enrollment courses to which three faculty are assigned, one takes the role of Lecturer, one is designated the Discussion Master, and one serves as Lab Master. (If there are more than two lecture sections, a fourth faculty member is assigned to play the Lecturer role.) All faculty participate in the preparation of the exams, which are common to all of the lecture sections. The Lecturer delivers the lectures from an existing set of lecture slides (PowerPoint), and therefore gives the same lecture twice. The Lecturer may choose to modify the pre-existing slides if she chooses, though she is constrained to maintain their “look and feel.” (At UIUC, she is further constrained by the fact that the students purchase a workbook at the beginning of the semester that contains paper copies of all of the lecture slides, so that any changes must be made before the workbooks are printed.)
The Discussion Master organizes the discussion sections, selecting the exercises that the students will work on in small groups each week. The exercises may be chosen from among a pre-existing set, or the Discussion Master may create or adapt new ones. This faculty member also teaches one or more of the discussion sections, and conducts a weekly meeting with the teaching assistants who teach the remaining sections. In this meeting she goes over the problems and identifies the particular aspects that are likely to be difficult for the students, giving tips to the teaching assistants about how best to guide the discussions. The Discussion Master is also responsible for preparing the weekly quizzes that are given in each discussion section (again, either by selecting from a pre-existing set or by preparing new ones) and for recording the scores the students receive.
The Lab Master is similarly responsible for the laboratory sections. She makes any necessary modifications to the existing exercises (this must be done before the laboratory manuals are printed), teaches one or more laboratory sections, and supervises the teaching assistants who teach the remaining sections. She conducts weekly meetings to prepare the assistants for their duties, and records the scores that the students receive.
Faculty who have team-taught introductory physics in this way at UIUC speak very highly of the system.90 They emphasize how much easier it is to “deliver” material that is pre-prepared than it is to have to invent it de novo. The effort required of each member of the team is significantly less than if each were responsible for all aspects of an independently-operated course section. As a result, many more faculty members have been willing to participate in the teaching of the introductory courses since team teaching was adopted, and none view such a teaching assignment as any more onerous than that of teaching a small upper-division course for physics majors. For faculty new to teaching, joining a team of more-experienced instructors allows for valuable mentoring opportunities (new faculty typically take the role of Lab Master initially while they observe the other team members). Because the lectures and the discussion section incorporate interactive engagement techniques, faculty members who learn to teach this way in the introductory courses often carry those techniques into other courses that they teach subsequently. They also have an opportunity to work closely with colleagues from other research areas.
As with any successful innovation, the final stage of this project is confirmation of the wisdom of its adoption, by positive outcomes. If we are to expend significant effort in making a change, it is important that we measure the degree to which we have achieved the goals that motivated the change. Change for change’s sake would not be an effective use of our human resources. External funding agencies that support the project also require that we assess its results, to justify the expenditure of the funds provided.
There are several ways in which we can think about assessing the effects of change. One is summative assessment, in which we evaluate the degree to which the goals of the project have been accomplished by its end. We are most familiar with this in the form of examinations, by which we evaluate whether or not the students have learned the material presented in the course. We should also build into the project means of formative assessment, which is meant to allow us to evaluate how well the project is progressing toward its goals, and to guide us in making changes if that progress is unsatisfactory. In the classroom context, this is analogous to the conceptual question posed in a lecture to assess whether or not the students have understood the concept just presented. We should engage in both kinds of assessment for all aspects of the project.
This project has three types of goals: those associated with learning outcomes, those associated with the sustainable management of instructional resources, and those associated with educational leadership.
The goals associated with learning outcomes are twofold. The first is simple: we want the students who take our introductory physics courses to achieve a deeper and more coherent understanding of the fundamental concepts of physics, and be able to apply them more effectively in a wide variety of contexts. The employment of interactive engagement methods in the classroom will help us accomplish this. It will be possible to assess the efficacy of these methods by using standard instruments that have been developed to measure conceptual understanding in physics (see Section I.B.4). By comparing students’ scores on these tests before and after instruction, we can have a measure of the degree to which instruction has changed their conceptual understanding. By comparing the average change that occurs in classes taught in the traditional way with those taught using interactive engagement, we can assess whether or not the new techniques are more effective than the old. This type of learning outcomes assessment has been widely used in the physics community11, so it will be possible to compare our achievement with what has been accomplished elsewhere.
The second learning outcome goal is more subtle. By undertaking this project, we seek to have our students come away from their (often only) physics course with a more positive, and more accurate, view of the subject and its relevance. It has been shown that students typically enter their first college physics course with expectations about the nature of physics, what they are supposed to do, and what kinds of materials they are supposed to learn27 that are often counterproductive to helping them develop a strong understanding of physics or expert problem-solving skills.28 The truly depressing finding of these surveys is that the tendency of the students to agree with the instructors about what physics is and how best to learn it declined in almost every case after traditional instruction. The health of our department and others like it, and the future of our discipline also depend upon a steady flow of bright, talented, and motivated young physicists. If we want to maintain or increase the number of physics majors, we must provide good teaching in the “gateway courses” that introduce the students to our discipline.17 There are a number of measures that we can use to see if we are accomplishing this second learning outcome goal. One is to use survey instruments specifically developed for that purpose29 (see Section II.A.3). Another is to examine measures of “student happiness” such as the student evaluations of instructors that are conducted in all of our courses each semester. Students who have a more positive attitude toward physics, because they have a better understanding of its nature and importance, are likely to respond more positively when asked to evaluate the instruction they have received. Significant gains in student evaluations have been achieved in other physics departments that have introduced interactive engagement into their classrooms.91
The second type of project goal, the sustainable management of instructional resources, concerns faculty. For long-term sustainability, faculty members who have not taught these courses before must be able to do so effectively without compromising their ability to accomplish our other missions of research and advanced physics education. Because of the significant effort that is inherent in teaching large introductory courses, we would like to have a large pool of potential instructors to draw from. Generally, faculty members who demonstrate significant skill at teaching introductory courses also have talents and knowledge that could be put to excellent use in other courses at the advanced undergraduate or graduate level. For long-term sustainability, it is also vital that we bring junior faculty into the pool. The development of a common set of teaching materials (based on interactive engagement) for new instructors to use, coupled with an appropriate program of mentoring and faculty development, can make high-quality introductory physics teaching sustainable in the long term. We will be able to assess our progress toward this goal in two ways. The more formal one will be through interviews with faculty members conducted by an independent group (see Section V.F). Informally, we can count ourselves successful when a significant fraction of the department’s faculty are willing to teach these courses as part of their normal teaching assignments, and the Chair feels confident that they will do so effectively. When it becomes routine for faculty to rotate through these courses from year to year, the instructional resource will have become sustainable.
The third type of goal concerns educational leadership. Despite this national problem quantified by physics education researchers and others, it is all but unknown for a major research university physics department to totally transform its introductory teaching without the catalyst of either an indigenous physics education research group or a major external threat to its resources. The project described here will therefore serve as a model in two ways. A physics department that has passed through the phases92 of knowledge, persuasion and decision in regard to innovation in pedagogy, but which has only limited resources to proceed to the implementation stage, can make use of the specific instructional materials in the forms adapted by UNC-CH. Beyond the specific modifications in physics pedagogy, this project can serve as a second type of model, one of institutional transformation, which is applicable to other disciplines and other institutions. We will be able to say that we have been successful in this goal when we see other departments and other institutions adopting our model.
In our department, it is the custom that the faculty member assigned to teach a course be responsible for determining what is taught and how. There are limits to this freedom, however. In some cases the syllabus of the course is determined at least in part by it serving as a prerequisite to a later course that students are also required to take (as for the calculus-based introductory physics courses or the first semester of the two-semester intermediate E&M or quantum mechanics sequence). The syllabus may also be constrained by a comprehensive examination that includes material expected to be covered in the course (as for graduate core courses that precede the graduate written exam, or the algebra-based introductory course that among other things prepares students for the MCAT exam). When multiple sections of a course are taught and the students in different lecture sections are mixed in other meetings of the course (such as recitations and labs), a certain degree of coordination of syllabus and schedule is necessary if the students are not to be disadvantaged. This may also lead to cooperation among faculty to share homework assignments or exams in common, resulting in a saving of time and effort as well as a more uniform experience for the students independent of the lecture section in which they enroll.
What is proposed here is a simple extension of this prevailing custom. The decisions about what to teach in the introductory courses (within the limitations noted above) and how to teach it will be made by the faculty assigned to the courses. The differences are that the decisions are to be made in common and by consensus among the faculty assigned to the four courses, and that the decisions will also apply to offerings of the courses in subsequent years. This necessitates participation in the decision-making by faculty members who are likely to teach the courses in subsequent years. The adoption of a common set of teaching materials in different sections of the same course will allow the sharing of homework assignments and exams, which will reduce duplication of effort.
In our introductory physics courses, graduate student teaching assistants are an important part of the instructional staff. They are responsible for a significant fraction of the contact hours (as much as half in courses that have a recitation). It is therefore appropriate for some senior graduate students with several years of teaching experience to participate in the method selection, since they will be expected to use some of the methods when they teach recitations and laboratory sections. Special efforts will be made to include graduate students (or postdocs) who intend to pursue academic careers, so they can become better informed about physics pedagogy before they are expected to engage in it independently. A new UNC initiative based in the Center for Teaching and Learning (CTL), the Graduate Teaching Certificate Program, will facilitate the involvement of graduate students by enhancing their expertise in higher education pedagogy. Through this program, graduate students will be trained in essential post-secondary teaching techniques through formal coursework, workshops, mentoring, and on-the-job experience. This program can furnish skilled assistance to the transformation project described here, which in turn can provide enriching experiences to the graduate students involved. Selected undergraduate students will also be included to give the perspective of those upon whom the methods will act. Finally, staff members from CTL and the Center for Instructional Technology (CIT) will contribute their particular expertise to the evaluation of various methods and the feasibility of implementing them in the local environment.
A timeline for the transformation project is given below. Stage I is the enumeration and description of the pedagogical methods that are available, which is essentially complete with the completion of this document. Stage II is the selection of the methods to be used. Stage III is the development and adaptation of the specific instructional materials to be used for each course, and Stage IV is the initial offering of the courses using the new methods. Stage V is the evaluation of the success of the new schema, which will begin with the collection of baseline data from the courses taught in the traditional way and will end with assessment of the courses after they have been taught at least twice in the new way. The project will therefore take four years to complete, which will allow plenty of time for “mid-course adjustment” and for faculty to develop familiarity with the new way of conducting the courses.
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As noted above, the product of this stage is essentially the document here presented. Section III above is a collection of descriptions of a wide range of interactive engagement methods, together with references to research on their efficacy and to available materials (commercial or otherwise) that can be used when the methods are employed. While it would be overwhelming (and probably counterproductive) to adopt all of the methods described, there is enough variety among the well-documented methods that a rich feast can be selected from this menu.
The second stage of the project is to select the pedagogical methods to be used in common. As noted above, this selection should be made by a group of faculty and students who will use the methods, aided by staff members from CTL and CIT who bring particular expertise to bear. This group might be called the Introductory Physics Task Force (IPTF), and according to the timeline it is to do its work in the Spring semester 2005. The task force will be rather larger (most likely ~ 20 people) than is convenient for detailed action as a single entity, so it would be most efficient for it to divide itself into subgroups. Each group could investigate and evaluate methods to be used in a different part of the course (lecture, recitation, laboratory, homework, etc.), and then bring its recommendations to the entire task force for discussion. Other divisions of labor are also possible at the task force’s discretion. The task force must decide if common exams are to be given for multiple sections of a course, or if the exams are simply to have a common format (comprising questions that reflect the new pedagogical methods employed). The use of multiple-choice vs. worked problem exams (or hybrids thereof) is also an issue. Whether or not team-teaching (with division of labor by task rather than section) is to be employed is also an important question to be explored. Note that it is entirely possible that the decisions on these questions would not be the same for the P24/25 sequence as for P26/27, but they should be uniform within a sequence.
While the decisions of the task force will necessarily be constrained by the realities of the resources available for the teaching of the introductory courses, it should not construe those constraints too narrowly. For example, the algebra-based courses do not include a recitation at present (though they carry the same course credit as the calculus-based courses, which do), but the task force may well conclude that one would be desirable. Implementing this recommendation would require either increasing the required contact hours or else a change in the use of some of the existing contact hours. These possibilities can be explored. It might also necessitate an increase in the number of teaching assistant FTEs associated with the courses. Whether or not this would be possible given the available instructional resources would depend on other changes that might be made in the course structure (e.g. a reduction in the preparation time and grading expected of recitation TAs so that they could cover more sections, or the uses of senior undergraduates as TAs) and adjustments that might be made in the use of TAs in other courses.
The final decisions to be made by the task force are to choose the pilot course for the first implementation of the new methods. There are a number of considerations that will influence this decision. First, it seems sensible to choose the first semester of one of the sequences (i.e. either P24 or P26). There is more instructional material available for mechanics than for E&M and optics, which will make the Stage III task of materials adaptation and development easier. If the second course transformed is the course that follows the pilot course in the sequence, the students will have a uniform experience throughout the year. The timeline calls for the initial implementation (beginning of Stage IV) to take place in Spring 2006, when the enrollment in P24 can be expected be smaller (by approximately a factor of two) than it is in the fall semester. (The distribution of students in P26 between Fall and Spring is much more even, with a variation of only ~ 30%.)
The second consideration in the choice of pilot course is which sequence to select. There are more students in P24 the spring than in P26 (165 vs. 104 on average), making the initial implementation somewhat more challenging. On the other hand, the benefits of the changes will accrue to more students sooner if the larger-enrollment course is transformed first. Changes in the contact hours or their utilization (which are less likely to be needed in P26 since it already includes a recitation) may be difficult to arrange by Spring 2006. Transforming P26 first would mean that potential physics majors are affected sooner, which may or may not be an advantage depending on how successful the first implementation of the new methods (before a process of feedback and modification can take place) is likely to be.
The final consideration in the choice of which course to use as the pilot will be the willingness of some “early adopter” faculty to be the first to teach the course in the new way. The implementation of the changes is most likely to be successful if the “pioneers” are enthusiastic volunteers who are willing and able to devote a greater-than-usual effort to their teaching in that first semester. Once the courses reach “steady state,” it should be no more difficult to teach them in the new way than it is in the traditional way, but making a significant change in one’s pedagogy clearly requires a significant commitment of time and effort.
Once the pedagogical methods to be used and the course that will serve as the pilot are chosen, a subset of the IPTF (which should include instructors who will teach the pilot course) will develop the detailed instructional materials needed to implement those methods in that course. For example, if interactive lecturing (Section III.B.2.a) is to be adopted, conceptual questions appropriate for each lecture topic must be selected (or created) and prepared in the desired form (PowerPoint slide, transparency). If tutorials (see Section III.C.2.a) are to be used in recitation, selection of the exercises to be used each week (and any desired modification of existing materials) must be made. If the same PowerPoint slides are to be used in lectures by all instructors (as is done in the team-teaching method used at UIUC, see Section III.F), these must be prepared in advance, especially if they are to be made available to the students to bring to the lecture. If JiTT methods (Section III.B.2.d) are to be used, the Web page for the Warm-up for each lecture must be prepared and mounted on an appropriate platform, and a convenient means of accessing the student responses must be created (the assistance of the CIT staff members should make this task considerably easier). Exam questions reflecting the new methods (e.g. conceptual questions, tutorial-type questions, strategy writing) should also be prepared, whether or not common exams are to be given.
It should be emphasized that the task of materials development is largely one of adaptation, not invention. A great deal of instructional material is readily obtained from the physicists responsible for the creation of each of the methods described in Section III. Often the material can be easily downloaded from the Web, since its development was funded by NSF with the requirement that it be made freely and widely available to the entire physics community. Other material can be obtained from commercial publishers, either in a form to be used by instructors (e.g. Peer Instruction24 or Physlets: Teaching Physics with Interactive Curricular Material72) or for purchase and direct use by students (e.g. Tutorials for Introductory Physics58 or Interactive Physics84). The job of preparing the materials for an entire course is therefore less daunting than it might at first appear. However, this work will still involve a very significant effort, and it should be considered a one-course teaching assignment for those engaged in the task. Funds to support this course reduction have been requested from FIPSE and NSF, and other funding sources will be explored (see Section VI.B.3).
Because the pedagogical methods to be implemented are new to most of the faculty and all of the graduate teaching assistants, an ongoing program of development and mentoring will be necessary. During the early part of Stage III, experts in the specific methods selected for adoption will be brought to the department to hold workshops. This will allow the instructors to see the methods in action rather than just read about them, and to get a chance to try the methods out for themselves. The workshop leaders will also provide guidance in the development of an ongoing program of TA training, which is clearly vital to the long-term success of the transformation. (CTL can also assist with the development of the TA training program.) Funding for these workshops is being sought both externally and internally. Once a cadre of faculty has gained experience in using these methods, new faculty can be trained via an organized program of teamwork and mentoring. The transformation will thereby become sustainable over the long term.
Stage III of this project will extend over four semesters, ending in Spring 2007 with the preparation of materials for the second course in the second sequence. The same IPTF members need not participate each semester, but rather the group should include volunteers who are willing to be the pioneer instructors for each course. After the first semester of Stage III, those engaged in the materials preparation will benefit from feedback from the instructors of the courses that are already being taught in the new way. For methods that use information technology (e.g. JiTT70), appropriate template files and response recovery schemes will be developed in the first semester, leaving only the task of content preparation for subsequent semesters. Because of the large overlap of content between the two introductory sequences, it will also be possible to use much of the material developed for one sequence to teach the other. Stage III will thus be most difficult at the beginning and will become easier as it progresses.
In Stage IV, the four introductory physics courses will be taught in the new way for the first time. The pilot course for the project is to be taught in Spring 2006, with the remaining courses making their debut one by one in the following three semesters. Thus by the time the last course is taught for the first time in its new form (in Fall 2007), there will be the equivalent of six semesters’ worth of departmental experience with interactive engagement methods to draw on. Presumably the inevitable glitches and difficulties with implementation of specific methods will have been ironed out by the time the last course is launched. The pioneer instructors for the final course will therefore not need to be quite as adventurous (!) as those who participate at the beginning of Stage IV. By Fall 2007 it may even have been feasible for other instructors to replace those who pioneered the first two courses, so that the cadre of instructors with experience in the new methods can begin to increase even further. Ultimately a substantial fraction of the department’s faculty can be expected to teach these courses from time to time.
Once Stage IV is complete in Spring 2008, the teaching of the introductory physics courses will be in a steady state. It should not be necessary to make substantial changes in them for a considerable period. Instructors assigned to the courses will naturally work to improve them, by developing and testing additional instructional materials for the various methods employed or by “tweaking” the existing materials. New instructors will need to be mentored by more-experienced ones as they learn how to use interactive engagement techniques. An ongoing program of TA training will assure that the methods continue to be used effectively in all parts of the courses. At this point, the resources (human , physical, and financial) needed to teach the courses well should be no greater than those that were expended in teaching in the traditional way.
The final stage of the project consists of the assessment of whether or not it has accomplished its goals. This stage overlaps with the materials development and implementation stages, because it will be important to have baseline data with which to compare the data collected from the transformed courses. External funding agencies mandate that a formal assessment be conducted by an independent entity, and we are lucky at UNC-CH that we have a suitable entity available on our own campus.
The evaluation of the project will be performed by the Evaluation, Assessment and Policy Connections (EvAP) group of the UNC-CH School of Education. Baseline data on student learning outcomes will be gathered from the untransformed courses beginning in Spring 2005. The same measures will be employed in the transformed courses beginning in Spring 2006, continuing through Spring 2008 when all of the courses will have been taught in the new form at least twice. The evaluation instruments to be used will include items from nationally-normed tests of physics conceptual understanding and problem-solving ability such as the Force Concept Inventory, the Mechanics Baseline Test, and the Conceptual Survey of Electricity and Magnetism. In addition to these student outcome measures, semester course evaluation will be conducted and used for course improvement. Of great importance to this study will be the process data collected from participating faculty through focus groups and interviews that will chronicle the transformation of the introductory physics courses. This information will explain how the courses were modified and the impact of curriculum reform on faculty. The external evaluator will meet annually with the PI to draft a detailed evaluation plan. Data summaries will be provided as they are available, and it is likely that the project will result in contributions to the educational research literature. By employing this detailed and comprehensive evaluation scheme, the learning outcome goals will be assessed and the educational leadership goals will be advanced.
This project will require the commitment of significant resources, largely in the form of personnel and time. Stage I has been completed by means of the release time granted the author by a Chapman Family Faculty Fellowship (administered through the Institute for the Arts and Humanities). The product of this stage, namely this document, will serve as a resource for Stage II.
Stage II will begin with the formation of the Introductory Physics Task Force composed of faculty, graduate students and postdocs, undergraduate students, and CIT and CTL staff. Faculty members from the NCAT and AAMU Physics Departments will also participate, engaging in discussions via video conference. This group will be charged with selecting pedagogical methods to be used in the introductory courses. This document will provide a starting point for the evaluation of the methods, but members of the task force will undoubtedly wish to investigate some methods in more detail. This will be more efficiently done if the task force divides into small subgroups (perhaps each assigned to a particular portion of the course, such as lecture or laboratory) that report their findings back to the entire group for discussion. Because the actual development of daily teaching materials is not a goal of this stage, the effort involved should be comparable to that of a significant faculty committee assignment. It may be necessary to relieve some of the participants of other significant administrative duties that they normally perform, with these duties to be taken up by other faculty members not involved in this project. Since the project will benefit the entire department, such a shifting of responsibilities would be appropriate. However, faculty, graduate students and postdocs who participate should be able to do so without additional relief from their ordinary teaching and research responsibilities. CTL and CIT staff will participate as part of their duties in support of instruction. The only resources required for this stage are therefore funds for minor purchases such as sample textbooks and software. Some of these purchases could be made with unexpended funds associated with the author’s Chapman Fellowship.
In Stage III a small group of faculty and students will prepare teaching materials for one course each semester for a period of two years. The participants will be members of the task force, and therefore will be familiar with the pedagogical methods for which the materials are needed. Based on the experience of other departments, two faculty members per semester should be able to accomplish this task, especially since much of the material already exists and requires only adaptation. However, particularly during the first two semesters, this will require a significant effort that would be insupportable if undertaken in addition to a full load of regular duties. It will therefore be necessary to relieve the faculty participants of responsibility for one course during a semester in which they prepare materials. In practical terms this means that funding to pay temporary faculty to replace this teaching must be sought. If such funding is not available, it may be possible to shift the load to other faculty (as is done for unfunded research & study leaves), but this is not desirable. It would also be advantageous to have funding to support a TA participant at least part-time, rather than diverting the efforts of some of the pool ordinarily devoted to providing instruction. Funding to “buy out” some of the time of the CTL and CIT participants would assure that they are able to devote significant attention to this task.
Besides funds to support relief of participants from other duties, the other significant costs in Stage III arise from the need for workshops to train faculty and TAs in the new techniques. While much can be learned from the published accounts of the new pedagogical methods, there is no substitute for in-person demonstration of the techniques and training in their use. The costs for these workshops include honoraria for the workshop leaders, travel and subsistence costs for the leaders, and refreshments (typically box lunches) for the leaders and participants. There may also be minor expenditures for books and other supplies.
It is reasonable to expect that the costs associated with Stage III of the project will be greatest in the first half of the stage. The workshops will also be most valuable if they occur before instructors begin to implement the methods, so they should take place as early as possible. Much of the instructional material developed for the first two classes (either P24/P25 or P26/27) will also be suitable for the second two, since there is significant overlap in the topics covered in the two sequences. It may therefore be possible to have only one faculty participant relieved of classroom teaching duties in the third and fourth semesters of this stage.
In Stage IV (which overlaps with Stage III) the new methods will be implemented, one course at a time over a period of two years. The instructors who “pioneer” these courses will do so as part of their ordinary teaching duties. There may be some costs associated with equipment, such as receivers for electronic response systems or new equipment for the laboratories. These costs can be shared over all of the courses.
Stage V, the evaluation, will overlap Stages II-IV. The evaluation must begin with the collection of baseline data in the courses as they are taught in the traditional way. With these data it will be possible to compare the effectiveness of the new and old methods, and to engage in formative assessment as the implementation of the methods is refined from semester to semester. The costs associated with this stage result from the need to administer and score exams (e.g. the Force Concept Inventory) and surveys. More in-depth information and analysis of the data will require the participation of an expert in educational research, and therefore of appropriate compensation for that person. Fortunately such experts are available in our own School of Education, at a cost considerably less than in the private sector.
The NSF Division of Undergraduate Education (DUE, within the Education and Human Resources Directorate) sponsors the Course, Curriculum and Laboratory Improvement (CCLI) program. One track within that program is Adaptation and Implementation, to which projects to adapt and make use of existing instructional methods and materials (often developed initially with NSF support) can be proposed. A proposal for support of this transformation project has been submitted in December 2004, with a start date of July 2005 (i.e. at the beginning of Stage III). The budget for a proposal submitted to this program has a cap of 200 k$, or ~137 k$ in direct costs. This is sufficient to cover the hiring of two temporary instructors per semester for two years (to replace the teaching of the Stage III participants) as well as the costs of workshops for faculty and TA development and the costs of the (mandated) evaluation program. The participation of graduate students and of CTL and CIT personnel will constitute a form of in-kind cost sharing. The expected funding level for all four tracks in the CCLI program is 40 M$ in the current round.
The Fund for Improvement of Post-Secondary Education (FIPSE) of the federal Dept. of Education also offers support for transformation projects of this type. The submission process begins with a pre-proposal round, and a request for support of this project was submitted in November 2004. Approximately 10%-15% of the pre-proposals are expected to result in an invitation to submit a full proposal, and 25%-30% of the full proposals are expected to receive funding. The invitations for full proposals will be issued in January 2005, with proposals due in March 2005. The estimated number of new awards is 50-60, for a total of 12.7 M$ in new award funding in FY2005. The institution is expected to “significantly support the project both philosophically and financially,” meaning that that it is expected to “contribute substantial resources, in some cases even matching or exceeding the Federal request.” The indirect cost rate is also expected to be similar to the Dept. of Education training rate of 8%. These considerations led to the total direct cost in the budget for the pre-proposal to be very similar to that used for the NSF proposal described above.
The needs associated with this project are relatively modest compared to those of a major research effort, and they are limited to a short period of time. Because the result of the project will be improved education for a large number of students, it may prove to be an attractive target for fundraising from private sources. This will be especially true if government grants can be obtained for the bulk of the necessary support. The UNC-CH Parents’ Council has donated money to CTL for the development of instructional materials (pre-lab videos) for introductory chemistry classes, and may also be willing to provide partial support for this project. Other private donors can be approached as well. Discussions with the Development Office will begin immediately.
From time to time it has been possible to obtain modest funding for course development within the College, especially when the funds can be used to incorporate the use of technology into teaching. Other support from discretionary funds available to the Dean could also be requested, especially as a supplement to an external grant.
The primary goals of this project are local, associated with learning outcomes and the utilization of instructional resources. We want the students who take our introductory physics courses to achieve a deeper and more coherent understanding of the fundamental concepts of physics, and be able to apply them more effectively in a wide variety of contexts. We also want them to come away from their (often only) physics course with a more positive, and more accurate, view of the subject and its relevance. We want to have a cadre of faculty members who can teach the introductory courses effectively without compromising their ability to accomplish our other missions of research and advanced physics education. Completing this project will benefit our department, and will enable us to accomplish this portion of our education mission (which involves a large fraction of our FTEs) at a higher level of quality.
As an outstanding educational institution, however, we have an obligation to exercise educational leadership of our peers and of other institutions that may seek to emulate us. Serving as a model for other disciplines and institutions is therefore a secondary goal of this project. To achieve the goals of educational leadership, the impact of this project must extend beyond courses that are taught in our own department. Despite the national problem of ineffective instruction that has been quantified by physics education researchers and others, it is all but unknown for a major research university physics department to totally transform its introductory teaching without the catalyst of either an indigenous physics education research group or a major external threat to its resources. The project described here will therefore serve as a model in two ways.
One target for leadership and dissemination is departments that have a desire to improve their teaching but lack the institutional resources to engage in a complete transformation such as that proposed here. A physics department that has passed through the phases92 of knowledge, persuasion and decision in regard to innovation in pedagogy, but which has only limited resources to proceed to the implementation stage, can make use of the specific instructional materials in the forms adapted by UNC-CH, which will all be made freely available via the World Wide Web.vi (It is worth noting in this regard that much of the source material that we will adapt for our use will have been obtained in this same way.) Recognition of the profound underrepresentation of racial and ethnic minorities in physics leads to the conclusion that one important group of departments that can be targeted in this way are those of Historically Minority Universities, where a significant fraction of all minority physicists are trained. The participation of faculty from NCAT and AAMU in the project will be a first step in this regard. Additional solicitation of “early adopters” can take place in presentations at conferences and articles published in appropriate journals and via a comprehensive Web site prepared with the assistance of CTL staff.
As a model for institutional transformation, this project also has much to offer to physics departments at UNC-CH’s peer institutions, namely other major research universities. A department that wishes to make a similar transformation could make use of the comprehensive compilation and evaluation of pedagogical methods that will result from Stages I and II. This information will be made available via a Web page dedicated to the project. Faculty at each department will of course wish to make their own selection of methods that they feel are appropriate to their local circumstances. To the degree that they select the same methods that are chosen at UNC-CH, they will be able to make use of the instructional materials that will be adapted and developed in Stage III. Their selections could also be guided by the results of the evaluation that constitutes Stage V of the project. Perhaps most important, the project will offer a model for how a comprehensive transformation of a set of introductory physics courses can be carried out at such an institution. Members of our department can disseminate information about this model in presentations at peer institutions, as have faculty from other departments such as UIUC and UC-Boulder.
Beyond the specific modifications in physics pedagogy, this project can serve as a second type of model, one of institutional transformation, which is applicable to other disciplines. Other units within UNC-CH, including the Dept. of Chemistry and the School of Nursing, have expressed interest in using this project as a model for the transformation of their own introductory teaching. The project is also seen as complementary to the Large Enrollment Course Redesign initiative taking place on multiple campuses in the UNC system, and has been endorsed by the Senior Vice-President for Academic Affairs, Dr. Gretchen Bataille. The dissemination of information beyond the physics community can take place via presentations at educational leadership conferences, and by articles to be published in the educational research and higher education literature.
The purpose of this project is to effect a transformation in the way that we teach introductory physics at UNC-CH to achieve more of our learning goals in a sustainable way. To do this, we will adapt and implement a set of instructional materials that will permit the introduction of a common set of interactive engagement techniques throughout all phases of all of the introductory physics classes at UNC-CH. The motivation for undertaking this project is the realization, drawn from the findings of cognitive science and physics education research, that the traditional approach to physics instruction used here and elsewhere is not effective. The failure is not that of the students or the instructor, but of the method of instruction. We can mitigate this failure in a sustainable way, by making a complete transformation of the way introductory physics courses at UNC-CH are taught. Faculty members who have not taught these courses will be able to do so effectively, without compromising their ability to accomplish our other missions of research and advanced physics education. The development of a common set of teaching materials (based on interactive engagement) for all instructors to use, with mentoring and faculty development, will make high-quality introductory physics teaching sustainable in the long term. By accomplishing this project, we will also provide educational leadership to other physics departments, and to the broader higher education community. Excellence in undergraduate education is one of our primary missions, and a significant fraction of all the students we teach are in the introductory courses. The resources available to us are commensurate to the task before us. It is the right thing to do.