ࡱ> ` bjbj 06       * QQQ8QL6R4* ܽ2vTTTTT}U"U U[]]]]]]$hv 0X}U}U0X0X  TTZZZ0X T T[Z0X[ZZK  TjT R|BQX۫>'40ܽFYF|F (UhVJZeV<VUUUFZdUUUܽ0X0X0X0X* * * *4* * * 4* * *        Masters Paper Physics 690 March 8, 2005 Chris Olszewski Conceptual Change of Good Teaching via Alternate Teacher Certification Program: A Personal Case Study Introduction One concept of teaching is that of changing the conceptions of the students [Refs]. Similarly, the development of the thinking of beginning teachers may also be described as changing their concepts of what constitutes good teaching [Refs]. As a participant in Buffalo State Colleges alternate teacher certification program for high school physics teachers [Ref], my concepts of good physics teaching have undergone changes more revolutionary than evolutionary. My perspective on physics teaching is unusual for a beginning high school physics teacher in that I already hold my doctorate in physics, and have had a twenty-year career in industrial research and engineering. This paper is presented as a personal case study on teacher conceptual change of good physics teaching, and the program elements that brought about these changes. Case studies constitute a valid component of teaching research which illustrate the development (or lack thereof) of actual people in actual programs [Ref]. That an author presents himself as a case study is unusual, but on the other hand, my perspective is also unusual. I believe this paper to be a valid contribution to education research on alternate teacher certification programs. Motivation and Uses Three groups of people could reasonably be expected to use the information reported in this paper: Those who will be making use of alternate teacher certification programs. There is projected to be a large shortage of science and mathematics teachers, and one place that these teachers could be drawn from is from the ranks of industrial researchers and engineers [Ref]. This information could be used to prepare them for the changes to their concepts of good teaching they are likely to undergo. Those who develop and coordinate alternate teacher certification programs. This information presents a case-study perspective on which elements in these programs are effective in promoting conceptual change. Those who study alternate teacher preparation programs. This information could be used as part of the basis for a more quantitative study of such programs. Methodology The information presented on my initial preconceptions of good teaching are those that I have held for many years, and are recorded in some respects in my letter of intent submitted as an applicant to the alternate teacher certification program, as well as in descriptions of my philosophy of teaching. Information regarding changes to my conceptions of good physics teaching was specifically recorded in my class notes and class assignments during some of the courses of the alternate certification program. Some of the information also comes from my descriptions of observations I made of actual physics teachers and students. Although some elements of case studies are necessarily related to the specific individuals involved, I have been trained as a scientist and record observations carefully. Because memories can often fade, I try to write down as much as possible of events I am trying to observe and record. Initial Participation in Alternate Teacher Certification Program To be able to evaluate changes in my conceptions of good teaching, it is necessary to know the conceptions before I participated in the alternate teacher certification program. Parts of these pre-conceptions are based in my educational and professional backgrounds, so they are also described here. In addition, similarities and differences between me and other participants in the program are described, as well, to show the applicability, or lack thereof, of generalizations from the single example I represent. Personal Background My background is somewhat rare for teaching at the high-school level, although not unique. I received my doctorate in physics about 20 years ago at the University of Illinois, and thereafter took a systems engineering/applied research position at Bell Labs. I continued my career in this area for the next twenty years, until the small start-up company I where I worked failed. Then, for a variety of personal and professional reasons, I decided to go into teaching at the secondary level. Although I had no intention of teaching when I first began my professional career, several formal and informal teaching opportunities I took advantage of convinced me that I would find teaching extremely satisfying. From these teaching experiences, I also decided that I would find teaching high school students the most personally rewarding. So, I decided to become a full-time teacher and enrolled in an alternate teacher certification program at Buffalo State College in New York [Ref]. With my extensive physics background, I did not believe that I needed (or wanted) to complete a four-year program to become a certified physics teacher. Initial Preconceptions of Good Teaching While I considered the prospect of enrolling in the alternate teacher certification program, I admit to having several prejudices about the program and many pre-conceived notions regarding good teaching. My incoming prejudices were: I believed that I had more than adequate subject-matter mastery. I had studied physics as an undergrad and as a graduate student, with about 60 undergrad hours and about 20 graduate credits. Additionally, I had done research for my doctoral degree. I felt I did not need to learn more physics merely better ways to teach physics. I had several ideas of how to I expected to teach physics. Most of my undergrad and graduate courses were taught in a traditional lecture format: the instructor designing and delivering lectures, and preparing assignments for the students to complete. In these classes, the students generally sat passively taking notes, and learned the material by studying and completing the assignments. My expectations of teaching physics well were to show the relevance of physics to everyday life, and to use my ability to explain physical/scientific concepts clearly. However, I did not expect to stray much outside the boundaries of the typical lecture format. I did not anticipate more than small incremental learning in the alternate teacher certification program. I expected to learn how people learn and acquire some new techniques and approaches to teach physics in ways to make the material more interesting and relevant to students. Although I had heard that You cant just lecture to these students anymore, I still expected these techniques to be within the framework of a traditional lecture. I did not expect my approach towards teaching to be revolutionized. From what little I knew of educational theories, I was not positively disposed towards constructivism. I believed that knowledge of the physical world was more-or-less absolute, and the idea of students (or anyone) constructing their own knowledge verged on the incomprehensible. My initial ideas regarding physics teaching were formed from my own experiences learning physics: essentially, to teach as I was taught. I also thought to try to include techniques that would have helped me to learn the material faster. Generally, I believed that the content of science (including physics) was factual: the students needed to learn and understand a wide variety of scientific facts, and know how to apply them. The teachers job was to make this acquisition of facts as smooth and as easy as possible, within reason. The teacher should try to avoid frustrating the students, and when the students have questions, the teacher should address them as quickly and accurately as possible. Indeed, the best way of communicating this information to the students would be through very clear lectures, demonstrations, and going through appropriate examples. Ideally, students following this path would pick up the habit of thinking for themselves; but, if they do not, the students could still learn enough of the material to earn a passing grade. Whether the teacher began with abstract concepts and then showed how they apply to specific examples, or began with specific examples and then showed how they could be generalized, was largely a matter of the teachers discretion. Indeed, starting with abstract information would give the students a framework with which to interpret later examples and demonstrations. Further, if students had a difficult time grasping the material during the lectures, they would learn it on there own as they attempted the problems assigned by the instructor. Initially, the students should have very little prior knowledge about the subject. Although it would be desirable to connect the new information to their normal lives, this task may not be possible. Thus, the information learned by students might be isolated and disconnected, but the instructor would attempt to give the students enough knowledge to form a basis to build their physical conceptual understanding. The students might find some of the activities and demonstrations chosen by the instructor as boring, but these items would be determined by the teacher to be the most appropriate examples. Audio and visual information (lectures, lecture notes, and textbooks) would be the primary means of delivering information to the students. Other media and modes (movement, feeling, color, etc.) may be interesting and diverting, but would not function as primary sources of usable information. Furthermore, most useful information in the class would flow from the instructor to the students by these audio or visual means. Since the instructor is presumably the person who knows the subject matter best, it makes sense that most useful information would come from the instructor to the students. Although the students may try to explain what they see, hear, or experience, it is generally the instructor who provides the best explanation. Explanations from the students are frequently in error, and will tend to slow down and confuse the class. Science may be done in groups at the research level, but at the high-school level the students would be better off learning the material individually on their own. After all, they will be responsible as individuals on their tests. When students ask questions, it would generally be because they do not understand something. While one goal of instruction would be to give the students an Aha! experience, in which seemingly incommensurate ideas suddenly become comprehensible as a part of a whole entire concept, these moments occur very infrequently. There would not be much to be done to increase their frequency, since they are essentially random events. Demonstrations used in the class should be thoroughly gone over before hand, to ensure that the demonstrations work properly and are not confusing. Smaller, less significant details should be pushed to the background or eliminated to make the demonstration clearer. Additionally, laboratory investigations would be merely activities that illustrate concepts from the lectures. A clear set of steps and procedures should be given to the students when they are engaged in laboratory work to preclude the students making mistakes and not getting the proper result. Computers and technology would certainly be very useful tools, but would not be essential. They would not materially accelerate the students learning. Finally, many topics of modern physics could not adequately be addressed at the high school level (e.g., particle physics). Rather than discuss topics of doubtful relevance and limited understanding to the students, these topics should not be addressed at all. Similarity to Other Participants From discussions I had during my introduction to the alternative certification program, my initial views were not too dissimilar from other new participants. My physics background was stronger than the other participants, but many of the other participants were also practicing teachers. Many of the other participants came from engineering backgrounds, and did have a solid physics and mathematics foundation. Many of the other participants expectations were similar to mine: that is, they had a pretty secure physics background, although they might learn some new physics; they believed they would learn some new techniques in teaching physics; and did not believe that we would learn a different philosophy of teaching and learning. Alternate Teacher Certification Program The alternate teacher certification program at Buffalo State College is described elsewhere [Ref]. At its heart are their Summer Institute classes, at which participants take part in modeling instruction of basic mechanics and electricity and magnetism, as well as a new physics teacher workshop. During these classes, participants are asked to experience the teaching practices both as an incoming high-school student would (to get the students perspective), and as an instructor, reflecting on the teaching techniques and consequences. During these classes, I found that my conceptions of good physics teaching were revolutionized. In addition to the summer institute classes, the program also consists of a core of physics classes, as well as pedagogical courses encompassing educational / adolescent psychology, exceptional education, and literacy. These courses provide some theoretical basis for the practical pedagogical content knowledge of the summer institute classes, as well as prepare the incoming teacher to teach effectively to a wide range of incoming students. These classes also help satisfy state educational requirements for teachers. Finally, the alternate certification program also contains a requirement of field work, in which the teacher-to-be must go out and observe physics teaching and learning taking place. This component allows the participant to confront a host of issues related to teaching, learning, and real students, and provides a wealth of practical information. Although the field task is theoretically set up as an observation, the experience can be augmented to a large degree by the assistance of the teachers being observed. Significant Changes in Conceptions of Good Teaching Many of my conceptions of good teaching were changed (revolutionized) by my participation in the summer institute courses of the alternate certification program. A list of the many conceptions that changed is given in Table 1, showing both my initial concept, and then the resulting concept of good instruction that was developed during my participation. This table was developed as a list of my conceptions of good learning that occurred during these classes, as supported either by my class notes or by class assignments I had completed during the course. On reflection, I tried to relate these new concepts I had of good teaching with previous assumptions of instruction I held prior to my enrolling in the program. I was very much surprised at the multiplicity and magnitude of the changes my thinking had undergone. To provide more definite illustrations of the events that changed my conceptions in some of these areas, I will describe the changes in my conceptions for the importance of: Different kinds of knowledge Student verbalization Open-ended and non-structured lab activities. I consider these to be major changes in my conception of good physics / science teaching. Other aspects of my conceptual changes will be described elsewhere [Ref]. Different Kinds of Knowledge The change in my conception of using different kinds of knowledge in teaching physics began with an exercise in which I and others in the program were asked to duplicate with the motion of our bodies certain kinematics graphs (position vs. time, velocity vs. time, etc.) using a motion sensor connected to a computer display. The display was able to provide real-time feedback regarding a successful or unsuccessful trial, and was also fun to watch and participate in. I found the kinesthetic knowledge of this motion to be quite different from my usual way of viewing kinematics, which usually incorporates one or more kinematic equations. Having such a hands-on knowledge of the underlying motion provides a real embodiment of the various kinematics concepts. For a new student just learning these concepts, this very tangible experience can very useful. To generalize from this example, information about a topic in physics can be conveyed in many ways: verbally, visually, by touch, moving, pictures, graphs, equations, written words, etc. Not only do students have varying abilities in each of these areas (thus, making some modes easier for some students than others), but asking the students to translate between these multiple representations engages their minds in multiple ways. As they translate concepts between different representations, they gain more facility with the act of translation, and also become more familiar with the subject of translation. This familiarity helps to embed the knowledge into their minds, and also can provide insights into the material from different perspectives. This increased familiarity allows the students to actually be able to use the information they are learning more easily. Beyond the multiple representations of the knowledge, learning something through various modes presents the student with different kinds of knowledge. One can have an appreciation of the sight of a physical configuration, or the feel of a physical process on the fingertips, or a kinesthetic sense of motion as one moves in a certain pattern. These types of knowledge can stand on their own, to an extent. But it is in their relationships between each other that I believe can substantially benefit the students. These islands of different types of knowledge are bridged by the students understanding of the underlying principles. Having multiple islands allows the students to draw connections between them, and build up their knowledge from multiple sources. Having multiple sources can give a solid anchor to abstract concepts, so that the students can not only remember them better, they can make use of this knowledge in multiple ways. As mentioned, some students will have more facility in one mode than another. Multiple modes and representations lets the student shore up those areas they are weak in, while at the same time building on those areas they are strong in. Different types of knowledge can also provide insights into the underlying physical phenomenon. Student Verbalizations and Explanations My appreciation of the importance of students verbalizing their understanding, and trying to explain what they think they know, was triggered during a small group activity during one of the summer classes. In talking to my other group partner and trying to figure out how to approach a specific task we were given, I realized that I was listening to myself speak. It was in the act of speaking that I was actually putting my thoughts together, so that we were both hearing them for the first time. My partner then took my ideas, and extrapolated from them in ways that were both very useful and unexpected to me. Such interactions are very natural when people are researching new ideas or problems in industry or research, but I had not seen them applied in quite this way in teaching. I now believe that student discourse is extremely valuable for multiple reasons as the students learn and use course information. As students construct their knowledge and try to incorporating new information, they may try several ways to integrate this new information into their existing schema. Talking, as the students listen to each other and to themselves, helps them figure out how to connect them together. Humans are verbal animals, and it helps the students understand their own thoughts if they verbally describe or explain a concept, principle, or observation. This projection of knowledge into a concrete form helps them clarify their thoughts. If they are not able to explain something clearly, it may be because they are not thinking clearly. Giving them the opportunity, the guidance, and even the challenge to make their thoughts clear to others and themselves helps them learn. It also teaches them to express themselves. Both are good things. While the teacher may be able to offer ab initio a reasonable and coherent explanation of some phenomenon, this explanation may not find its way into the students brains. The real work of making sense of a phenomenon, and integrating that new knowledge into the students already existing knowledge, lies with the students. Verbally forming these explanations is correlated with better conceptual understanding and student performance [Ref]. When students express themselves to each other, they will make noise. If multiple small groups are talking among themselves, the noise level will rise. As they help and challenge each other to develop acceptable explanations, they are also likely to become excited about the material and their understanding. This excitement will probably increase the noise level further. In contrast to traditional courses (lecturer delivering material quietly), such sessions will probably be very boisterous. Traditionally, most information flow in a classroom is from the teacher to the students. However, I now believe that verbal exchanges between students, and from student to teacher, are extremely valuable. Lab Activities Lab activities have traditionally been used to demonstrate some principle or aspect of physics that was covered during a traditional lecture. The students generally are given a specific procedure to carry out for the lab, and then must write a report on their activities. Very little room is usually left for student creativity or insight. The possible importance of open-ended and unstructured lab activities to learning physics and other sciences was evident during such a lab activity during the summer classes. Our lab group had to determine the relationship between two quantities: no other instructions were given. So, we had to determine how we could measure these quantities, determine the materials we would need, make up our own procedure, and decide on our data analysis. All these activities captured the essence of scientific investigation: there is no one way to do things, and there is no instruction book for the world that tells us how to investigate it. While we in our group had some inkling of what we would discover, incoming students would probably not: they would essentially be doing science. Thus, I now believe that giving students open-ended and non-structured lab assignments will teach them about the scientific process and logical thinking. This approach is can be generalized to other aspects of their lives. In contrast with the traditional approach, the open-ended assignments are much closer to research carried out academically and industrially. In these situations, the goal is usually clear, but he way to achieve it is not. Such open-ended lab activities give the students the opportunity to use information they learn in class and to apply their own creativity and ingenuity as they seek to measure something or to achieve some goal. This arrangement gives the students the need to integrate creative thinking with their beginning knowledge of scientific investigations. In this endeavor, the instructor should be nearby to help the students formulate and analyze approaches to take, as well as provide needed assistance at times. By calling on very high-level cognitive functions, the students are forced to deal with the material they have been learning in a meaningful and very real-world way. The students could use this approach as they deal with real-world problems after they have finished the course and in their future careers. Program Elements Fostering Conceptual Change The program elements that encouraged my conceptual change can be broadly classified into two areas: student-like experiences and reflections on those experiences. Student Experiences At the heart of the summer courses are many modeling activities that mimic the activities that incoming physics students would go through. During these activities, participants try to see the activities as a new physics student would, to try to understand what the physics students would be thinking in this situation. This projection of the teachers into their students minds is a part of the pedagogical content knowledge needed by teachers [Ref]. These student experiences, including exposure to different types of knowledge, the discovery of the value of student discourse and open-ended lab activities, as well as to many other valuable elements of student learning and useful instruction, can change teachers conceptions of good teaching as it has changed mine. As we participants went through these experiences, we came away with ideas on what was valuable about each of these exercises. I expect to use this knowledge as I begin teaching students. Reflection The other major component of the summer courses is reflection on what the participants learned during various activities. During these forced reflections, we focused on how our knowledge changed as a result of our student experiences. Thus our concepts changed, and we became explicitly aware of the change. Reflection on conceptual change is a necessary part of learning to teach [Ref]. As we, as teachers-to-be, reflect on how our knowledge has increased, we can apply that to the expected evolution of our students knowledge and capabilities. Conclusion What I learned from my participation in the alternate certification program radically changed my concepts of teaching, learning, and what constitutes good instruction. One fundamental change is my understanding of what is important in good science teaching: I now believe that it is more important what students are actually able to do and learn by themselves than what information they may be able to memorize. Specifically, I believe what is important are what the students do as part of an open-ended lab activity, or what they learn through multiple senses, and how they verbalize their understandings to themselves and each other. As the emphasis in class focuses more on what the students do, the specific actions of the teacher become less important and the role of the teacher changes but is still crucial. Although in this perspective the teacher may not have to prepare clear lectures and develop good exercises for the students, the role of the instructor becomes much broader. The teacher takes responsibility for the whole teaching environment: the activities, materials, goals, and questions for the students. While the class-time itself becomes more student-driven, the instructor must both create this active learning environment for the students and guide the students through it. Unless the instructor has training or experience in the construction and use of such an environment, it will be very difficult if not impossible for the students to use it effectively. The instructor needs knowledge of: The base level of core content. What students know, or are likely to know. How students learn and comprehend information. Effective techniques that will help students learn the content (these last three are sometimes called Pedagogical Content Knowledge [Ref]) In making a career change from a technical field into teaching, I have found that my self-assessment of competence has changed significantly. From working in areas that I have already developed competence and expertise, I now find myself in an area that I do not have nearly as much competence. However, based on previous situations mastering unfamiliar information and tasks, I expect to see a rapid increase in expertise as my experience grows. Another large change in my conception of teaching is my perception of the importance of reflection. It is important to see how oneself learns. As I consider my preconceptions, I believe that they were rooted in my own pedagogical journey: mainly teaching as I was taught. With the advantage of hindsight, I can now see that in most of my physics learning I constructed my own knowledge from the lectures, textbooks, and assignments I had. Knowing the source of my learning now, I can see the importance of that type of learning. Indeed, this is truly the only way one really learns. Thus, I find my preconceptions naive. From my perspective now, I hold a much different conception of what constitutes good instruction. I believe that others following a similar path would have similar experiences. A similar progression of teaching conceptions among beginning teachers has been reported [Refs]. The major changes in my conceptions of good teaching dictate that the way I propose to teach also change. From my original intention, which was largely to teach as I was taught, I now expect to teach with an emphasis on student-centric activities that change the students own conceptions. Although not expert in all of these techniques, I believe now that they are extremely effective and that they are appropriately aimed at influencing the concepts held by the students. This effectiveness has been demonstrated through research, which correlates increased student performance with increased student appropriate activity [Ref]. The summer courses in the alternate teacher certification program allowed me to experience the effectiveness of these techniques as a student sees them. Table  SEQ Table \* ARABIC 1. Preconceptions and evolved conceptions of good learning. What I believed thenWhat I believe nowGoal/subject of instructionSubject of ScienceScientific literacy: factsScientific literacy: processesEncouragement of ThinkingFrustration in students should be minimized by the teacher by clear explanations and appropriate problems and demosStudents should encounter frustration regularly as they learn: intellectual dissonance/discomfort are essentialThe teacher should provide a smooth path of learning to the studentsWe want to challenge and engage students intellects, and develop critical thinking skillsAnswer questions immediately to address student misconceptionsDont answer questions right away: let the students stewWhy should students think?Students dont like to thinkStudent ThinkingProgression of KnowledgeBeginning with abstract concepts gives the students a framework from which to interpret further demos and examplesConcepts and topics should be introduced with concrete examples and demos first, and gradually abstracted to physical conceptsIf students to not understand a concept, reliance on the equations can help generate that understandingStudents should learn the general concepts first, then learn (or determine) equations to capture these conceptsConstruction of KnowledgeKnowledge is a given: the students just need to learn it.Students (like people) make their own knowledge as they learn (consistent with physical reality to be useful)Some knowledge cannot be connected, so you have to start in the wildernessKnowledge must be connected to what the students already know (even if its wrong)Student Engagement and ActivitiesEngagement of Student AttentionShowing the demonstration is more important than getting the students to think about whats going to happen beforehand. The important point is that they remember what happened afterwards.Asking the students to predict the outcome of demonstrations and exercises draws them into learning about what they see, hear, and experienceStudents should learn from the most appropriate activities (whether fun or not)Fun activities will help motivate students to learnDifferent Types of KnowledgeReally, audio and visual input are the keys: the teacher speaking, and the students listeningUsing multiple representations (and, having student use multiple representations) helps more students, even those that are supposedly smartSuch demonstrations are cute and interesting, but really do not advance the understanding of the studentsKinesthetic learning experiences (and other sensory experiences) give students a good basis for new knowledge in an entirely different wayStudent Verbalization & ExplanationsClarity of teachers explanation(s) should make material clear for studentsStudent verbalizations/explanations/ descriptions are essential to student understandingMost useful discourse in a classroom flows from the teachers mouth to the students ears.When students are engaged in the intellectual dance of science, they are frequently noisy and talk quickly to one another. This should be encouragedSince the teacher is the person who knows the subject best, the teacher should ensure that correct explanations are held by the studentsLet kids explore what interests them, and come up with their own explanations of phenomenaStudent-to-student discourse can be, but is usually not, usefulStudent discourse is (in)valuableStudent explanations are frequently in error: teacher-given explanations are much preferableHaving students explain their reasoning is valuable to them and their classmatesElements of LearningProcess of Science / LearningAt this level, students should do most of their learning on their own: theyll have to learn to work on their own eventually anyway.Science is done frequently in groups. Therefore, many activities are done in groups, as a demonstration of real scienceImportant Elements to LearningCommon knowledge Questions indicate non-comprehension One explanation (the correct one) is enough One representation is enough, tooUncommon knowledge: Open questions Developing multiple explanations Using multiple representationsAhas are important, but cannot be predicted or encouragedAhas are important, can be encouraged: Discourse Doing things Aware of incomplete knowledgeExamples and LabsRealistic ExamplesActivities and demos should be thoroughly worked out and practiced beforehand, minimizing any chance of discrepanciesThe physics and examples we present do not have to be perfect. In fact, imperfections may lead to more discussion (which is good)Sweep some things under the rug, so the students dont get too confusedBe correct (if not perfect): dont sugar-coat phenomenaLab ActivitiesLaboratory exercises should have a clear procedure, to minimize the students chance of making mistakes and errorsMost laboratory exercises should be open-ended unstructured activities, with broad clear goals calling on student creativity and thoughtfulnessTechnology of TeachingIntroduction of TechnologyComputers and software are good to have, but are not essential to developing a good physical understandingComputers and peripherals (motion sensors, force probes, graphing software) can provide immediate feedback to increase student learningProcess of Science / ContentMost modern science should not be addressed too esotericSome equipment (e.g., cloud chambers) can show that there are some phenomena that are not easily observableGood Processes and PracticesScience as subject-matter Science as memorization of facts and rules (comforting for really good students)Good learning: Hands-on Open-ended questions Creativity and enthusiasm Cognitive dissonance Reflections Good wait timeCompartmentalized topics: Set of process skills / thinking Application to disparate subjectsSprialing Builds up new knowledge and old Reinforces old Good environment Student input Labs first, then worksheets -> Organic whole (or something like that)Traditional lectures: Info from lectures Problem sets, too for reinforcement Labs to demonstrate principles from lecturesActive engagement Peer-to-peer communication Immediate feedback Multimodal exposure Science is doing Lecture info and working knowledge References: Hake, R. Interactive-engagement vs. traditional methods: A six-thousand-student survey of mechanics test data for introductory physics (1998). American Journal of Physics, 66, 64-74. MacIsaac, D. & Falconer, K. (2002). Reforming physics instruction via RTOP. The Physics Teacher 40, 479-485. 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