Using Interviews to Identify Student Misconceptions in Dynamics

Session S3D

Using Interviews to Identify Student Misconceptions in Dynamics Devlin Montfort 1, Shane Brown 2, and Kip Findley 3 Abstract - There is substantial evidence that most students graduating with engineering degrees do not possess basic scientific knowledge. Assessments of conceptual understanding have shown repeatedly that students are unable to answer qualitative questions about even the most fundamental physical phenomena. One approach to correcting this lack of knowledge is based on addressing what Michelene Chi calls misconceptions. Misconceptions are the set of students’ preexisting beliefs about physical phenomena which are persistent and preclude more correct understandings. The purpose of this study is to begin to identify some of the misconceptions held by students in engineering dynamics through individual clinical interviews with a small group of students who received A’s or B’s in a recently completed dynamics course. By asking students open-ended conceptual questions researchers are able to observe misconceptions in action. The interviews were analyzed qualitatively to discover patterns of thought in each individual student. Although specific misconceptions cannot be identified from the small number of interviews performed, trends in student responses can be used in future interviews to more thoroughly uncover errors in student reasoning. Index Terms – Conceptual understanding, interview procedure misconceptions. INTRODUCTION The Force Concept Inventory [1] was the first in a long series of research about students’ conceptual understanding of fundamental physical phenomena. In general, this research has revealed that even academically successful students cannot apply the basic concepts of science to qualitative analyses. An example of a basic concept in physics is that any change in velocity is an acceleration, and an example of qualitative analysis would be predicting whether a given situation would result in an acceleration or not. This means that students who are able to calculate the acceleration required for a rocket to reach geostationary orbit cannot consistently identify when an object is accelerating. Application of validated concept inventories also suggests that standard instruction does not significantly improve student understanding of these basic concepts [2]. Theory suggests that it is difficult to increase students’ conceptual understanding because most students enter the classroom with a set of existing beliefs about

physical phenomena which may be difficult to change. The process of identifying students’ preexisting beliefs requires indepth, qualitative methods. I. Literature Review Michelene Chi and Rod Roscoe categorize students’ preexisting knowledge into preconceptions and misconceptions [3]. While preconceptions are conscious beliefs that students can easily correct when they are contradicted, Chi and Roscoe define misconceptions as a “type of naïve knowledge [that] seems highly resistant to change…. [which] persist strongly even when they are confronted by ingenious forms of instruction.” Underlying this definition are the constructivist assumptions that every person forms their own understanding of the world, and a theory of cognitive development which states that individual beliefs are organized in the context of larger mental models. If mental models are pictured as trees of related knowledge, Chi’s preconceptions could be thought of as individual leaves that are upside down, and misconceptions would be entire branches or trunks that point in the wrong direction. A common example of a misconception is that many students believe that buoyant force increases when objects are held deeper underwater. Students who have successfully completed an introductory physics course can be assumed to have learned that buoyant force is equal to the weight of the water displaced if that subject was covered in the course. In a study of student understanding of floating [4] students who had completed coursework in hydrostatics frequently predicted that heavier objects would float deeper in the water than lighter objects of the same volume. This prediction is evidence of a misconception because the students involved in the study knew that buoyant force only depended on volume, but this knowledge was superseded by some stronger belief. This fits the definition of a misconception also because this stronger belief was likely based on previous life experiences where buoyant objects held deeper underwater seemed to pop up more quickly (because they’ve had more time to accelerate, not because the buoyant force was greater). Chi and Roscoe define misconceptions as persistent even when they are directly addressed. Without specific knowledge of students’ misconceptions, though, traditional lecture never will address them; the students in the study undoubtedly worked through problems that required them to calculate the buoyant force using the volume of water displaced, but the

1

Devlin Montfort, Graduate Student, Civil and Environmental Engineering, Washington State University, [email protected] Shane Brown, Clinical Professor, Civil and Environmental Engineering, Washington State University, [email protected] 3 Kip Findley, Research Professor, Mechanical Engineering, Washington State University, [email protected] 2

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Session S3D belief that deeper water pushes harder was never specifically addressed. Addressing a misconception, even when they are well defined, can be difficult. This process, concept change, not only requires students to correct certain facts in their mind, but to adjust their intuitions about what makes sense. Students are more likely to misinterpret or ignore new, contradictory information than to adjust the intuition that is being contradicted. A preliminary step in identifying student misconceptions is measuring their conceptual understanding of a topic. When a particular concept is difficult for many students a misconception may be present. The most common method to measure conceptual understanding is the concept inventory. The Force Concept Inventory (FCI) was designed in the 1980’s to measure students’ knowledge of the fundamentals of physics [5], and inspired researchers to create concept inventories in a range of different fields. In recent years concept inventories have been developed for topics such as dynamics [6], strength of materials [7], and thermodynamics [8]. The design of these assessments includes collecting faculty impressions of student difficulties, student interviews, and a great deal of validity and reliability testing. Concept inventories are a means to collect a little data from a lot of students. Widespread application of concept inventories can tell researchers how many students understand which concepts. In order to correct the gaps in understanding, however, researchers need to know more about why students can’t solve a particular problem. Once widespread difficulties have been identified by concept inventories, deeper qualitative methods are required to investigate the causes of those difficulties. A leader in this field, the University of Washington’s Physics Education Group (UW Group) uses student interviews to identify misconceptions [9]. In their interviews a student is “confronted with a simple physical situation and asked to respond to a specified sequence of questions [10].” These interviews are constructed around Jean Piaget’s famous clinical interviewing process in which the primary purpose is to draw out the interviewee’s thinking without applying the interviewer’s own biases. After enough interviews to represent the population of interest, the researchers design surveys to test hypotheses about widespread student misconceptions. Using data collected using the surveys and interviews, the UW Group designs inductive curricular materials to help students address their own misconceptions. This methodology has shown statistically significant improvement in students’ conceptual understanding in topics such as one-dimensional velocity [10]; the work-energy and impulse-momentum principles [11]; Archimedes principle [4] and the ideal gas law [12, 13]. II. Purpose of Study This study represents an intermediary step in identifying student misconceptions in engineering dynamics. After applying the Dynamics Concept Inventory [2] to approximately 100 students at Washington State University,

this series of student interviews was undertaken to follow-up on the results. This pilot study aims to develop a practical, effective methodology to identify student misconceptions within the students’ own contexts, to begin to identify areas of students’ conceptual difficulty that might be evidence of underlying misconceptions. While the UW Physics Group’s basic research model is being used, we aim to develop this methodology to better suit our particular applications and theoretical assumptions. METHODS It is important to note that this section describes the methodological elements adopted from the UW Group’s basic approach. Because one of the desired outcomes of this pilot study was a more detailed and theoretically-based methodology, the adjustments made to the UW Group’s methods will be described and supported with student quotes in the Results and Discussion section. In the following section the data collection will be explained first by describing the sample selection and the interview procedures. Then the data analysis procedures will be explained. I. Sample Selection The study sample consists of two students who were chosen by convenience from a summer session of Dynamics at Washington State University. Students who were identified by the professor as being likely to participate were offered a $20 gift card as incentive to give an hour-long interview. These two students will obviously not be sufficient to allow generalizations to larger student populations, and that is not the intent of this study. Research such as Halloun and Hestenes’ Force Concept Inventory and the UW Group’s interviews have shown that students with deep conceptual understandings are the exception. These two students were self-reportedly academically successful, with A’s or B’s in most of their courses. These students represent cases studies undertaken to begin to characterize the difficulties observed from the application of the Dynamics Concept Inventory. The students will be referred to pseudonymously throughout the rest of this paper as Stan and Kris, and though Stan will be referred as a male and Kris as a female, their genders were not considered in their selection for inclusion in the study or the analysis of their interviews. Possible threats to internal validity resulting from the selection process include diffusion and experimenter effects. The threat of diffusion is that students interviewed later may hear about the process from the students who have already been interviewed and be better prepared. This is threat is not significant because the students being interviewed had, theoretically, both already prepared for several semesters in their courses for these interviews, and a week of additional study would not likely make a significant contribution to their conceptual understanding of the material. Unlike diffusion, experimenter effects do not require time to be significant. Because the interviews proceeded based on

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Session S3D the interviewers’ perceptions and hypotheses about the students’ understanding, they are a subjective method of collecting data. Although these threats need to be considered, they do not impair the usefulness of these methods. The analysis of this data may not allow the researchers to absolutely identify student beliefs, but the purpose of the study is to develop methodologies and guide future research. The analysis of these interviews will certainly allow the researchers to identify areas of student uncertainty, or areas of common difficulty that will be used to direct future interviews. II. Interview Procedure Both interviews began with a description of a disc and a hoop of equal mass and equal radius about to roll down an inclined plane. After this situation was thoroughly explored, including counter-examples or comparisons to analogous situations, the second problem was discussed. The second problem involved comparing two systems: the first had two weights hanging over a pulley, with one weight being 10 Newtons heavier; the second system had the same set-up, but the heavier weight was replaced with a downward force. Because these figures and problem set-ups have been taken from the Dynamics Concept Inventory, and dissemination of these problems would inhibit its usefulness, figures will not be included in this paper. Details of the example situations will be provided as necessary to understand student statements. For both problems the students were asked first to generally describe the motions of the contrasted systems, and then to compare them. Most of the questions asked the student to describe or predict certain characteristics of the examples, or describe how they would try to calculate a certain property given all the necessary information. These problem situations were chosen because less than 15% of the 100 students tested correctly answered questions involving moment of inertia in the Dynamics Concept Inventory. The first situation with the disc and hoop required students to recognize the causes and results of the moment of inertia. They needed to know that the disc would have a higher moment of inertia, and that this would mean it would accelerate more slowly than the hoop under the same force. The second case could be considered in the same way, but it could also be analyzed without the pulleys. Students had to know that less weight meant less inertia, which results in greater acceleration. This second problem requires the simplest application of the concept of inertia, but in a rotational setting. It was included in order to determine if students had difficulty analyzing any rotational motion, or just the moment of inertia. Starting with these situations each interview was dictated by the student’s responses in a deliberately non-standardized way. Using the general approach suggested by Herbert Ginsburg’s description [15] of Piaget’s clinical interviewing procedure, the interviewers continually assessed the students’ reasoning and pursued new lines of questioning to test their assessments. The tone of the interviews was informal with long pauses to allow both interviewers and interviewees to think. Students

were encouraged to think aloud, and affirming statements or gestures were used to elicit further elaboration as well as clarifying questions. If a student began to appear uncomfortable about their statements, the interviewers verbally addressed the student’s discomfort, but continued in the line of questioning. In each case, the interviewee was seated at the end of a conference table in the civil engineering department’s conference room. Interviewers sat on either side, and supplied the student with scratch paper. The demonstration materials were placed on the table between the interviewers and directly in front of the interviewee. The interviews began with a brief discussion of the research, and the presentation and signing of a consent form. Each interview was audio and video recorded. The interviews each took approximately 50 minutes, with 10 minutes at the end to clarify the situations and answer any content questions the students had after the interview. These sessions were also recorded and considered data, though not specifically evidence of the students’ own understanding. III. Data Analysis Between the first and second interviews the researchers met to discuss the methodology and compare impressions. This was an important step in the process because it allowed the second interview to be used as a test for better methods. This discussion, and two more after the completion of the second interview, comprised the analysis of the methods. Analysis of the interviews began with the transcription process. The primary author of this paper transcribed each interview using the audio recordings, and annotated the transcripts by hand using the video recordings. The first stage of analysis established general trends in student responses, and required some analysis to determine when students’ reasoning was incorrect. The transcription process also familiarized the primary author with each student’s vocabulary so that distinctions could be made between sloppy wordings and actual errors in reasoning. The purpose of the video recording was both to provide information during the silent portions of the interview, and to record the students’ general aspect throughout the interview. Kris, for example, laughed often throughout the interview, but would put down her pen and lean away from the table when feeling unconfident about her answers. The video transcriptions also helped the researchers identify when the students were answering spontaneously from their own judgment, and when they were gauging their responses to satisfy the interviewers. Although it is unclear how the students would adjust their answers based on what they observed in the interviewers, it useful to identify statements that are qualified in this way. The video annotations also helped researchers relate the figures and notes the students had drawn during the interview to particular questions. The three coauthors of this paper met using the video and transcripts to discuss their impression of the trends in student responses. After informal discussions of what impresses each researcher about the interviews, each coauthor performed a separate analysis using qualitative analysis software. The

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Session S3D purpose of beginning the analysis independently was to broaden the analysis, and to make a basic check about the reliability of this analysis method. In another meeting the analyses were compared. The researchers each identified the same general trends, but identified them using different perspectives and quoted different parts of the interviews as evidence. The primary author combined and deepened these analyses to produce the findings reported in this paper. RESULTS AND DISCUSSION The following discussion of the results will be divided into two main sections: the first will begin by describing some characteristics of the students observed, and end with a brief discussion of how these characteristics could be accounted for in an interview protocol. The second section will present and discuss some preliminary results in student understanding in dynamics. I. Additions to Interview and Analysis Methods The students interviewed needed a little guided practice to be able to think and talk about their own reasoning. Part of this may have been reluctance to participate, or fear of saying something wrong. In the beginnings of the interviews then, the content questions were interspersed with prompts to remind the students that their reasoning was of interest, not the correct answer to any particular problem. There was very little that the students would state confidently and consistently. Once a student’s line of reasoning in particular problem had been fully revealed and tested with new questions, the interviewers would introduce new information to test the development of the student’s thinking. For example, Stan initially predicted that the disc and hoop would reach the bottom of the ramp at the same time. By asking him to explain his analysis of the forces in more detail, and pursuing a stray comment about rotation, Stan was lead to considering the moment of inertia, and revised his initial prediction to say that the disc would reach the end of the ramp first. Stan reverted to his original prediction that they would move at the same speed, however, after being asked to further explain his analysis of the energies of the disc and hoop. Such reversals were common, and were used to try to uncover students’ underlying difficulties. Directed questioning was used to encourage the students to state two of their contradictory beliefs during the same line of discussion. For Kris, this involved a scenario where the disc and hoop had cranks in the middle and she had to turn them. After first saying, “If one was twice as big as the other it would take twice as much cranking,” Kris immediately revised this statement to match a previous, opposite statement. Eventually, the interviewer asked, “but what made you think that?” Kris’s response, “just looking at the equations and trying to figure out whether it’d be a two or a one-half,” is revealing of how students address contradictions in their internal models. Stan’s response to a similar situation, “I use the equation sheets for a reason,” follows the same pattern. Both students described their typical problem-solving strategy as trying to apply the information given to them to an equation

based mostly on matching the variables: if the problem gives x, a and V, they would look for an equation with x, a and V, regardless of what those variables might represent. Both students surprised the interviewers by seeming to be unaware of what the major topics of dynamics are. When asked how she might go about calculating a velocity given the forces on a body (a basic application of kinetics), Kris said “yeah I always like to use kinematic equations [laughs].” Kinematics (which relate position, velocity and acceleration) and kinetics (which describe causes and resistances to motion) are the two main parts of any dynamics class, and represent different skills used to solve different problems. Kris demonstrated her preference for kinematic equations by attempting to apply them to each new kinetic problem presented. In one instance she recalled an impressive string of kinematic equations, but seemed unsure if there was an equation that would relate forces to acceleration, even though this simple equation (F=ma) probably related to fully half of the course. These students’ characteristics—a reluctance to think about their thinking, an inconsistent knowledge base, an inability to adjust their mental models, an unpredictable conception of what is important in dynamics, and a reliance on memorized equations—all require flexibility in the interviewing procedure. A predetermined set of questions would not have let Kris settle in to describing her calculations without actually doing them, or helped Stan to realize that we want to know how he remembers as much as what he remembers. It would be difficult to determine a list of things these students knew or didn’t know, because many items would be on both lists. Flexibility is most important because interviewers cannot predict what shape students’ mental models will take. Stan was quite able to perform energy analyses, kinetic analyses and analyses of rotating bodies as separate tasks, and because experts often divide the topics this way for pedagogical purposes, it might appear that Stan has a strong conceptual understanding of the causes of rolling motion. In the context of an informal discussion, however, it became apparent that Stan did not relate these skills, and did not fully understand when to apply them. In order to discover this disparity, it was necessary to allow the interview to follow Stan’s line of reasoning, and develop following Stan’s sense of context. Finally, these trends emphasize the role that the student culture plays in learning. What the students value, what they perceive as the purpose of homework or lectures, and what they think of science in general will definitely affect how their conceptual understanding develops. II. Student Understanding in Dynamics In the case of the discs rolling down an inclined plane, the students seemed to have difficulty relating gravity to the cause of motion. The word “torque” was not mentioned by either student during the course of the interviews, even in response to more than 15 questions about the causes of rolling motion or acceleration. In one of the more obvious applications, the interviewer asked “How would you describe the cause of

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Session S3D rotation?” and Stan responded, “[slight pause] Uhm because of the friction that we have between the object and the ramp, instead of just sliding down it’s enough that it’s basically…the uh [pause, 4 seconds] Well the center of gravity is moving and the point of contact is, its instantaneous velocity is zero. Sooo…if we’re on an zero there and this is moving… effectively that’s rotating around that. And as it continues on down we get the rotation.” Stan’s first statement brings him very close to describing the moment arm or torque that causes the motion, but he does not. Instead he gives a fairly complex description of what rolling motion looks like. For Stan, rotation is not a part of his analyses of motion or energy, but a separate topic. This type of information is directly related to students’ mental models and is vital in identifying their misconceptions. Kris was less comfortable with rotation than Stan, and was unable to define inertia or apply it to the problems. Stan had a stable definition of inertia, but it was strongly linked to his experience with flywheels. This reliance on a particular life experience in addition to the poor student performance on the questions involving inertia on the Dynamics Concept Inventory suggests that more students are more similar to Kris than to Stan in their understanding of inertia. When asked, “When I say inertia, what comes to mind,” Kris responded “I’m trying to think of…things that involve inertia, but, it’s…nothing’s really coming to mind right now!” Later in the interview, when discussing the discs with crank handles as described above, the interviewer asked “What are you pushing against?” It became apparent again that inertia is not a part of Kris’s mental model of motion when she responded, “I’m just imagining like a spring or something inside of it that, you know, you wind it up and then it has that much energy waiting to…release it.” Both Stan and Kris relied on imagined forces—friction, air resistance or the spring—to account for the effects of inertia in the cases examined. When asked to move beyond trying to remember equations, Stan and Kris continued to have very similar responses. Both students attempted to visualize the situation as a single instant, and analyze the forces as a statics problem. They started with free-body diagrams showing the force of gravity, and the resultant force from the ground, and then stopped for a moment. Stan said, “I’m looking at balance of forces. That’s one thing I always had to do on these things is I had to start with them as a static and then say ‘Okay, let’s start moving it.’” He described this process as one of the most difficult parts of dynamics for him, and eventually gave up and returned to the more familiar ground of his free-body diagram. Kris wasn’t able to translate the static image to a continuous motion either, and used the distinctive image of infinitely tiny bounces to describe rolling, saying “Like…because gravity just wants to move vertically, like, it just wants it to keep going down, but every time it tries to go down it runs into the slope a little bit so it just…moves…kinda sideways. So, I don’t know. Like, it’s just like a little stairstep pattern but it’s so…tiny that it just looks…smooth.” Both students were provided with or helped to develop analogous situations involving blocks sliding instead of rolling. Stan

reasoned that a larger mass would be harder to “get moving,” and Kris worked through a detailed theoretical derivation to support the same conclusion. Neither student, however, was able to apply these conclusions to the rotational cases. For both students, attempting to animate their understandings of the forces at work was a new exercise in visualization, and proved too difficult. IMPLICATIONS Standardized interviews are easier to analyze, but can’t address the basic unpredictability of student responses. If students’ models of phenomena were just simplified versions of professors’, all of teaching would be a matter of filling in the blanks. The flexibility available to attentive clinical interviewers allows researchers to collect information about what students understand, what context they understand it best in, how much confidence they have about their understanding, and what cultural factors have helped or interfered with the development of that understanding. The concepts these students struggled with suggest the shapes of some possible underlying misconceptions. Even though Stan had shown an adeptness at energy-balance calculations and a robust understanding of inertia he did not understand the basic differences between linear and rolling motion. The broad concepts of motion—net forces cause acceleration proportional to inertia can be applied to linear or rotational motion with equal simplicity. These students’ difficulty in “putting it into circular terms,” as Kris phrased it, suggests an underlying difficulty with the overall concepts of Newtonian physics. More revealing than their inability to apply Newton’s fundamental laws to rotational motion, is the fact that the students could not identify the faults in their descriptions of forces and motions. This suggests that a fundamental misconception regarding forces and motions may be present. These difficulties can be taken as evidence of misconceptions and not simply a lack of knowledge, because they seem to be “highly resistant to change.” The students demonstrated knowledge in the content area, just not conceptual understanding. In two instances, Kris recalled lengthy kinematics equations and tried to apply them the example situations. Both students recalled particular homework problems and lectures that related to the interviews, but could not apply those memories to help them answer the interviewers’ questions. Even with the interviewers’ help after the official interviews the students could not describe why their initial predictions about the example situations were wrong. This indicates the interference of a previously formed, robust belief—what Chi and Roscoe would call a definition. Further interviews will focus on the problems observed and include a much larger sample group. Instead of presenting the students with a few example situations to analyze, future interviews will ask students to generate and evaluate specific statements about example situations. The shift from general analysis to statements of fact will make the interviews more comparable between students, and emphasize beliefs over skills.

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Session S3D Despite their obvious lack of understanding of the causes of rotational motion and inertia, these students were successful in their dynamics course. The students’ preferred method of matching meaningless variables to a list of equations served them well in this course, and was likely developed over the course of semesters. This suggests that the innovative curricular interventions required to address student misconceptions will also need to propose ways to help students adjust their study habits. These students’ success has implications for assessment practices, as well. Based on the assessments given to them in their courses, the students have mastered the basics of dynamics. These students have developed a significant set of skills—recall Kris’s derivation of the forces necessary to move sliding blocks—important abilities are impaired by their lack of conceptual understanding of what their calculations mean. Without further work and study, they will not be able to apply their knowledge to the variety of complex situations found in the real world. CONCLUSION By viewing these two interviews as case studies, useful conclusions can be drawn about the clinical interview methodology, and guidelines for future research into students’ misconceptions can be generated. Even though it must be possible to look for common themes across the interviews, the best way to allow that is to match each interview to the student. Part of the information being gathered is how students connect the information they have, and this is only possible to observe by allowing the discussion to follow the students’ lead. The two students interviewed showed commonalities in their approaches and difficulties despite their marked demographic differences. Their mental models of kinetics were largely dependent on the context, as exemplified by Stan’s commingling of friction and inertia and both students’ inability to apply Newton’s laws to rotational motion. Because both students are academically successful, and displayed a strong recall of the events of the class, these difficulties suggest the presence of underlying misconceptions.

[6]

Gray, G.L., et al., Toward a Nationwide Dynamics Concept Inventory Assessment Test, in American Society for Engineering Education Annual Conference & Exposition. 2003.

[7]

Richardson, J., J. Morgan, and D. Evans, Development of an Engineering Strength of Material Concept Inventory Assessment Instrument, in ASEE/IEEE Frontiers in Education Conference. 2001: Reno, NV.

[8]

Midkiff, K.C., T.A. Litzinger, and D.L. Evans, Development of Engineering Thermodynamcis Concept Inventory Instruments, in ASEE/IEEE Frontiers in Education Conference. 2001: Reno, NV.

[9]

McDermott, L.C., Physics by Inquiry. Vol. I & II. 1996, New York: John Wiley & Sons, Inc.

[10]

Trowbridge, D.E. and L.C. McDermott, "Investigation of student understanding of the concept of velocity in one dimension", American Journal of Physics, 1980, 48 No. 12, p. 1020-1028

[11]

Lawson, R.A. and L.C. McDermott, "Student understanding of the work-energy and impulse-momentum theorems", American Journal of Physics, 1986, 55 No. 9, p. 811-817

[12]

Kautz, C.H., et al., "Student Understanding of the Ideal Gas Law, Part I: A macroscopic perspective", American Journal of Physics, 2005, 73 No. 11, p. 1055-1063

[13]

Kautz, C.H., et al., "Student understanding of the ideal gas law, Part II: A microscopic perspective", American Journal of Physics, 2005, 73 No. 11, p. 1064-1071

[14]

Gray, G.L., et al., Dynamics Concept Inventory, version 1.00. 2005.

[15]

Ginsburg, H.P., Entering the Child's Mind: The Clinical Interview in Psychological Research and Practice. 1997, New York: Cambridge University Press.

REFERENCES [1]

Halloun, I.A. and D. Hestenes, "The initial knowledge state of college physics students", American Journal of Physics, 1985, 53 No. 11, p. 1043-1048

[2]

Gray, G.L., et al., The Dynamics Concept Inventory Assessment Test: A Progress Report and Some Results, in American Society for Engineering Education Annual Conference & Exposition. 2005.

[3]

Chi, M.T.H. and R.D. Roscoe, The Processes and Challenges of Conceptual Change, in Reconsidering Conceptual Change: Issues in Theory and Practice, M. Limón and L. Mason, Editors. 2002, Kluwer Academic Publishers: Boston.

[4]

Loverude, M.E. and L.C. McDermott, "Helping students develop an understanding of Archimedes' principle, I: Research on student understanding", American Journal of Physics, 2003, 71 No. 11, p. 1178-1187

[5]

Hestenes, D., M. Wells, and G. Swackhamer, "Force Concept Inventory", The Physics Teacher, 1992, 30 No., p. 141-158

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