Teaching Deductive Reasoning to Pre-service Teachers: Promises and Constraints
International Journal of Science and Mathematics Education
Kostas Hatzikiriakou and Panayiota Metallidou
Elementary Education, University of Thessaly, Argonafton & Filellinon, Volos, 38221, Greece
Kostas Hatzikiriakou
Email: kxatzkyr@uth.gr
Received: 22 June 2006 Accepted: 13 November 2007 Published online: 25 December 2007
This paper broadly addresses the question of whether university students whose major does not require expertise in logic can improve their ability in deductive reasoning by taking an introductory course in logic. In particular, our study aims to evaluate a course in deductive logic offered by one of the authors in a department of elementary education. Two experiments were conducted by using a pretest-posttest design with an experimental and a control group as well as a follow-up test after 6 months on the experimental group. The results of the analyses showed that the course mainly succeeded in strengthening students’ general logical ability in the experimental group and these gains were retained 6 months later in the follow-up test. Promises and constraints of the study are discussed in the educational context.
Key words arguments - deductive reasoning - logical thinking - pre-service teachers - tableau method - truth tables - Venn diagrams
The names of the authors are listed alphabetically.
2007-12-25
2007-12-18
Baviskar Hartle Whitney - IJSE 2007
Essential Criteria to Characterize Constructivist Teaching: Derived from a review of the literature and applied to five constructivist-teaching method articles
International Journal of Science Education
Sandhya N. Baviskar; R. Todd Hartle; Tiffany Whitney
Idaho State University, USA
First Published on: 18 December 2007
Constructivism is an important theory of learning that is used to guide the development of new teaching methods, particularly in science education. However, because it is a theory of learning and not of teaching, constructivism is often either misused or misunderstood. Here we describe the four essential features of constructivism: eliciting prior knowledge, creating cognitive dissonance, application of new knowledge with feedback, and reflection on learning. We then use the criteria we developed to evaluate five representative published articles that claim to describe and test constructivist teaching methods. Of these five articles, we demonstrate that three do not adhere to the constructivist criteria, whereas two provide strong examples of how constructivism can be employed as a teaching method. We suggest that application of the four essential criteria will be a useful tool for all professional educators who plan to implement or evaluate constructivist teaching methods.
DOI: 10.1080/09500690701731121
International Journal of Science Education
Sandhya N. Baviskar; R. Todd Hartle; Tiffany Whitney
Idaho State University, USA
First Published on: 18 December 2007
Constructivism is an important theory of learning that is used to guide the development of new teaching methods, particularly in science education. However, because it is a theory of learning and not of teaching, constructivism is often either misused or misunderstood. Here we describe the four essential features of constructivism: eliciting prior knowledge, creating cognitive dissonance, application of new knowledge with feedback, and reflection on learning. We then use the criteria we developed to evaluate five representative published articles that claim to describe and test constructivist teaching methods. Of these five articles, we demonstrate that three do not adhere to the constructivist criteria, whereas two provide strong examples of how constructivism can be employed as a teaching method. We suggest that application of the four essential criteria will be a useful tool for all professional educators who plan to implement or evaluate constructivist teaching methods.
DOI: 10.1080/09500690701731121
2007-12-17
Hamza Wickman - Science Education 2008
Describing and analyzing learning in action: An empirical study of the importance of misconceptions in learning science
Sci Ed 92:141-164, 2008
Karim M. Hamza *, Per-Olof Wickman
Department of Curriculum Studies and Communication, Stockholm Institute of Education, SE-100 26 Stockholm, Sweden
email: Karim M. Hamza (karim.hamza@lhs.se)
*Correspondence to Karim M. Hamza, Department of Curriculum Studies and Communication, Stockholm Institute of Education, SE-100 26 Stockholm, Sweden
This study is part of the project How Can Teachers Aid Students Towards Scientific Reasoning funded by the Swedish Research Council.
Although misconceptions in science have been established in interview studies, their role during the learning process is poorly examined. In this paper, we use results from a classroom study to analyze to what extent nonscientific ideas in electrochemistry that students report in interviews enter into their learning in a more authentic setting. We audio-recorded talk between eight pairs of Swedish upper secondary students during a practical on electrochemical cells. Learning was operationalized on a discursive level as a description of what students do and say when taking part in an activity. This enabled an analysis of how encounters with misconceptions influenced the development of students' reasoning, compared to other encounters during the learning experience. Misconceptions did not constrain the development of students' reasoning. Rather, their reasoning developed in response to the contingencies of the specific situation. When misconceptions were encountered, they appeared as alternatives and questions not actively defended. Sometimes, encounters with these misconceptions were generative of the students' reasoning. The results indicate that demonstrating misconceptions in interviews is not enough to assume that they interfere with learning in other contexts. Educational implications and future lines of research based on these findings and on the methodology applied are discussed. © 2007 Wiley Periodicals, Inc.
Received: 28 November 2006; Revised: 2 July 2007; Accepted: 2 July 2007
DOI: 10.1002/sce.20233
Sci Ed 92:141-164, 2008
Karim M. Hamza *, Per-Olof Wickman
Department of Curriculum Studies and Communication, Stockholm Institute of Education, SE-100 26 Stockholm, Sweden
email: Karim M. Hamza (karim.hamza@lhs.se)
*Correspondence to Karim M. Hamza, Department of Curriculum Studies and Communication, Stockholm Institute of Education, SE-100 26 Stockholm, Sweden
This study is part of the project How Can Teachers Aid Students Towards Scientific Reasoning funded by the Swedish Research Council.
Although misconceptions in science have been established in interview studies, their role during the learning process is poorly examined. In this paper, we use results from a classroom study to analyze to what extent nonscientific ideas in electrochemistry that students report in interviews enter into their learning in a more authentic setting. We audio-recorded talk between eight pairs of Swedish upper secondary students during a practical on electrochemical cells. Learning was operationalized on a discursive level as a description of what students do and say when taking part in an activity. This enabled an analysis of how encounters with misconceptions influenced the development of students' reasoning, compared to other encounters during the learning experience. Misconceptions did not constrain the development of students' reasoning. Rather, their reasoning developed in response to the contingencies of the specific situation. When misconceptions were encountered, they appeared as alternatives and questions not actively defended. Sometimes, encounters with these misconceptions were generative of the students' reasoning. The results indicate that demonstrating misconceptions in interviews is not enough to assume that they interfere with learning in other contexts. Educational implications and future lines of research based on these findings and on the methodology applied are discussed. © 2007 Wiley Periodicals, Inc.
Received: 28 November 2006; Revised: 2 July 2007; Accepted: 2 July 2007
DOI: 10.1002/sce.20233
Roth Tobin Ritchie - Science Education 2008
Time and temporality as mediators of science learning
Wolff-Michael Roth 1 *, Kenneth Tobin 2, Stephen M. Ritchie 3
1Applied Cognitive Science, University of Victoria, Victoria, BC V8W 3N4, Canada
2Urban Education, Graduate Center, City University of New York, New York, NY 10016-4309, USA
3Mathematics, Science, and Technology Education, Queensland University of Technology, Kelvin Grove, Q'ld 4059, Australia
email: Wolff-Michael Roth (mroth@uvic.ca)
*Correspondence to Wolff-Michael Roth, Applied Cognitive Science, University of Victoria, Victoria, BC V8W 3N4, Canada
Few studies have focused on understanding how teaching and learning in classrooms are mediated by other dimensions of the organizational systems of which education is an integral part. Our 7-year ethnographic study of an urban high school shows how time and temporality constitute key practical and theoretical resources to the actors in the cultural organization of schools, a product of transactions involving individuals and artifacts that traverse multiple cultural fields, each with its own distinctive structures. © 2007 Wiley Periodicals, Inc. Sci Ed 92:115-140, 2008
Received: 6 May 2007; Revised: 17 July 2007; Accepted: 18 July 2007
DOI: 10.1002/sce.20238
Wolff-Michael Roth 1 *, Kenneth Tobin 2, Stephen M. Ritchie 3
1Applied Cognitive Science, University of Victoria, Victoria, BC V8W 3N4, Canada
2Urban Education, Graduate Center, City University of New York, New York, NY 10016-4309, USA
3Mathematics, Science, and Technology Education, Queensland University of Technology, Kelvin Grove, Q'ld 4059, Australia
email: Wolff-Michael Roth (mroth@uvic.ca)
*Correspondence to Wolff-Michael Roth, Applied Cognitive Science, University of Victoria, Victoria, BC V8W 3N4, Canada
Few studies have focused on understanding how teaching and learning in classrooms are mediated by other dimensions of the organizational systems of which education is an integral part. Our 7-year ethnographic study of an urban high school shows how time and temporality constitute key practical and theoretical resources to the actors in the cultural organization of schools, a product of transactions involving individuals and artifacts that traverse multiple cultural fields, each with its own distinctive structures. © 2007 Wiley Periodicals, Inc. Sci Ed 92:115-140, 2008
Received: 6 May 2007; Revised: 17 July 2007; Accepted: 18 July 2007
DOI: 10.1002/sce.20238
Robinett - arxiv.org 2007
Using Physics to Learn Mathematica to Do Physics: From Homework Problems
to Research Examples
arxiv.org
R. W. Robinett
arXiv:0712.2358
Fri, 14 Dec 2007 14:22:39 GMT (182kb)
We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard introductory and intermediate level Physics homework-style problems are used to teach Mathematica commands and programming methods, which are then applied, in turn, to more sophisticated problems in some of the core undergraduate subjects, along with making contact with recent research papers in a variety of fields.
(this paper doesn't seem to be PER, but Robinett is the co-author of the QMVI, and this paper can be filtered through the perspectives provided by Bing and Redish - arxiv.org 2007.)
to Research Examples
arxiv.org
R. W. Robinett
arXiv:0712.2358
Fri, 14 Dec 2007 14:22:39 GMT (182kb)
We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard introductory and intermediate level Physics homework-style problems are used to teach Mathematica commands and programming methods, which are then applied, in turn, to more sophisticated problems in some of the core undergraduate subjects, along with making contact with recent research papers in a variety of fields.
(this paper doesn't seem to be PER, but Robinett is the co-author of the QMVI, and this paper can be filtered through the perspectives provided by Bing and Redish - arxiv.org 2007.)
2007-12-12
Henderson Yerushalmi Kuo Heller Heller - Phys Rev 2007
Physics faculty beliefs and values about the teaching and learning of problem solving. II. Procedures for measurement and analysis
Charles Henderson *
Western Michigan University, Kalamazoo, Michigan 49008, USA
Edit Yerushalmi *
Weizmann Institute of Science, Rehovot, Israel, 76100
Vince H. Kuo †, Kenneth Heller, and Patricia Heller
University of Minnesota, Minneapolis, Minnesota 55455, USA
Physical Review Special Topics Physics Education Research
Received 28 October 2005; published 12 December 2007
To identify and describe the basis upon which instructors make curricular and pedagogical decisions, we have developed an artifact-based interview and an analysis technique based on multilayered concept maps. The policy capturing technique used in the interview asks instructors to make judgments about concrete instructional artifacts similar to those they likely encounter in their teaching environment. The analysis procedure alternatively employs both an a priori systems view analysis and an emergent categorization to construct a multilayered concept map, which is a hierarchically arranged set of concept maps where child maps include more details than parent maps. Although our goal was to develop a model of physics faculty beliefs about the teaching and learning of problem solving in the context of an introductory calculus-based physics course, the techniques described here are applicable to a variety of situations in which instructors make decisions that influence teaching and learning.
©2007 The American Physical Society
URL: http://link.aps.org/abstract/PRSTPER/v3/e020110
DOI: 10.1103/PhysRevSTPER.3.020110
PACS: 01.40.Fk, 01.40.G−, 01.40.J−, 01.50.Kw
* Previously at School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA.
† Present address: Department of Physics: Colorado School of Mines, Golden, CO, 80401, USA.
Charles Henderson *
Western Michigan University, Kalamazoo, Michigan 49008, USA
Edit Yerushalmi *
Weizmann Institute of Science, Rehovot, Israel, 76100
Vince H. Kuo †, Kenneth Heller, and Patricia Heller
University of Minnesota, Minneapolis, Minnesota 55455, USA
Physical Review Special Topics Physics Education Research
Received 28 October 2005; published 12 December 2007
To identify and describe the basis upon which instructors make curricular and pedagogical decisions, we have developed an artifact-based interview and an analysis technique based on multilayered concept maps. The policy capturing technique used in the interview asks instructors to make judgments about concrete instructional artifacts similar to those they likely encounter in their teaching environment. The analysis procedure alternatively employs both an a priori systems view analysis and an emergent categorization to construct a multilayered concept map, which is a hierarchically arranged set of concept maps where child maps include more details than parent maps. Although our goal was to develop a model of physics faculty beliefs about the teaching and learning of problem solving in the context of an introductory calculus-based physics course, the techniques described here are applicable to a variety of situations in which instructors make decisions that influence teaching and learning.
©2007 The American Physical Society
URL: http://link.aps.org/abstract/PRSTPER/v3/e020110
DOI: 10.1103/PhysRevSTPER.3.020110
PACS: 01.40.Fk, 01.40.G−, 01.40.J−, 01.50.Kw
* Previously at School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA.
† Present address: Department of Physics: Colorado School of Mines, Golden, CO, 80401, USA.
Yerushalmi Hendersen Heller Heller Kuo - Phys Rev 2007
Physics faculty beliefs and values about the teaching and learning of problem solving. I. Mapping the common core
E. Yerushalmi *
Weizmann Institute of Science, Rehovot, Israel, 76100
C. Henderson *
Department of Physics, Western Michigan University, Kalamazoo, Michigan 49008, USA
K. Heller, P. Heller, and V. Kuo †
School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
Physical Review Special Topics Physics Education Research
Received 28 October 2005; published 12 December 2007
In higher education, instructors’ choices of both curricular material and pedagogy are determined by their beliefs about learning and teaching, the values of their profession, and perceived external constraints. Dissemination of research-based educational reforms is based on assumptions about that mental structure. This study reports the initial phase of an investigation of the beliefs and values of physics professors as they relate to the teaching and learning of problem solving in introductory physics. Based on an analysis of a series of structured interviews with six college physics faculty, a model of a common structure of such beliefs for all physics faculty teaching introductory physics was constructed. This preliminary model, when tested and modified by future research, can be used by curriculum developers to design materials, pedagogy, and professional development that gain acceptance among instructors.
©2007 The American Physical Society
URL: http://link.aps.org/abstract/PRSTPER/v3/e020109
DOI: 10.1103/PhysRevSTPER.3.020109
PACS: 01.40.Fk, 01.40.G−, 01.40.J−, 01.50.Kw
* Previously at School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA.
† Present address: Department of Physics, Colorado School of Mines, Golden, CO, 80401, USA.
E. Yerushalmi *
Weizmann Institute of Science, Rehovot, Israel, 76100
C. Henderson *
Department of Physics, Western Michigan University, Kalamazoo, Michigan 49008, USA
K. Heller, P. Heller, and V. Kuo †
School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
Physical Review Special Topics Physics Education Research
Received 28 October 2005; published 12 December 2007
In higher education, instructors’ choices of both curricular material and pedagogy are determined by their beliefs about learning and teaching, the values of their profession, and perceived external constraints. Dissemination of research-based educational reforms is based on assumptions about that mental structure. This study reports the initial phase of an investigation of the beliefs and values of physics professors as they relate to the teaching and learning of problem solving in introductory physics. Based on an analysis of a series of structured interviews with six college physics faculty, a model of a common structure of such beliefs for all physics faculty teaching introductory physics was constructed. This preliminary model, when tested and modified by future research, can be used by curriculum developers to design materials, pedagogy, and professional development that gain acceptance among instructors.
©2007 The American Physical Society
URL: http://link.aps.org/abstract/PRSTPER/v3/e020109
DOI: 10.1103/PhysRevSTPER.3.020109
PACS: 01.40.Fk, 01.40.G−, 01.40.J−, 01.50.Kw
* Previously at School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA.
† Present address: Department of Physics, Colorado School of Mines, Golden, CO, 80401, USA.
Walsh Howard Bowe - Phys Rev 2007
Phenomenographic study of students’ problem solving approaches in physics
Laura N. Walsh, Robert G. Howard, and Brian Bowe
Physics Education Research Group, School of Physics, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland
Physical Review Special Topics Physics Education Research
Received 28 February 2007; published 12 December 2007
This paper describes ongoing research investigating student approaches to quantitative and qualitative problem solving in physics. This empirical study was conducted using a phenomenographic approach to analyze data from individual semistructured problem solving interviews with 22 introductory college physics students. The main result of the study is a hierarchical set of categories that describe the students’ problem solving approaches in the context of introductory physics.
©2007 The American Physical Society
URL: http://link.aps.org/abstract/PRSTPER/v3/e020108
DOI: 10.1103/PhysRevSTPER.3.020108
PACS: 01.40.Fk
(Laura Walsh flew in from Ireland to attend the 2005 Foundations and Frontiers of Physics Education Research meeting, for those who might recognize the name...)
Laura N. Walsh, Robert G. Howard, and Brian Bowe
Physics Education Research Group, School of Physics, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland
Physical Review Special Topics Physics Education Research
Received 28 February 2007; published 12 December 2007
This paper describes ongoing research investigating student approaches to quantitative and qualitative problem solving in physics. This empirical study was conducted using a phenomenographic approach to analyze data from individual semistructured problem solving interviews with 22 introductory college physics students. The main result of the study is a hierarchical set of categories that describe the students’ problem solving approaches in the context of introductory physics.
©2007 The American Physical Society
URL: http://link.aps.org/abstract/PRSTPER/v3/e020108
DOI: 10.1103/PhysRevSTPER.3.020108
PACS: 01.40.Fk
(Laura Walsh flew in from Ireland to attend the 2005 Foundations and Frontiers of Physics Education Research meeting, for those who might recognize the name...)
2007-12-10
Bing Redish - arxiv.org 2007
Symbolic Manipulators Affect Mathematical Mindsets
Thomas J. Bing and Edward F. Redish
arXiv:0712.1187
Date: Fri, 7 Dec 2007 16:57:24 GMT (202kb)
Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely offer a convenient way to perform the computations students would have otherwise wanted to do by hand. This paper presents examples from the work of upper level physics majors where Mathematica plays an active role in focusing and sustaining their thought around calculation. These students still engage in powerful mathematical reasoning while they calculate but struggle because of the narrowed breadth of their thinking. Their reasoning is drawn into local attractors where they look to calculation schemes to resolve questions instead of, for example, mapping the mathematics to the physical system at hand. We model the influence of Mathematica as an integral part of the constant feedback that occurs in how students frame, and hence focus, their work.
Thomas J. Bing and Edward F. Redish
arXiv:0712.1187
Date: Fri, 7 Dec 2007 16:57:24 GMT (202kb)
Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely offer a convenient way to perform the computations students would have otherwise wanted to do by hand. This paper presents examples from the work of upper level physics majors where Mathematica plays an active role in focusing and sustaining their thought around calculation. These students still engage in powerful mathematical reasoning while they calculate but struggle because of the narrowed breadth of their thinking. Their reasoning is drawn into local attractors where they look to calculation schemes to resolve questions instead of, for example, mapping the mathematics to the physical system at hand. We model the influence of Mathematica as an integral part of the constant feedback that occurs in how students frame, and hence focus, their work.
2007-12-04
Scherr Hammer - arxiv.org 2007
Student Behavior and Epistemological Framing: Examples from Collaborative Active-Learning Activities in Physics
Rachel E. Scherr and David Hammer
arXiv:0712.0211
Date: Mon, 3 Dec 2007 03:25:00 GMT
Questions of participant understanding of the nature of an activity have been addressed in anthropology and sociolinguistics with the concepts of frames and framing. For example, a student may frame a learning activity as an opportunity for sensemaking or as an assignment to fill out a worksheet. The student's understanding of the nature of the activity affects what she notices, what knowledge she accesses, and how she thinks to act. Previous analyses have found evidence of framing primarily in linguistic markers associated with speech acts. In this paper, we show that there is useful evidence of framing in easily observed features of students' behavior. We apply this observational methodology to explore dynamics among behavior, framing, and the conceptual substance of student reasoning in the context of collaborative active-learning activities in an introductory university physics course.
(This paper has been submitted to Cognition and Instruction, the arxiv.org posting is of the preprint draft.)
Rachel E. Scherr and David Hammer
arXiv:0712.0211
Date: Mon, 3 Dec 2007 03:25:00 GMT
Questions of participant understanding of the nature of an activity have been addressed in anthropology and sociolinguistics with the concepts of frames and framing. For example, a student may frame a learning activity as an opportunity for sensemaking or as an assignment to fill out a worksheet. The student's understanding of the nature of the activity affects what she notices, what knowledge she accesses, and how she thinks to act. Previous analyses have found evidence of framing primarily in linguistic markers associated with speech acts. In this paper, we show that there is useful evidence of framing in easily observed features of students' behavior. We apply this observational methodology to explore dynamics among behavior, framing, and the conceptual substance of student reasoning in the context of collaborative active-learning activities in an introductory university physics course.
(This paper has been submitted to Cognition and Instruction, the arxiv.org posting is of the preprint draft.)
Scherr - arxiv.org 2007
UPDATED: 2008 Jan 27: The final version of this paper (with all video attached) was published in the Physical Reviews. More information at Scherr - Phys Rev 2008.
Gesture analysis for physics education researchers
Rachel E. Scherr
arXiv:0712.0581
Date: Tue, 4 Dec 2007 18:07:46 GMT (544kb)
Systematic observations of student gestures can not only fill in gaps in students' verbal expressions, but can also offer valuable information about student ideas, including their source, their novelty to the speaker, and their construction in real time. This paper provides a review of the research in gesture analysis that is most relevant to physics education researchers and illustrates gesture analysis for the purpose of better understanding student thinking about physics.
This paper has been accepted in the Physical Review Special Topics - Physics Education Research, and is published here in its preprint draft version.
Gesture analysis for physics education researchers
Rachel E. Scherr
arXiv:0712.0581
Date: Tue, 4 Dec 2007 18:07:46 GMT (544kb)
Systematic observations of student gestures can not only fill in gaps in students' verbal expressions, but can also offer valuable information about student ideas, including their source, their novelty to the speaker, and their construction in real time. This paper provides a review of the research in gesture analysis that is most relevant to physics education researchers and illustrates gesture analysis for the purpose of better understanding student thinking about physics.
This paper has been accepted in the Physical Review Special Topics - Physics Education Research, and is published here in its preprint draft version.
2007-12-03
Springuel Wittmann Thompson - Phys Rev 2007
Applying clustering to statistical analysis of student reasoning about two-dimensional kinematics
R. Padraic Springuel, Michael C. Wittmann, and John R. Thompson
Department of Physics and Astronomy, Center for Science and Mathematics Education Research, College of Education and Human Development, University of Maine, Orono, Maine 04469, USA
Received 24 May 2007; published 3 December 2007
We use clustering, an analysis method not presently common to the physics education research community, to group and characterize student responses to written questions about two-dimensional kinematics. Previously, clustering has been used to analyze multiple-choice data; we analyze free-response data that includes both sketches of vectors and written elements. The primary goal of this paper is to describe the methodology itself; we include a brief overview of relevant results.
©2007 The American Physical Society
URL: http://link.aps.org/abstract/PRSTPER/v3/e020107
DOI: 10.1103/PhysRevSTPER.3.020107
PACS: 01.40.Fk, 01.40.gf
R. Padraic Springuel, Michael C. Wittmann, and John R. Thompson
Department of Physics and Astronomy, Center for Science and Mathematics Education Research, College of Education and Human Development, University of Maine, Orono, Maine 04469, USA
Received 24 May 2007; published 3 December 2007
We use clustering, an analysis method not presently common to the physics education research community, to group and characterize student responses to written questions about two-dimensional kinematics. Previously, clustering has been used to analyze multiple-choice data; we analyze free-response data that includes both sketches of vectors and written elements. The primary goal of this paper is to describe the methodology itself; we include a brief overview of relevant results.
©2007 The American Physical Society
URL: http://link.aps.org/abstract/PRSTPER/v3/e020107
DOI: 10.1103/PhysRevSTPER.3.020107
PACS: 01.40.Fk, 01.40.gf
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