Understanding the use of two integration methods on separable first order differential equations
arXiv:0902.0748, submitted to Physical Review Special Topics - Physics Education Research
Katrina E. Black, Michael C. Wittmann
We present evidence from three student interactions in which two types of common solution methods for solving simple first-order differential equations are used. We describe these using the language of resources, considering epistemic games as particular pathways of solutions along resource graphs containing linked procedural and conceptual resources. Using transcript data, we define several procedural resources, show how they can be organized into two facets of a previously described epistemic game, and produce a resource graph that allows visualization of this portion of the epistemic games. By representing two correct mathematical procedures in terms of shared resources, we help clarify the types of thinking in which students engage when learning to apply mathematical reasoning to physics and illustrate how a "failure to connect" two ideas often hinders students' successful problem solving.
Showing posts with label Wittmann. Show all posts
Showing posts with label Wittmann. Show all posts
2009-02-04
2009-02-02
Hayes Wittmann - arxiv.org 2009
The role of sign in students' modeling of scalar equations
arXiv:0901.4912v1 [physics.ed-ph], to be published in The Physics Teacher
Kate Hayes, Michael C. Wittmann
We describe students revising the mathematical form of physics equations to match the physical situation they are describing, even though their revision violates physical laws. In an unfamiliar air resistance problem, a majority of students in a sophomore level mechanics class at some point wrote Newton's Second Law as F = -ma; they were using this form to ensure that the sign of the force pointed in a direction consistent with the chosen coordinate system while assuming that some variables have only positive value. We use one student's detailed explanation to suggest that students' issues with variables are context-dependent, and that much of their reasoning is useful for productive instruction.
arXiv:0901.4912v1 [physics.ed-ph], to be published in The Physics Teacher
Kate Hayes, Michael C. Wittmann
We describe students revising the mathematical form of physics equations to match the physical situation they are describing, even though their revision violates physical laws. In an unfamiliar air resistance problem, a majority of students in a sophomore level mechanics class at some point wrote Newton's Second Law as F = -ma; they were using this form to ensure that the sign of the force pointed in a direction consistent with the chosen coordinate system while assuming that some variables have only positive value. We use one student's detailed explanation to suggest that students' issues with variables are context-dependent, and that much of their reasoning is useful for productive instruction.
2008-12-17
Black Wittmann - arxiv.org 2008
Visualizing changes in student responses using consistency plots
arxiv.org (Submitted on 16 Dec 2008)
Katrina E. Black, Michael C. Wittmann
Traditional methods of reporting changes in student responses have focused on class-wide averages. Such models hide information about the switches in responses by individual students over the course of a semester. We extend unpublished work by Steven Kanim on "escalator diagrams" which show changes in student responses from correct to incorrect (and vice versa) while representing pre- and post-instruction results on questions. Our extension consists of "consistency plots" in which we represent three forms of data: method of solution and correctness of solution both before and after instruction. Our data are from an intermediate mechanics class, and come from (nearly) identical midterm and final examination questions.
(This paper has been submitted to PRST-PER, and this link will be replaced if and when the paper is accepted and published. The new page will contain a link to the original arxiv.org submission at that time.)
arxiv.org (Submitted on 16 Dec 2008)
Katrina E. Black, Michael C. Wittmann
Traditional methods of reporting changes in student responses have focused on class-wide averages. Such models hide information about the switches in responses by individual students over the course of a semester. We extend unpublished work by Steven Kanim on "escalator diagrams" which show changes in student responses from correct to incorrect (and vice versa) while representing pre- and post-instruction results on questions. Our extension consists of "consistency plots" in which we represent three forms of data: method of solution and correctness of solution both before and after instruction. Our data are from an intermediate mechanics class, and come from (nearly) identical midterm and final examination questions.
(This paper has been submitted to PRST-PER, and this link will be replaced if and when the paper is accepted and published. The new page will contain a link to the original arxiv.org submission at that time.)
2008-11-12
Sayre Wittmann - PRST-PER 2008
Plasticity of intermediate mechanics students’ coordinate system choice
Phys. Rev. ST Phys. Educ. Res. 4, 020105 (2008)
Eleanor C. Sayre, Michael C. Wittmann
We investigate the interplay between mathematics and physics resources in intermediate mechanics students. In the mechanics course, the selection and application of coordinate systems is a consistent thread. At the University of Maine, students often start the course with a strong preference to use Cartesian coordinates, in accordance with their prior physics and mathematics classes. In small-group interviews and in homework help sessions, we ask students to define a coordinate system and set up the equations of motion for a simple pendulum for which polar coordinates are more appropriate. We analyze video data from several encounters using a combination of Process/Object theory and Resource Theory. We find that students sometimes persist in using an inappropriate Cartesian system. Furthermore, students often derive (rather than recall) the details of the polar coordinate system, indicating that their knowledge is far from solid. To describe our work more precisely, we define a scale of plasticity and several heuristics for defining resources and their plasticity.
Phys. Rev. ST Phys. Educ. Res. 4, 020105 (2008)
Eleanor C. Sayre, Michael C. Wittmann
We investigate the interplay between mathematics and physics resources in intermediate mechanics students. In the mechanics course, the selection and application of coordinate systems is a consistent thread. At the University of Maine, students often start the course with a strong preference to use Cartesian coordinates, in accordance with their prior physics and mathematics classes. In small-group interviews and in homework help sessions, we ask students to define a coordinate system and set up the equations of motion for a simple pendulum for which polar coordinates are more appropriate. We analyze video data from several encounters using a combination of Process/Object theory and Resource Theory. We find that students sometimes persist in using an inappropriate Cartesian system. Furthermore, students often derive (rather than recall) the details of the polar coordinate system, indicating that their knowledge is far from solid. To describe our work more precisely, we define a scale of plasticity and several heuristics for defining resources and their plasticity.
2008-09-10
Smith Wittmann - PRST-PER 2008
Applying a resources framework to analysis of the Force and Motion Conceptual Evaluation
Phys. Rev. ST Phys. Educ. Res. 4, 020101 (2008) [12 pages]
Trevor I. Smith and Michael C. Wittmann
We suggest one redefinition of common clusters of questions used to analyze student responses on the Force and Motion Conceptual Evaluation. Our goal is to propose a methodology that moves beyond an analysis of student learning defined by correct responses, either on the overall test or on clusters of questions defined solely by content. We use the resources framework theory of learning to define clusters within this experimental test that was designed without the resources framework in mind. We take special note of the contextual and representational dependence of questions with seemingly similar physics content. We analyze clusters in ways that allow the most common incorrect answers to give as much, or more, information as the correctness of responses in that cluster. We show that false positives can be found, especially on questions dealing with Newton’s third law. We apply our clustering to a small set of data to illustrate the value of comparing students’ incorrect responses which are otherwise identical on a correct or incorrect analysis. Our work provides a connection between theory and experiment in the area of survey design and the resources framework.
Phys. Rev. ST Phys. Educ. Res. 4, 020101 (2008) [12 pages]
Trevor I. Smith and Michael C. Wittmann
We suggest one redefinition of common clusters of questions used to analyze student responses on the Force and Motion Conceptual Evaluation. Our goal is to propose a methodology that moves beyond an analysis of student learning defined by correct responses, either on the overall test or on clusters of questions defined solely by content. We use the resources framework theory of learning to define clusters within this experimental test that was designed without the resources framework in mind. We take special note of the contextual and representational dependence of questions with seemingly similar physics content. We analyze clusters in ways that allow the most common incorrect answers to give as much, or more, information as the correctness of responses in that cluster. We show that false positives can be found, especially on questions dealing with Newton’s third law. We apply our clustering to a small set of data to illustrate the value of comparing students’ incorrect responses which are otherwise identical on a correct or incorrect analysis. Our work provides a connection between theory and experiment in the area of survey design and the resources framework.
2008-06-11
Wittmann Thompson - AJP 2008
Integrated approaches in physics education: A graduate level course in physics, pedagogy, and education research
American Journal of Physics, Volume 76, Number 7 (July 2008), pp. 677-683
Michael C. Wittmann, John R. Thompson
We describe a course designed to help future educators develop an integrated understanding of different elements of physics education research (PER), including research into student learning, content knowledge from the perspective of how it is learned, and reform-based curricula, together with evidence of their effectiveness. Course elements include equal parts of physics study through proven curricula and discussion of research results in the context of the PER literature. We provide examples of the course content and structure and representative examples of student learning in the class.
American Journal of Physics, Volume 76, Number 7 (July 2008), pp. 677-683
Michael C. Wittmann, John R. Thompson
We describe a course designed to help future educators develop an integrated understanding of different elements of physics education research (PER), including research into student learning, content knowledge from the perspective of how it is learned, and reform-based curricula, together with evidence of their effectiveness. Course elements include equal parts of physics study through proven curricula and discussion of research results in the context of the PER literature. We provide examples of the course content and structure and representative examples of student learning in the class.
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
2007-11-13
Smith Wittmann - arxiv.org 2007
Toward a more effective use of the Force and Motion Conceptual Evaluation
Trevor I. Smith, Michael C. Wittmann
contact: Trevor.I.Smith@umit.maine.edu and wittmann@umit.maine.edu
(Submitted on 12 Nov 2007)
We suggest one redefinition of common clusters of questions used to analyze student responses on the Force and Motion Conceptual Evaluation (FMCE). Our goal is to move beyond the expert/novice analysis of student learning based on pre-/post-testing and the correctness of responses (either on the overall test or on clusters of questions defined solely by content). We base our work in resource theory, taking special note of the context dependence of questions with seemingly similar physics content. We analyze clusters in ways that allow the most common incorrect answers to give as much, or more, information as the correctness of responses in that cluster. Using this dichotomy of correct and most common incorrect models (in clusters defined by common models) we can apply Model Analysis to help better map a class's thinking about the physics on the FMCE. We give one example of such an analysis as a proof-of-concept of our approach.
Comments: 13 pages, 7 figures, submitted to Phys. Rev. ST Phys. Educ. Res
Subjects: Physics Education (physics.ed-ph)
Cite as: arXiv:0711.1838v1 [physics.ed-ph]
Submission history
[v1] Mon, 12 Nov 2007 18:11:32 GMT (250kb,D)
Trevor I. Smith, Michael C. Wittmann
contact: Trevor.I.Smith@umit.maine.edu and wittmann@umit.maine.edu
(Submitted on 12 Nov 2007)
We suggest one redefinition of common clusters of questions used to analyze student responses on the Force and Motion Conceptual Evaluation (FMCE). Our goal is to move beyond the expert/novice analysis of student learning based on pre-/post-testing and the correctness of responses (either on the overall test or on clusters of questions defined solely by content). We base our work in resource theory, taking special note of the context dependence of questions with seemingly similar physics content. We analyze clusters in ways that allow the most common incorrect answers to give as much, or more, information as the correctness of responses in that cluster. Using this dichotomy of correct and most common incorrect models (in clusters defined by common models) we can apply Model Analysis to help better map a class's thinking about the physics on the FMCE. We give one example of such an analysis as a proof-of-concept of our approach.
Comments: 13 pages, 7 figures, submitted to Phys. Rev. ST Phys. Educ. Res
Subjects: Physics Education (physics.ed-ph)
Cite as: arXiv:0711.1838v1 [physics.ed-ph]
Submission history
[v1] Mon, 12 Nov 2007 18:11:32 GMT (250kb,D)
2007-10-30
Smith and Wittmann - Phys Rev 2007
From the Physical Review - Special Topics Physics Education Research:
Comparing three methods for teaching Newton’s third law
Phys. Rev. ST Phys. Educ. Res. 3, 020105 (2007)
Trevor I. Smith and Michael C. Wittmann
Department of Physics and Astronomy, College of Education and Human Development, Center for Science and Mathematics Education Research, University of Maine, Orono, Maine 04469, USA
Received 20 April 2006; revised 11 December 2006; published 18 October 2007
Although guided-inquiry methods for teaching introductory physics have been individually shown to be more effective at improving conceptual understanding than traditional lecture-style instruction, researchers in physics education have not studied differences among reform-based curricula in much detail. Several researchers have developed University of Washington–style tutorial materials, but the different curricula have not been compared against each other. Our study examines three tutorials designed to improve student understanding of Newton’s third law: the University of Washington’s Tutorials in Introductory Physics (TIP), the University of Maryland’s Activity-Based Tutorials (ABT), and the Open Source Tutorials (OST) also developed at the University of Maryland. Each tutorial was designed with different goals and agendas, and each employs different methods to help students understand the physics. We analyzed pretest and post-test data, including course examinations and data from the Force and Motion Conceptual Evaluation (FMCE). Using both FMCE and course data, we find that students using the OST version of the tutorial perform better than students using either of the other two.
©2007 The American Physical Society
URL: http://link.aps.org/abstract/PRSTPER/v3/e020105
DOI: 10.1103/PhysRevSTPER.3.020105
PACS: 01.40.Fk, 01.40.G−, 01.40.gb
Comparing three methods for teaching Newton’s third law
Phys. Rev. ST Phys. Educ. Res. 3, 020105 (2007)
Trevor I. Smith and Michael C. Wittmann
Department of Physics and Astronomy, College of Education and Human Development, Center for Science and Mathematics Education Research, University of Maine, Orono, Maine 04469, USA
Received 20 April 2006; revised 11 December 2006; published 18 October 2007
Although guided-inquiry methods for teaching introductory physics have been individually shown to be more effective at improving conceptual understanding than traditional lecture-style instruction, researchers in physics education have not studied differences among reform-based curricula in much detail. Several researchers have developed University of Washington–style tutorial materials, but the different curricula have not been compared against each other. Our study examines three tutorials designed to improve student understanding of Newton’s third law: the University of Washington’s Tutorials in Introductory Physics (TIP), the University of Maryland’s Activity-Based Tutorials (ABT), and the Open Source Tutorials (OST) also developed at the University of Maryland. Each tutorial was designed with different goals and agendas, and each employs different methods to help students understand the physics. We analyzed pretest and post-test data, including course examinations and data from the Force and Motion Conceptual Evaluation (FMCE). Using both FMCE and course data, we find that students using the OST version of the tutorial perform better than students using either of the other two.
©2007 The American Physical Society
URL: http://link.aps.org/abstract/PRSTPER/v3/e020105
DOI: 10.1103/PhysRevSTPER.3.020105
PACS: 01.40.Fk, 01.40.G−, 01.40.gb
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