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 resources. Show all posts
Showing posts with label resources. Show all posts
2009-02-04
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.
2008-05-27
Taber - IJSE 2008
Conceptual Resources for Learning Science: Issues of transience and grain-size in cognition and cognitive structure
International Journal of Science Education, Volume 30, Number 8 (June 2008)
Keith Taber
Many studies into learners' ideas in science have reported that aspects of learners' thinking can be represented in terms of entities described in such terms as alternative conceptions or conceptual frameworks, which are considered to describe relatively stable aspects of conceptual knowledge that are represented in the learner's memory and accessed in certain contexts. Other researchers have suggested that learners' ideas elicited in research are often better understood as labile constructions formed in response to probes and generated from more elementary conceptual resources (e.g. phenomenological primitives or 'p-prims'). This 'knowledge-in-pieces perspective' (largely developed from studies of student thinking about physics topics), and the 'alternative conceptions perspective', suggests different pedagogic approaches. The present paper discusses issues raised by this area of work. Firstly, a model of cognition is considered within which the 'knowledge-in-pieces' and 'alternative conceptions' perspectives co-exist. Secondly, this model is explored in terms of whether such a synthesis could offer fruitful insights by considering some candidate p-prims from chemistry education. Finally, areas for developing testable predictions are outlined, to show how such a model can be a 'refutable variant' of a progressive research programme in learning science.
International Journal of Science Education, Volume 30, Number 8 (June 2008)
Keith Taber
Many studies into learners' ideas in science have reported that aspects of learners' thinking can be represented in terms of entities described in such terms as alternative conceptions or conceptual frameworks, which are considered to describe relatively stable aspects of conceptual knowledge that are represented in the learner's memory and accessed in certain contexts. Other researchers have suggested that learners' ideas elicited in research are often better understood as labile constructions formed in response to probes and generated from more elementary conceptual resources (e.g. phenomenological primitives or 'p-prims'). This 'knowledge-in-pieces perspective' (largely developed from studies of student thinking about physics topics), and the 'alternative conceptions perspective', suggests different pedagogic approaches. The present paper discusses issues raised by this area of work. Firstly, a model of cognition is considered within which the 'knowledge-in-pieces' and 'alternative conceptions' perspectives co-exist. Secondly, this model is explored in terms of whether such a synthesis could offer fruitful insights by considering some candidate p-prims from chemistry education. Finally, areas for developing testable predictions are outlined, to show how such a model can be a 'refutable variant' of a progressive research programme in learning science.
2008-05-13
Meredith Marrongelle - AJP 2008
How students use mathematical resources in an electrostatics context
American Journal of Physics -- June 2008 -- Volume 76, Issue 6, pp. 570-578
Dawn C. Meredith, Karen A. Marrongelle
We present evidence that although students' mathematical skills in introductory calculus-based physics classes may not be readily applied in physics contexts, these students have strong mathematical resources on which to build effective instruction. Our evidence is based on clinical interviews of problem solving in electrostatics, which are analyzed using the framework of Sherin's symbolic forms. We find that students use notions of “dependence” and “parts-of-a-whole” to successfully guide their work, even in novel situations. We also present evidence that students' naive conceptions of the limit may prevent them from viewing integrals as sums.
American Journal of Physics -- June 2008 -- Volume 76, Issue 6, pp. 570-578
Dawn C. Meredith, Karen A. Marrongelle
We present evidence that although students' mathematical skills in introductory calculus-based physics classes may not be readily applied in physics contexts, these students have strong mathematical resources on which to build effective instruction. Our evidence is based on clinical interviews of problem solving in electrostatics, which are analyzed using the framework of Sherin's symbolic forms. We find that students use notions of “dependence” and “parts-of-a-whole” to successfully guide their work, even in novel situations. We also present evidence that students' naive conceptions of the limit may prevent them from viewing integrals as sums.
2008-03-05
Gupta Redish Hammer - PERC 2007
Coordination of Mathematics and Physical Resources by Physics Graduate Students
arxiv.org and PERC 2007
Ayush Gupta, Edward F. Redish, and David Hammer
We investigate the dynamics of how graduate students coordinate their mathematics and physics knowledge within the context of solving a homework problem for a plasma physics survey course. Students were asked to obtain the complex dielectric function for a plasma with a specified distribution function and find the roots of that expression. While all the 16 participating students obtained the dielectric function correctly in one of two equivalent expressions, roughly half of them (7 of 16) failed to compute the roots correctly. All seven took the same initial step that led them to the incorrect answer. We note a perfect correlation between the specific expression of dielectric function obtained and the student's success in solving for the roots. We analyze student responses in terms of a resources framework and suggest routes for future research.
Journal-ref: 2007 Physics Education Research Conference. AIP Conference Proceedings, Volume 951, pp. 104-107 (2007)
DOI: 10.1063/1.2820906
arxiv.org and PERC 2007
Ayush Gupta, Edward F. Redish, and David Hammer
We investigate the dynamics of how graduate students coordinate their mathematics and physics knowledge within the context of solving a homework problem for a plasma physics survey course. Students were asked to obtain the complex dielectric function for a plasma with a specified distribution function and find the roots of that expression. While all the 16 participating students obtained the dielectric function correctly in one of two equivalent expressions, roughly half of them (7 of 16) failed to compute the roots correctly. All seven took the same initial step that led them to the incorrect answer. We note a perfect correlation between the specific expression of dielectric function obtained and the student's success in solving for the roots. We analyze student responses in terms of a resources framework and suggest routes for future research.
Journal-ref: 2007 Physics Education Research Conference. AIP Conference Proceedings, Volume 951, pp. 104-107 (2007)
DOI: 10.1063/1.2820906
Gupta Hammer Redish - arxiv.org 2008
The Case for Dynamic Models of Learners' Ontologies in Physics
arxiv.org
Ayush Gupta, David Hammer, and Edward F. Redish
Submitted to The Journal of the Learning Sciences on 02/28/2008
In a series of well-known papers, Chi and Slotta (Chi, 1992; Chi & Slotta, 1993; Chi, Slotta & de Leeuw, 1994; Slotta, Chi & Joram, 1995; Chi, 2005; Slotta & Chi, 2006) have contended that a reason for students' difficulties in learning physics is that they think about concepts as things rather than as processes, and that there is a significant barrier between these two ontological categories. We contest this view, arguing that expert and novice reasoning often and productively traverses ontological categories. We cite examples from everyday, classroom, and professional contexts to illustrate this. We agree with Chi and Slotta that instruction should attend to learners' ontologies; but we find these ontologies are better understood as dynamic and context-dependent, rather than as static constraints. To promote one ontological description in physics instruction, as suggested by Slotta and Chi, could undermine novices' access to productive cognitive resources they bring to their studies and inhibit their transition to the dynamic ontological flexibility required of experts.
arxiv.org
Ayush Gupta, David Hammer, and Edward F. Redish
Submitted to The Journal of the Learning Sciences on 02/28/2008
In a series of well-known papers, Chi and Slotta (Chi, 1992; Chi & Slotta, 1993; Chi, Slotta & de Leeuw, 1994; Slotta, Chi & Joram, 1995; Chi, 2005; Slotta & Chi, 2006) have contended that a reason for students' difficulties in learning physics is that they think about concepts as things rather than as processes, and that there is a significant barrier between these two ontological categories. We contest this view, arguing that expert and novice reasoning often and productively traverses ontological categories. We cite examples from everyday, classroom, and professional contexts to illustrate this. We agree with Chi and Slotta that instruction should attend to learners' ontologies; but we find these ontologies are better understood as dynamic and context-dependent, rather than as static constraints. To promote one ontological description in physics instruction, as suggested by Slotta and Chi, could undermine novices' access to productive cognitive resources they bring to their studies and inhibit their transition to the dynamic ontological flexibility required of experts.
2008-01-02
Linhares Brum - Cognitive Science 2007
Understanding Our Understanding of Strategic Scenarios: What Role Do Chunks Play?
Cognitive Science: A Multidisciplinary Journal
2007, Vol. 31, No. 6, Pages 989-1007
Alexandre Linhares and Paulo Brum
EBAPE/FGV, Rio de Janeiro, Brazil
There is a crucial debate concerning the nature of chess chunks: One current possibility states that chunks are built by encoding particular combinations of pieces-on-squares (POSs), and that chunks are formed mostly by "close" pieces (in a "Euclidean" sense). A complementary hypothesis is that chunks are encoded by abstract, semantic information. This article extends recent experiments and shows that chess players are able to perceive strong similarity between very different positions if the pieces retain the same abstract roles in both of them. This casts doubt on the idea that POS information is the key information encoded in chess chunks, and this article proposes, instead, that the key encoding involves the abstract roles that pieces (and sets of pieces) play–a theoretical standpoint in line with the research program in semantics that places analogy at the core of cognition.
(doi:10.1080/03640210701703725)
Cognitive Science: A Multidisciplinary Journal
2007, Vol. 31, No. 6, Pages 989-1007
Alexandre Linhares and Paulo Brum
EBAPE/FGV, Rio de Janeiro, Brazil
There is a crucial debate concerning the nature of chess chunks: One current possibility states that chunks are built by encoding particular combinations of pieces-on-squares (POSs), and that chunks are formed mostly by "close" pieces (in a "Euclidean" sense). A complementary hypothesis is that chunks are encoded by abstract, semantic information. This article extends recent experiments and shows that chess players are able to perceive strong similarity between very different positions if the pieces retain the same abstract roles in both of them. This casts doubt on the idea that POS information is the key information encoded in chess chunks, and this article proposes, instead, that the key encoding involves the abstract roles that pieces (and sets of pieces) play–a theoretical standpoint in line with the research program in semantics that places analogy at the core of cognition.
(doi:10.1080/03640210701703725)
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
Taber - IJSE 2007
Conceptual Resources for Learning Science: Issues of transience and grain-size in cognition and cognitive structure
International Journal of Science Education (1):1-27. (2008).
Keith Taber
Faculty of Education, University of Cambridge, UK
Abstract
Many studies into learners' ideas in science have reported that aspects of learners' thinking can be represented in terms of entities described in such terms as alternative conceptions or conceptual frameworks, which are considered to describe relatively stable aspects of conceptual knowledge that are represented in the learner's memory and accessed in certain contexts. Other researchers have suggested that learners' ideas elicited in research are often better understood as labile constructions formed in response to probes and generated from more elementary conceptual resources (e.g. phenomenological primitives or 'p-prims'). This 'knowledge-in-pieces perspective' (largely developed from studies of student thinking about physics topics), and the 'alternative conceptions perspective', suggests different pedagogic approaches. The present paper discusses issues raised by this area of work. Firstly, a model of cognition is considered within which the 'knowledge-in-pieces' and 'alternative conceptions' perspectives co-exist. Secondly, this model is explored in terms of whether such a synthesis could offer fruitful insights by considering some candidate p-prims from chemistry education. Finally, areas for developing testable predictions are outlined, to show how such a model can be a 'refutable variant' of a progressive research programme in learning science.
Extra information:
This paper cites David Hammer and Andrea diSessa a lot, building a connection between a p-prims/resources/knowledge-in-pieces approach (quotinga across the literature) and the alternative conceptions world (quoting mainly from the 80s literature, I feel). For those interested in a continuation of Hammer's 1996 papers on "p-prims vs. misconceptions" or Scherr's "Modeling Student Reasoning" papers, this is a good read.
International Journal of Science Education (1):1-27. (2008).
Keith Taber
Faculty of Education, University of Cambridge, UK
Abstract
Many studies into learners' ideas in science have reported that aspects of learners' thinking can be represented in terms of entities described in such terms as alternative conceptions or conceptual frameworks, which are considered to describe relatively stable aspects of conceptual knowledge that are represented in the learner's memory and accessed in certain contexts. Other researchers have suggested that learners' ideas elicited in research are often better understood as labile constructions formed in response to probes and generated from more elementary conceptual resources (e.g. phenomenological primitives or 'p-prims'). This 'knowledge-in-pieces perspective' (largely developed from studies of student thinking about physics topics), and the 'alternative conceptions perspective', suggests different pedagogic approaches. The present paper discusses issues raised by this area of work. Firstly, a model of cognition is considered within which the 'knowledge-in-pieces' and 'alternative conceptions' perspectives co-exist. Secondly, this model is explored in terms of whether such a synthesis could offer fruitful insights by considering some candidate p-prims from chemistry education. Finally, areas for developing testable predictions are outlined, to show how such a model can be a 'refutable variant' of a progressive research programme in learning science.
Extra information:
This paper cites David Hammer and Andrea diSessa a lot, building a connection between a p-prims/resources/knowledge-in-pieces approach (quotinga across the literature) and the alternative conceptions world (quoting mainly from the 80s literature, I feel). For those interested in a continuation of Hammer's 1996 papers on "p-prims vs. misconceptions" or Scherr's "Modeling Student Reasoning" papers, this is a good read.
Subscribe to:
Posts (Atom)