Student Behavior and Epistemological Framing: Examples from Collaborative Active-Learning Activities in Physics
Cognition and Instruction, Volume 27, Issue 2 April 2009 , pages 147 - 174
Rachel E. Scherr; David Hammer
The concept of framing from anthropology and sociolinguistics is useful for understanding student reasoning. 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 framing affects what she notices, what knowledge she accesses, and how she thinks to act. We find evidence of framing in easily observed features of students' collaborative 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. We find evidence that certain student behaviors indicate and support a relatively sophisticated epistemological framing of these activities, one in which students discuss the substance of the ideas at hand.
An earlier draft of this paper was posted previously.
Showing posts with label Cog. Instr.. Show all posts
Showing posts with label Cog. Instr.. Show all posts
2009-04-19
2009-01-15
Son Goldstone - C&I 2009
Contextualization in Perspective
Cognition and Instruction,27:1,51 — 89
Ji Y. Son; Robert L. Goldstone
Instruction abstracted from specific and concrete examples is frequently criticized for ignoring the context-dependent and perspectival nature of learning (e.g., Bruner, 1962, 1966; Greeno, 1997). Yet, in the effort to create personally interesting learning contexts, cognitive consequences have often been ignored. To examine what kinds of personalized contexts foster or hinder learning and transfer, three manipulations of perspective and context were employed to teach participants Signal Detection Theory (SDT). In all cases, application of SDT principles was negatively impacted by manipulations that encouraged participants to consider the perspective of the signal detector (the decision maker in SDT situations): by giving participants active detection experience (Experiment 1), biasing them to adopt a first-person rather than third-person perspective (Experiment 2), or framing the task in terms of a well-known celebrity (Experiment 3). These contexts run the risk of introducing goals and information that are specific to the detector’s point of view, resulting in sub-optimal understanding of SDT.
Cognition and Instruction,27:1,51 — 89
Ji Y. Son; Robert L. Goldstone
Instruction abstracted from specific and concrete examples is frequently criticized for ignoring the context-dependent and perspectival nature of learning (e.g., Bruner, 1962, 1966; Greeno, 1997). Yet, in the effort to create personally interesting learning contexts, cognitive consequences have often been ignored. To examine what kinds of personalized contexts foster or hinder learning and transfer, three manipulations of perspective and context were employed to teach participants Signal Detection Theory (SDT). In all cases, application of SDT principles was negatively impacted by manipulations that encouraged participants to consider the perspective of the signal detector (the decision maker in SDT situations): by giving participants active detection experience (Experiment 1), biasing them to adopt a first-person rather than third-person perspective (Experiment 2), or framing the task in terms of a well-known celebrity (Experiment 3). These contexts run the risk of introducing goals and information that are specific to the detector’s point of view, resulting in sub-optimal understanding of SDT.
Inglis Mejia-Ramos - C&I 2009
The Effect of Authority on the Persuasiveness of Mathematical Arguments
Cognition and Instruction Volume 27, Number 1 (January 2009)
Matthew Inglis, Juan Pablo Mejia-Ramos
Three experiments are reported that investigate the extent to which an authority figure influences the level of persuasion undergraduate students and research-active mathematicians invest in mathematical arguments. We demonstrate that, in some situations, both students and researchers rate arguments as being more persuasive when they are associated with an expert mathematician than when the author is anonymous. We develop a model that accounts for these data by suggesting that, for both students and researchers, an authority figure only plays a role when there is already some uncertainty about the argument's mathematical status. Implications for pedagogy, and for future research, are discussed.
Cognition and Instruction Volume 27, Number 1 (January 2009)
Matthew Inglis, Juan Pablo Mejia-Ramos
Three experiments are reported that investigate the extent to which an authority figure influences the level of persuasion undergraduate students and research-active mathematicians invest in mathematical arguments. We demonstrate that, in some situations, both students and researchers rate arguments as being more persuasive when they are associated with an expert mathematician than when the author is anonymous. We develop a model that accounts for these data by suggesting that, for both students and researchers, an authority figure only plays a role when there is already some uncertainty about the argument's mathematical status. Implications for pedagogy, and for future research, are discussed.
Ares Stroup Schademan - C&I 2009
The Power of Mediating Artifacts in Group-Level Development of Mathematical Discourses
Cognition and Instruction Volume 27, Number 1 (January 2009)
Nancy Ares, Walter Stroup, Alfred Schademan
A new generation of networked classroom technology immerses students and teachers in the group-level construction of powerful mathematical and scientific concepts. We examine these networks from a sociocultural point of view as a new form of mediating artifact. We present a mixed-method, microgenetic analysis to characterize students' appropriation of mathematical content and practice as mediated by the Participatory Simulations system. Central findings of the study are that networked activities provided the opportunity for students and the teacher to: (a) act on multiple representations, (b) create collectively a linked set of mathematical objects that they could examine and discuss together, and (c) exercise agency in the production of mathematical discourse and practice. These opportunities fostered the development of powerful mathematical discourse.
Cognition and Instruction Volume 27, Number 1 (January 2009)
Nancy Ares, Walter Stroup, Alfred Schademan
A new generation of networked classroom technology immerses students and teachers in the group-level construction of powerful mathematical and scientific concepts. We examine these networks from a sociocultural point of view as a new form of mediating artifact. We present a mixed-method, microgenetic analysis to characterize students' appropriation of mathematical content and practice as mediated by the Participatory Simulations system. Central findings of the study are that networked activities provided the opportunity for students and the teacher to: (a) act on multiple representations, (b) create collectively a linked set of mathematical objects that they could examine and discuss together, and (c) exercise agency in the production of mathematical discourse and practice. These opportunities fostered the development of powerful mathematical discourse.
2008-09-29
Hill Blunk Charalambous Lewis Phelps Sleep Ball - C&I 2008
Mathematical Knowledge for Teaching and the Mathematical Quality of Instruction: An Exploratory Study
Cognition and Instruction, Volume 26, Number 4 (October 2008), 430 - 511
Heather Hill, Merrie Blunk, Charalambos Charalambous, Jennifer Lewis, Geoffrey Phelps, Laurie Sleep, Deborah Loewenberg Ball
This study illuminates claims that teachers' mathematical knowledge plays an important role in their teaching of this subject matter. In particular, we focus on teachers' mathematical knowledge for teaching (MKT), which includes both the mathematical knowledge that is common to individuals working in diverse professions and the mathematical knowledge that is specialized to teaching. We use a series of five case studies and associated quantitative data to detail how MKT is associated with the mathematical quality of instruction. Although there is a significant, strong, and positive association between levels of MKT and the mathematical quality of instruction, we also find that there are a number of important factors that mediate this relationship, either supporting or hindering teachers' use of knowledge in practice.
Cognition and Instruction, Volume 26, Number 4 (October 2008), 430 - 511
Heather Hill, Merrie Blunk, Charalambos Charalambous, Jennifer Lewis, Geoffrey Phelps, Laurie Sleep, Deborah Loewenberg Ball
This study illuminates claims that teachers' mathematical knowledge plays an important role in their teaching of this subject matter. In particular, we focus on teachers' mathematical knowledge for teaching (MKT), which includes both the mathematical knowledge that is common to individuals working in diverse professions and the mathematical knowledge that is specialized to teaching. We use a series of five case studies and associated quantitative data to detail how MKT is associated with the mathematical quality of instruction. Although there is a significant, strong, and positive association between levels of MKT and the mathematical quality of instruction, we also find that there are a number of important factors that mediate this relationship, either supporting or hindering teachers' use of knowledge in practice.
diSessa - C&I 2008
A “Theory Bite” on the Meaning of Scientific Inquiry: A Companion to Kuhn and Pease
Cognition and Instruction, Volume 26, Issue 4 October 2008 , pages 427 - 429
Andrea diSessa
No abstract given, but here's a description of a "theory bite" that suggests why you should read this:
Cognition and Instruction, Volume 26, Issue 4 October 2008 , pages 427 - 429
Andrea diSessa
No abstract given, but here's a description of a "theory bite" that suggests why you should read this:
With respect to dialectical approaches and also to theory, I have taken the privilege of exemplifying a small innovation focused on both of these in this issue. I call the genre a “theory bite,” and it was suggested to me by Bruce Sherin. The idea is to comment briefly on the theoretical perspective of a work in such a way as to (a) succinctly identify and clarify a theoretical position in an article, and (b) situate it with respect to alternatives. “Essences and possibilities” might be a helpful slogan. This is largely an analytical enterprise, and it can usually be carried out without the author staking a position. I hope for simple, clear, and short expositions that can illuminate background assumptions for senior researchers, and attune junior researchers to perspectives that they may miss because researchers in particular lines seldom go back to first principles, and, similarly, they seldom review very different framings. This dialectical genre is tricky to nurture. Editors in charge may be the best people to think about possible contributions, but rarely will they be the best people to make the contribution. It is easier to identify people who are allies of positions and lines, and those who will dispute them. Where neutral but illuminating analytical perspectives can come from is more problematic. So, initiative on the part of readers and contributors is urgently requested. You may use my note on the Kuhn and Pease article in this issue as a model, but I hope this modest example also spurs different and better innovations. Obviously, feedback on genres we do or could try out is strongly invited.
Kuhn Pease - C&I 2008
What Needs to Develop in the Development of Inquiry Skills?
Cognition and Instruction, Volume 26, Issue 4 October 2008 , pages 512 - 559
Deanna Kuhn; Maria Pease
To identify the challenges that students must meet to engage in effective self-directed inquiry, a class was followed for three years, from the fourth through the sixth grades, as they engaged in a sequence of progressively more demanding inquiry activities. Students made substantial progress in understanding the objectives of inquiry, identifying questions, attending to evidence, identifying patterns, making controlled comparisons, interpreting increasingly complex data, supporting claims, and drawing justified conclusions. Retaining awareness of inquiry objectives and integrating influences of multiple variables in predicting outcomes were two areas that remained challenging. A comparison group of seventh graders who had not been involved in the program displayed strikingly different approaches to an inquiry task, indicating that the skills identified here are not ones that develop in the absence of appropriate kinds of educational experiences.
Cognition and Instruction, Volume 26, Issue 4 October 2008 , pages 512 - 559
Deanna Kuhn; Maria Pease
To identify the challenges that students must meet to engage in effective self-directed inquiry, a class was followed for three years, from the fourth through the sixth grades, as they engaged in a sequence of progressively more demanding inquiry activities. Students made substantial progress in understanding the objectives of inquiry, identifying questions, attending to evidence, identifying patterns, making controlled comparisons, interpreting increasingly complex data, supporting claims, and drawing justified conclusions. Retaining awareness of inquiry objectives and integrating influences of multiple variables in predicting outcomes were two areas that remained challenging. A comparison group of seventh graders who had not been involved in the program displayed strikingly different approaches to an inquiry task, indicating that the skills identified here are not ones that develop in the absence of appropriate kinds of educational experiences.
2008-04-12
Li Ding Capraro Capraro - C&I 2008
Sources of Differences in Children's Understandings of Mathematical Equality: Comparative Analysis of Teacher Guides and Student Texts in China and the United States
Cognition and Instruction, Volume 26, Issue 2 April 2008 , pages 195 - 217
Xiaobao Li; Meixia Ding; Mary Margaret Capraro; Robert M. Capraro
This study reports findings from comparative samples of sixth-grade Chinese and U.S. students' interpretations of the equal sign. Ninety-eight percent of the Chinese sample correctly answered 4 items indicating conceptions of equality and provided conceptually accurate explanations. In contrast, only 28% of the U.S. sample performed at this level. We examine how teacher preparation materials, students' textbooks and teachers' guidebooks treat equality in each country. U.S. teacher preparation textbooks rarely interpreted the equal sign as equivalence. On the contrary, Chinese textbooks typically introduced the equal sign in a context of relationships and interpreted the sign as "balance," "sameness," or "equivalence" and only then embedded the sign with operations on numbers.
Cognition and Instruction, Volume 26, Issue 2 April 2008 , pages 195 - 217
Xiaobao Li; Meixia Ding; Mary Margaret Capraro; Robert M. Capraro
This study reports findings from comparative samples of sixth-grade Chinese and U.S. students' interpretations of the equal sign. Ninety-eight percent of the Chinese sample correctly answered 4 items indicating conceptions of equality and provided conceptually accurate explanations. In contrast, only 28% of the U.S. sample performed at this level. We examine how teacher preparation materials, students' textbooks and teachers' guidebooks treat equality in each country. U.S. teacher preparation textbooks rarely interpreted the equal sign as equivalence. On the contrary, Chinese textbooks typically introduced the equal sign in a context of relationships and interpreted the sign as "balance," "sameness," or "equivalence" and only then embedded the sign with operations on numbers.
Radinsky - C&I 2008
Students' Roles in Group-Work with Visual Data: A Site of Science Learning
Cognition and Instruction, Volume 26, Issue 2 April 2008 , pages 145 - 194
Josh Radinsky
Learning science includes learning to argue with inscriptions: images used to symbolize information persuasively. This study examined sixth-graders learning to invest inscriptions with representational status, in a geographic information system (GIS)-based science investigation. Learning to reason with inscriptions was studied in emergent participation patterns in groups, operationalized as roles. Cross-case analyses compared developmental trajectories for two roles in each group: competitive challenger and quiet bystander. Role development mediated learning to reason with inscriptions, including (1) co-assembling "representational states" of data and (2) managing dialectical tensions of argumentation. Role was operationalized as a site of learning, intersecting individual and collective processes, rather than a mechanism of one impacting another. Distributed conceptions of practice support this approach for understanding how students learn to do science.
Cognition and Instruction, Volume 26, Issue 2 April 2008 , pages 145 - 194
Josh Radinsky
Learning science includes learning to argue with inscriptions: images used to symbolize information persuasively. This study examined sixth-graders learning to invest inscriptions with representational status, in a geographic information system (GIS)-based science investigation. Learning to reason with inscriptions was studied in emergent participation patterns in groups, operationalized as roles. Cross-case analyses compared developmental trajectories for two roles in each group: competitive challenger and quiet bystander. Role development mediated learning to reason with inscriptions, including (1) co-assembling "representational states" of data and (2) managing dialectical tensions of argumentation. Role was operationalized as a site of learning, intersecting individual and collective processes, rather than a mechanism of one impacting another. Distributed conceptions of practice support this approach for understanding how students learn to do science.
Speer - C&I 2008
Connecting Beliefs and Practices: A Fine-Grained Analysis of a College Mathematics Teacher's Collections of Beliefs and Their Relationship to His Instructional Practices
Cognition and Instruction, Volume 26, Issue 2 April 2008 , pages 218 - 267
Natasha M. Speer
Findings about mathematics teachers' beliefs typically involve broad characterizations of those beliefs that are compared with general descriptions of practices. Teacher development research suggests that changes happen effectively from attention to specific practices. Few investigations of beliefs and practices are done at this level of detail. Thus, little is known about how beliefs shape practices at the very grain-size where development appears to happen most productively. This study focused on fine-grained details of beliefs, practices, and connections between them. Findings indicate that particular units of analysis ("collections of beliefs") are useful for investigating connections between beliefs and specific practices. Certain collections were also found to be especially influential, including beliefs about evidence of student understanding and about how learning happens.
Cognition and Instruction, Volume 26, Issue 2 April 2008 , pages 218 - 267
Natasha M. Speer
Findings about mathematics teachers' beliefs typically involve broad characterizations of those beliefs that are compared with general descriptions of practices. Teacher development research suggests that changes happen effectively from attention to specific practices. Few investigations of beliefs and practices are done at this level of detail. Thus, little is known about how beliefs shape practices at the very grain-size where development appears to happen most productively. This study focused on fine-grained details of beliefs, practices, and connections between them. Findings indicate that particular units of analysis ("collections of beliefs") are useful for investigating connections between beliefs and specific practices. Certain collections were also found to be especially influential, including beliefs about evidence of student understanding and about how learning happens.
2008-01-06
diSessa - C&I 2007
An Interactional Analysis of Clinical Interviewing
Cognition and Instruction
2007, Vol. 25, No. 4, Pages 523-565
Andrea A. diSessa
University of California, Berkeley, California
Clinical interviewing is viewed here as a social interactional pattern in order to examine the nature and limits of the technique as a means of scientific data acquisition. I defend the technique against criticisms that it is ecologically suspect and prone to systematic biases, mainly due to influence of the interviewer on the interviewee or to unnatural and biasing interactional patterns. The Central Hypothesis of this work is that at least some forms of clinical interviewing are derivative of naturally occurring patterns of activity and interaction. As such, they do not warrant unnecessary a priori suspicion. More importantly, this view leads to avenues of empirical examination that allow determination and checking of the character of the clinical interaction, which bears directly on how and when data extracted in clinical contexts are scientifically valid. Data from an extensive corpus involving a single subject are used to illustrate and substantiate claims.
doi:10.1080/07370000701632413
Cognition and Instruction
2007, Vol. 25, No. 4, Pages 523-565
Andrea A. diSessa
University of California, Berkeley, California
Clinical interviewing is viewed here as a social interactional pattern in order to examine the nature and limits of the technique as a means of scientific data acquisition. I defend the technique against criticisms that it is ecologically suspect and prone to systematic biases, mainly due to influence of the interviewer on the interviewee or to unnatural and biasing interactional patterns. The Central Hypothesis of this work is that at least some forms of clinical interviewing are derivative of naturally occurring patterns of activity and interaction. As such, they do not warrant unnecessary a priori suspicion. More importantly, this view leads to avenues of empirical examination that allow determination and checking of the character of the clinical interaction, which bears directly on how and when data extracted in clinical contexts are scientifically valid. Data from an extensive corpus involving a single subject are used to illustrate and substantiate claims.
doi:10.1080/07370000701632413
Ellis - C&I 2007
The Influence of Reasoning with Emergent Quantities on Students' Generalizations
Cognition and Instruction
2007, Vol. 25, No. 4, Pages 439-478
Amy B. Ellis
University of Wisconsin-Madison
This paper reports the mathematical generalizations of two groups of algebra students, one which focused primarily on quantitative relationships, and one which focused primarily on number patterns disconnected from quantities. Results indicate that instruction encouraging a focus on number patterns supported generalizations about patterns, procedures, and rules, while instruction encouraging a focus on quantities supported generalizations about relationships, connections between situations, and dynamic phenomena, such as the nature of constant speed. An examination of the similarities and differences in students' generalizations revealed that the type of quantitative reasoning in which students engaged ultimately proved more important in influencing their generalizing than a mere focus on quantities versus numbers. In order to develop powerful, global generalizations about relationships, students had to construct ratios as emergent quantities relating two initial quantities. The role of emergent-ratio quantities is discussed as it relates to pedagogical practices that can support students' abilities to correctly generalize.
doi:10.1080/07370000701632397
Cognition and Instruction
2007, Vol. 25, No. 4, Pages 439-478
Amy B. Ellis
University of Wisconsin-Madison
This paper reports the mathematical generalizations of two groups of algebra students, one which focused primarily on quantitative relationships, and one which focused primarily on number patterns disconnected from quantities. Results indicate that instruction encouraging a focus on number patterns supported generalizations about patterns, procedures, and rules, while instruction encouraging a focus on quantities supported generalizations about relationships, connections between situations, and dynamic phenomena, such as the nature of constant speed. An examination of the similarities and differences in students' generalizations revealed that the type of quantitative reasoning in which students engaged ultimately proved more important in influencing their generalizing than a mere focus on quantities versus numbers. In order to develop powerful, global generalizations about relationships, students had to construct ratios as emergent quantities relating two initial quantities. The role of emergent-ratio quantities is discussed as it relates to pedagogical practices that can support students' abilities to correctly generalize.
doi:10.1080/07370000701632397
SmithC - C&I 2007
Bootstrapping Processes in the Development of Students' Commonsense Matter Theories: Using Analogical Mappings, Thought Experiments, and Learning to Measure to Promote Conceptual Restructuring
Cognition and Instruction
2007, Vol. 25, No. 4, Pages 337-398
Carol L. Smith
University of Massachusetts at Boston
This study explores whether the development of students' understanding of matter as something that occupies space and has weight involves conceptual change and restructuring rather than only simple belief revision. Based on an analysis of how the concepts in students' initial matter theory (henceforth MT1) may differ from the concepts in the matter theory that is a target of middle school instruction (MT2), I propose ways that concepts in a given theory cohere with each other and identify the sources of the new ideas in MT2 and the learning processes by which those new ideas can be acquired. I test implications of these analyses by designing a curriculum unit that exploits these learning mechanisms, by using the curriculum with 4 classes of eighth-grade Earth Science students, and by assessing 42 students' thinking about matter, object size, and weight (via individual interviews and written tests) before and after the teaching unit. Consistent with the hypothesis of conceptual restructuring, the data not only show coherencies in students' thinking about matter, size, and weight before and after teaching, but also coordinated patterns of change. The implications for the design of science instruction are discussed.
doi:10.1080/07370000701632363
Cognition and Instruction
2007, Vol. 25, No. 4, Pages 337-398
Carol L. Smith
University of Massachusetts at Boston
This study explores whether the development of students' understanding of matter as something that occupies space and has weight involves conceptual change and restructuring rather than only simple belief revision. Based on an analysis of how the concepts in students' initial matter theory (henceforth MT1) may differ from the concepts in the matter theory that is a target of middle school instruction (MT2), I propose ways that concepts in a given theory cohere with each other and identify the sources of the new ideas in MT2 and the learning processes by which those new ideas can be acquired. I test implications of these analyses by designing a curriculum unit that exploits these learning mechanisms, by using the curriculum with 4 classes of eighth-grade Earth Science students, and by assessing 42 students' thinking about matter, object size, and weight (via individual interviews and written tests) before and after the teaching unit. Consistent with the hypothesis of conceptual restructuring, the data not only show coherencies in students' thinking about matter, size, and weight before and after teaching, but also coordinated patterns of change. The implications for the design of science instruction are discussed.
doi:10.1080/07370000701632363
Morris - C&I 2007
Factors Affecting Pre-Service Teachers' Evaluations of the Validity of Students' Mathematical Arguments in Classroom Contexts
Cognition and Instruction
2007, Vol. 25, No. 4, Pages 479-522
Anne K. Morris
University of Delaware
This study was designed to identify the types of understandings, skills, and beliefs that affect pre-service teachers' evaluations of students' mathematical arguments in classroom contexts. Thirty-four pre-service teachers read a transcript of a third grade lesson in which the students were expected to prove a generalization. To investigate whether pre-service teachers evaluate students' arguments in a consistent way across different classroom contexts, pre-service teachers' evaluations of the responses were examined in two experimental conditions. In the first condition, one student made a valid argument that proved why the generalization was true, and in the second condition, this student's response was omitted from the transcript. Findings included the following: 1) Pre-service teachers' evaluations of students' inductive arguments differed dramatically across conditions; 2) Pre-service teachers rarely used logical validity as a criterion for evaluating arguments; 3) Pre-service teachers exhibited a wide variety of conceptions about the relationships among mathematical proof, explaining why something is true in mathematics, and inductive arguments, and these conceptions affected their evaluations of students' arguments; 4) Many pre-service teachers were able to distinguish between student responses that did and did not explain why a generalization was true; and 5) Pre-service teachers used their own knowledge to fill in "holes" in students' arguments which led to inappropriate evaluations of students' arguments and understanding. Implications for teacher preparation programs are discussed.
doi:10.1080/07370000701632405
Cognition and Instruction
2007, Vol. 25, No. 4, Pages 479-522
Anne K. Morris
University of Delaware
This study was designed to identify the types of understandings, skills, and beliefs that affect pre-service teachers' evaluations of students' mathematical arguments in classroom contexts. Thirty-four pre-service teachers read a transcript of a third grade lesson in which the students were expected to prove a generalization. To investigate whether pre-service teachers evaluate students' arguments in a consistent way across different classroom contexts, pre-service teachers' evaluations of the responses were examined in two experimental conditions. In the first condition, one student made a valid argument that proved why the generalization was true, and in the second condition, this student's response was omitted from the transcript. Findings included the following: 1) Pre-service teachers' evaluations of students' inductive arguments differed dramatically across conditions; 2) Pre-service teachers rarely used logical validity as a criterion for evaluating arguments; 3) Pre-service teachers exhibited a wide variety of conceptions about the relationships among mathematical proof, explaining why something is true in mathematics, and inductive arguments, and these conceptions affected their evaluations of students' arguments; 4) Many pre-service teachers were able to distinguish between student responses that did and did not explain why a generalization was true; and 5) Pre-service teachers used their own knowledge to fill in "holes" in students' arguments which led to inappropriate evaluations of students' arguments and understanding. Implications for teacher preparation programs are discussed.
doi:10.1080/07370000701632405
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