Difference between revisions of "Nathan & Koedinger (2000) JRME"

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{{Title|The Real Story Behind Story Problems: Effects of Representations on Quantitative Reasoning}}
{{Title|Teachers' and Researchers' Beliefs About the Development of Algebraic Reasoning}}
__NOTOC__
__NOTOC__
* Authors: [[Kenneth Koedinger|Kenneth R. Koedinger]] and [[Mitchell Nathan|Mitchell J. Nathan]]
* Authors: [[Mitchell Nathan|Mitchell J. Nathan]] and [[Kenneth Koedinger|Kenneth R. Koedinger]]
* Journal: [[Journal of the Learning Sciences]]
* Journal: [[Journal for Research in Mathematics Education]]
* Year: 2004
* Year: 2000
* Source: http://www.jstor.org/stable/749750
* Source: http://www.jstor.org/stable/749750


==Abstract==
==Abstract==
This article explores how differences in problem representations change both the performance and underlying cognitive processes of beginning algebra students engaged in quantitative reasoning. Contrary to beliefs held by practitioners and researchers in mathematics education, students were more successful solving simple algebra story problems than solving mathematically equivalent equations. Contrary to some views of situated cognition, this result is not simply a consequence of situated world knowledge facilitating problem-solving performance, but rather a consequence of student difficulties with comprehending the formal symbolic representation of quantitative relations. We draw on analyses of students' strategies and errors as the basis for a cognitive process explanation of when, why, and how differences in problem representation affect problem solving. We conclude that differences in external representations can affect performance and learning when one representation is easier to comprehend than another or when one representation elicits more reliable and meaningful solution strategies than another.
Mathematics teachers and educational researchers ordered arithmetic and algebra problems according to their predicted problem-solving difficulty for students. Predictions deviated systematically from algebra students' performances but closely matched a view implicit in textbooks. Analysis of students' problem-solving strategies indicates specific ways that students' algebraic reasoning differs from that predicted by most teachers and researchers in the sample and portrayed in common textbooks. The Symbol Precedence Model of development of algebraic reasoning, in which symbolic problem solving precedes verbal problem solving and arithmetic skills strictly preceded algebraic skills, was contrasted with the Verbal Precedence Model of development, which provided a better quantitative fit of students' performance data. Implications of the findings for student and teacher cognition and for algebra instruction are discussed.
 
==Outline of Headings==
* Theoretical Framework: Factors Affecting Problem-Solving Difficulty
** Unknown Values
** Presentation Formats
** Students' Solution Strategies
* Method
** Participants
** Procedure
* Results
** Unknown Values
*** Teacher data
*** Researcher data
*** Relation to student performance
** Presentation Format
*** Teacher data
*** Researcher data
*** Relation to student performance
** Interactions
** Summary
* Discussion
** Symbol Precedence View
** Two Competing Developmental Models
** Quantitative Model Comparison
* Conclusions
** Implications for Research and Student Cognition and Development
** Implications for Research on Teacher Cognition
** Implications for Mathematics Instruction


==Corrolary==
==Corrolary==
;APA
;APA
: Koedinger, K. R., & Nathan, M. J. (2004). The real story behind story problems: Effects of representations on quantitative reasoning. ''Journal of the Learning Sciences, 13''(2), 129–164. http://doi.org/10.1207/s15327809jls1302_1
: Nathan, M. J., & Koedinger, K. R. (2000). Teachers' and researchers' beliefs about the development of algebraic reasoning. ''Journal for Research in Mathematics Education, 31''(2), 168–190. Retrieved from http://www.jstor.org/stable/749750
;BibTeX
;BibTeX
<pre>
<pre>
@article{Koedinger2004a,
@article{Nathan2000a,
author = {Koedinger, Kenneth R. and Nathan, Mitchell J.},
author = {Nathan, Mitchell J. and Koedinger, Kenneth R.},
doi = {10.1207/s15327809jls1302_1},
journal = {Journal for Research in Mathematics Education},
journal = {Journal of the Learning Sciences},
number = {2},
number = {2},
pages = {129--164},
pages = {168--190},
title = {{The real story behind story problems: Effects of representations on quantitative reasoning}},
title = {{Teachers' and researchers' beliefs about the development of algebraic reasoning}},
url = {http://www.jstor.org/stable/749750},
url = {http://www.jstor.org/stable/749750},
volume = {13},
volume = {31},
year = {2004}
year = {2000}
}
}
</pre>
</pre>


[[Category:Journal Articles]]
[[Category:Journal Articles]]
[[Category:Journal of the Learning Sciences]]
[[Category:Journal for Research in Mathematics Education]]
[[Category:2004]]
[[Category:2000]]
[[Category:Quantitative Reasoning]]
[[Category:Algebra]]
[[Category:Word Problems]]
[[Category:Beliefs]]

Latest revision as of 03:36, 16 July 2016

Teachers' and Researchers' Beliefs About the Development of Algebraic Reasoning

Abstract

Mathematics teachers and educational researchers ordered arithmetic and algebra problems according to their predicted problem-solving difficulty for students. Predictions deviated systematically from algebra students' performances but closely matched a view implicit in textbooks. Analysis of students' problem-solving strategies indicates specific ways that students' algebraic reasoning differs from that predicted by most teachers and researchers in the sample and portrayed in common textbooks. The Symbol Precedence Model of development of algebraic reasoning, in which symbolic problem solving precedes verbal problem solving and arithmetic skills strictly preceded algebraic skills, was contrasted with the Verbal Precedence Model of development, which provided a better quantitative fit of students' performance data. Implications of the findings for student and teacher cognition and for algebra instruction are discussed.

Outline of Headings

  • Theoretical Framework: Factors Affecting Problem-Solving Difficulty
    • Unknown Values
    • Presentation Formats
    • Students' Solution Strategies
  • Method
    • Participants
    • Procedure
  • Results
    • Unknown Values
      • Teacher data
      • Researcher data
      • Relation to student performance
    • Presentation Format
      • Teacher data
      • Researcher data
      • Relation to student performance
    • Interactions
    • Summary
  • Discussion
    • Symbol Precedence View
    • Two Competing Developmental Models
    • Quantitative Model Comparison
  • Conclusions
    • Implications for Research and Student Cognition and Development
    • Implications for Research on Teacher Cognition
    • Implications for Mathematics Instruction

Corrolary

APA
Nathan, M. J., & Koedinger, K. R. (2000). Teachers' and researchers' beliefs about the development of algebraic reasoning. Journal for Research in Mathematics Education, 31(2), 168–190. Retrieved from http://www.jstor.org/stable/749750
BibTeX
@article{Nathan2000a,
author = {Nathan, Mitchell J. and Koedinger, Kenneth R.},
journal = {Journal for Research in Mathematics Education},
number = {2},
pages = {168--190},
title = {{Teachers' and researchers' beliefs about the development of algebraic reasoning}},
url = {http://www.jstor.org/stable/749750},
volume = {31},
year = {2000}
}
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