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What Discussions Teach Us About Mathematical Understanding: Exploring and Assessing Students’ Mathematical Work in Classrooms

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Abstract:

This paper describes a tool we developed for analyzing small-group discussions in mathematics classrooms. We applied this tool to videotaped sessions of thirty groups of four students, each working together on an open-ended problem. Our analysis shows that small group discussions offer teachers and researchers important knowledge about student thinking and understanding. These insights are often invisible in the written work of the students. We also found that such student discussions frequently emulate discussions among professional mathematicians, thus creating authentic engagement experiences for the students. These findings may help bring traditionally disparate groups of thinkers together. Namely, teachers and researchers are presented with a common set of features to look for in mathematical discussions, and mathematical researchers and mathematicians are presented with striking parallels between student discussions and professional mathematical work.

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mathemat (106), student (102), work (47), group (40), discuss (35), understand (31), triangl (30), problem (30), teacher (27), girl (25), develop (23), use (23), relationship (20), 1 (19), boy (19), right (18), learn (17), written (17), tool (17), knowledg (17), find (16),
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Name: North American Chapter of the International Group for the Psychology of Mathematics Education
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MLA Citation:

Fiori, Nick., Jo, Boaler., Cleare, Nikki., DiBrienza, Jennifer., Sengupta, Tesha. and Shahan, Emily. "What Discussions Teach Us About Mathematical Understanding: Exploring and Assessing Students’ Mathematical Work in Classrooms" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada, Oct 21, 2004 <Not Available>. 2009-05-26 <http://www.allacademic.com/meta/p117658_index.html>

APA Citation:

Fiori, N. , Jo, B. , Cleare, N. , DiBrienza, J. , Sengupta, T. and Shahan, E. , 2004-10-21 "What Discussions Teach Us About Mathematical Understanding: Exploring and Assessing Students’ Mathematical Work in Classrooms" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada Online <.PDF>. 2009-05-26 from http://www.allacademic.com/meta/p117658_index.html

Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: This paper describes a tool we developed for analyzing small-group discussions in mathematics classrooms. We applied this tool to videotaped sessions of thirty groups of four students, each working together on an open-ended problem. Our analysis shows that small group discussions offer teachers and researchers important knowledge about student thinking and understanding. These insights are often invisible in the written work of the students. We also found that such student discussions frequently emulate discussions among professional mathematicians, thus creating authentic engagement experiences for the students. These findings may help bring traditionally disparate groups of thinkers together. Namely, teachers and researchers are presented with a common set of features to look for in mathematical discussions, and mathematical researchers and mathematicians are presented with striking parallels between student discussions and professional mathematical work.

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Document Type: .PDF
Page count: 9
Word count: 4213
Text sample:
What Discussions Teach Us About Mathematical Understanding: Exploring and Assessing Students' Mathematical Work in Classrooms Nick Fiori and Jo Boaler Stanford University "What is the oldest problem of pedagogy? The appearance of learning or `illusory understanding' that is the problem of people who appear to know something that they really don't know." -- Lee Shulman (2000 p. 131) The motivation for this paper comes from the great rewards we--as teachers and researchers--experience every time we listen to students' discussions
L. (2000). Teacher development: Roles of domain expertise and pedagogical content knowledge. Journal of Applied Developmental Psychology 21 129-135. Silver E. & Stein M. K. (1997). The QUASAR Project: The "Revolution of the Possible" in Mathematics Instructional Reform in Urban Middle Schools. Pittsburgh PA: Learning Research and Development Center University of Pittsburgh. Steffe L. P. (1990). Inconsistencies and Cognitive Conflict: A Constructivist View. Focus on Learning Problems in Mathematics 12(3-4) 99-109. Stillwell J. (1989). Mathematics and its History 2nd


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