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Cartesian Product–in–Action: Vergnaud's Theory Applied to Preservice-Secondary-Mathematics Teachers’ Interpretation of Polynomial Multiplication Modeled with Algebra Tiles

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Abstract:

This study examines preservice secondary mathematics teachers’ understanding and sense-making of polynomial multiplication modeled with algebra tiles. I base this research within a framework of concepts and theorems-in action (Vergnaud, 1983, 1988, 1994, 1997). My data consist of videotaped qualitative interviews. I generated a thematic analysis by undertaking a retrospective analysis, using constant comparison methodology. The main result of this study is that representational Cartesian products-in action at two different levels, indicators of multiplicative thinking, were available to two research participants only.

Most Common Document Word Stems:

x (89), y (62), multipl (54), time (48), linear (42), 1 (41), figur (39), tile (38), point (34), quantiti (33), 2x (30), action (29), product (26), concept (26), mathemat (26), represent (25), 2y (25), polynomi (25), nicol (24), box (23), irreduc (22),
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Association:
Name: North American Chapter of the International Group for the Psychology of Mathematics Education
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http://www.pmena.org


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URL: http://citation.allacademic.com/meta/p369629_index.html
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MLA Citation:

Caglayan, Gunhan. "Cartesian Product–in–Action: Vergnaud's Theory Applied to Preservice-Secondary-Mathematics Teachers’ Interpretation of Polynomial Multiplication Modeled with Algebra Tiles" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, OMNI Hotel, Atlanta, GA, Sep 23, 2009 <Not Available>. 2014-11-29 <http://citation.allacademic.com/meta/p369629_index.html>

APA Citation:

Caglayan, G. , 2009-09-23 "Cartesian Product–in–Action: Vergnaud's Theory Applied to Preservice-Secondary-Mathematics Teachers’ Interpretation of Polynomial Multiplication Modeled with Algebra Tiles" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, OMNI Hotel, Atlanta, GA Online <APPLICATION/PDF>. 2014-11-29 from http://citation.allacademic.com/meta/p369629_index.html

Publication Type: Brief Research Report
Review Method: Peer Reviewed
Abstract: This study examines preservice secondary mathematics teachers’ understanding and sense-making of polynomial multiplication modeled with algebra tiles. I base this research within a framework of concepts and theorems-in action (Vergnaud, 1983, 1988, 1994, 1997). My data consist of videotaped qualitative interviews. I generated a thematic analysis by undertaking a retrospective analysis, using constant comparison methodology. The main result of this study is that representational Cartesian products-in action at two different levels, indicators of multiplicative thinking, were available to two research participants only.


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