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Investigating students' opportunitie...

Stylianides, Gabriel J.

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Investigating students' opportunities to develop proficiency in reasoning and proving: A curricular perspective.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Investigating students' opportunities to develop proficiency in reasoning and proving: A curricular perspective./
作者:	Stylianides, Gabriel J.
面頁冊數:	208 p.
附註:	Source: Dissertation Abstracts International, Volume: 66-09, Section: A, page: 3245.
Contained By:	Dissertation Abstracts International66-09A.
標題:	Education, Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3186766
ISBN:	9780542302848

Investigating students' opportunities to develop proficiency in reasoning and proving: A curricular perspective.
Stylianides, Gabriel J.

Investigating students' opportunities to develop proficiency in reasoning and proving: A curricular perspective. - 208 p.

Source: Dissertation Abstracts International, Volume: 66-09, Section: A, page: 3245.

Thesis (Ph.D.)--University of Michigan, 2005.

Despite widespread agreement that all students should have opportunities to acquire proficiency in reasoning and proving in school mathematics, too little is known about how to design instruction to accomplish this goal. Curriculum materials undoubtedly have an important role to play in providing tasks for students' and teachers' classroom work, and in providing guidance for teachers in developing students' capacity in reasoning and proving. At this time, however, we lack detailed knowledge of how reasoning and proving is treated in contemporary curriculum materials. This study takes step toward addressing this limitation, with particular attention to one reform middle school curriculum and two research questions: (1) What opportunities are designed in the curriculum materials for students to engage in reasoning and proving? and (2) In what ways do the curriculum materials appear to be designed for helping students develop a capacity for both inductive and deductive modes of reasoning?

ISBN: 9780542302848Subjects--Topical Terms:

1017588
Education, Mathematics.

Investigating students' opportunities to develop proficiency in reasoning and proving: A curricular perspective.
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245 1 0 $a Investigating students' opportunities to develop proficiency in reasoning and proving: A curricular perspective.
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500 $a Source: Dissertation Abstracts International, Volume: 66-09, Section: A, page: 3245.
500 $a Chair: Edward A. Silver.
502 $a Thesis (Ph.D.)--University of Michigan, 2005.
520 $a Despite widespread agreement that all students should have opportunities to acquire proficiency in reasoning and proving in school mathematics, too little is known about how to design instruction to accomplish this goal. Curriculum materials undoubtedly have an important role to play in providing tasks for students' and teachers' classroom work, and in providing guidance for teachers in developing students' capacity in reasoning and proving. At this time, however, we lack detailed knowledge of how reasoning and proving is treated in contemporary curriculum materials. This study takes step toward addressing this limitation, with particular attention to one reform middle school curriculum and two research questions: (1) What opportunities are designed in the curriculum materials for students to engage in reasoning and proving? and (2) In what ways do the curriculum materials appear to be designed for helping students develop a capacity for both inductive and deductive modes of reasoning?
520 $a This study includes both conceptual and empirical analyses. I begin by defining reasoning and proving so that it is both honest to the discipline of mathematics and useful in a curriculum analysis. In brief, I define reasoning and proving to encompass the breadth of the activity associated with identifying patterns, making conjectures, providing proofs, and providing non-proof arguments. Using my definition of reasoning and proving and the findings of pertinent educational/psychological research, an analytic framework is proposed to investigate the opportunities that are designed in the mathematics curriculum for students to engage in reasoning and proving. The analytic framework is used to analyze the algebra, geometry, and number theory units of Connected Mathematics. Also examined is the support the curriculum materials provide for teachers to enact the proof opportunities designed.
520 $a Some major findings from my curriculum analysis are the following: (1) about 40% of the tasks are designed to engage students in reasoning and proving; (2) many more opportunities are designed for students to use inductive than deductive modes of reasoning; (3) reasoning and proving opportunities are distributed unevenly across grade levels and content areas; and (4) very limited guidance is provided to teachers to support their use of proof tasks.
520 $a The framework and the empirical findings contained herein have potential implications for curriculum design, and they provide pointers to possible links between students' difficulties in reasoning and proving and the treatment of this practice in curriculum materials. Also, the framework and associated methodology can provide a platform for conducting detailed analyses on the interplay of curriculum materials and teaching/learning in reasoning and proving.
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