The introduction of proof in secondary geometry textbooks

•Reasoning-and-proving opportunities in 6 geometry textbooks were analyzed.•Opportunities in textbook exposition tended to be general whereas exercises were particular.•Within introductory proof chapters, opportunities more often involved conjectures than proof.•Opportunities to reflect on reasoning...

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Veröffentlicht in:International journal of educational research 2014, Vol.64, p.107-118
Hauptverfasser: Otten, Samuel, Males, Lorraine M., Gilbertson, Nicholas J.
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container_title International journal of educational research
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creator Otten, Samuel
Males, Lorraine M.
Gilbertson, Nicholas J.
description •Reasoning-and-proving opportunities in 6 geometry textbooks were analyzed.•Opportunities in textbook exposition tended to be general whereas exercises were particular.•Within introductory proof chapters, opportunities more often involved conjectures than proof.•Opportunities to reflect on reasoning-and-proving were common in introductory proof chapters.•Opportunities to reflect were rare in the remaining chapters, where students proved more often. Explicit reasoning-and-proving opportunities in the United States are often relegated to a single secondary geometry course. This study analyzed the reasoning-and-proving opportunities in six U.S. geometry textbooks, giving particular attention to the chapter that introduced proof. Analysis focused on the types of reasoning-and-proving activities expected of students and the type of mathematical statement around which the reasoning-and-proving took place, be it general or particular. Results include the fact that reasoning-and-proving opportunities in student exercises were predominantly of the particular type, whereas textbook exposition most commonly had general statements. Within the chapters introducing proof, opportunities for students to develop proofs were less common than exercises involving conjectures and statements or exercises about the reasoning-and-proving process. Opportunities to reflect on the reasoning-and-proving process were prevalent in the introduction chapters, though rare in the remainder of the books.
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Explicit reasoning-and-proving opportunities in the United States are often relegated to a single secondary geometry course. This study analyzed the reasoning-and-proving opportunities in six U.S. geometry textbooks, giving particular attention to the chapter that introduced proof. Analysis focused on the types of reasoning-and-proving activities expected of students and the type of mathematical statement around which the reasoning-and-proving took place, be it general or particular. Results include the fact that reasoning-and-proving opportunities in student exercises were predominantly of the particular type, whereas textbook exposition most commonly had general statements. Within the chapters introducing proof, opportunities for students to develop proofs were less common than exercises involving conjectures and statements or exercises about the reasoning-and-proving process. 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Explicit reasoning-and-proving opportunities in the United States are often relegated to a single secondary geometry course. This study analyzed the reasoning-and-proving opportunities in six U.S. geometry textbooks, giving particular attention to the chapter that introduced proof. Analysis focused on the types of reasoning-and-proving activities expected of students and the type of mathematical statement around which the reasoning-and-proving took place, be it general or particular. Results include the fact that reasoning-and-proving opportunities in student exercises were predominantly of the particular type, whereas textbook exposition most commonly had general statements. Within the chapters introducing proof, opportunities for students to develop proofs were less common than exercises involving conjectures and statements or exercises about the reasoning-and-proving process. 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subjects Geometry
Proof
Reasoning
Secondary
Textbook analysis
Textbooks
title The introduction of proof in secondary geometry textbooks
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