| 1. |
- Raman, Manya, 1971-, et al.
(författare)
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Key ideas and insights in the context of three high school geometry proofs
- 2006
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Ingår i: Mathematics Teacher. - 0025-5769 .- 2330-0582. ; 99:9, s. 644-649
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Tidskriftsartikel (refereegranskat)abstract
- How the concept of "key idea" can be used in high school geometry. Article discusses connecting students' intuitive informal arguments with rigorous formal mathematical proofs. Includes three examples.
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| 2. |
- Raman Sundström, Manya, 1971-, et al.
(författare)
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The case of Brandon : the dual nature of key ideas in the classroom
- 2009
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Ingår i: Nordisk matematikkdidaktikk. - 1104-2176. ; 14:2, s. 29-47
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Tidskriftsartikel (refereegranskat)abstract
- This paper looks at proof production in the midst of classroom interaction. The setting is a collegelevel geometry course in which students are working on the following task: Prove that two paralleltransported lines in the plane are parallel in the sense that they do not intersect. A proof of this statement istraced from a student's idea, through a small group discussion, to a large class discussion moderated by ateacher. As the proof emerges through a series of increasingly public settings we see ways in which the keyidea of the proof serves to both open and close class discussion. We look at several examples of openingand closing, showing how not only the key idea, but the warrants and justifications connected to it, play animportant role in the proof development.
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| 3. |
- Stanley, Dick, et al.
(författare)
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Extended analyses : finding deep structure in standard high school mathematics
- 2007
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Ingår i: Journal of Mathematics Teacher Education. - : Springer Science and Business Media LLC. - 1386-4416 .- 1573-1820. ; 10:4-6, s. 391-397
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Tidskriftsartikel (refereegranskat)abstract
- This paper describes an approach for pre-service or in-service mathematics education thatteaches sophisticated mathematics using only the tools of high school mathematics. The idea is to start witha standard problem from high school mathematics and let the solution to this problem serve as a platform forasking good mathematical questions and searching for deeper mathematical structure beyond the obvious"answer" to the question. Surprisingly, it turns out that high school mathematics is remarkably open to thissort of analysis, and the results are more interesting mathematically than one might initially think.
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