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- W320425232 abstract "(a + b)(a 2 ‐ ab + b 2 ) = a 3 + b 3 . This activity was inspired by the work of Goldenberg (2003), who outlined a similar activity designed to support students in re-inventing the difference of squares identity (a ‐ b)(a + b) = a 2 ‐ b 2 . In an effort to understand the sources of their difficulties in deriving the sum/difference of cubes identity, our report explores aspects of expressions to which students attended. We detail the instructional activity and its outcomes, and we suggest refinements to the activity that might better support this population of students in achieving the intended learning goals. Setting and Participants Our study was conducted in the context of an intact intermediate-level algebra course offered at a large urban university in the Pacific northwestern United States. The course is designed for students who have not had Algebra II or who require a review of elementary algebra concepts and techniques. The students in this class have a wide variety of dispositions and experiences related to mathematics, a variety of educational backgrounds and interests, and a wide spectrum of ages. The 15 students who participated in our study reflect this diversity. We initiated our study during the third week of classes, after students had developed some experience in multiplying polynomial expressions and factoring perfect square trinomials and differences of squares. The data we report on are drawn from students’ individual written work on the first two parts of the activity. We examined their work for evidence of patterns they might have construed from the sum/difference of cubes expressions generated by the CAS and for connections they drew between those expressions and their factored forms." @default.
- W320425232 created "2016-06-24" @default.
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- W320425232 date "2007-01-01" @default.
- W320425232 modified "2023-10-12" @default.
- W320425232 title "ATTENDING TO STRUCTURE AND FORM IN ALGEBRA: CHALLENGES IN DESIGNING CAS-CENTERED INSTRUCTION THAT SUPPORTS CONSTRUING PATTERNS AND RELATIONSHIPS AMONG ALGEBRAIC EXPRESSIONS (1)" @default.
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