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Improving Students’ Algebraic Thinking: The Case Of Talia, Kien H. Lim
Improving Students’ Algebraic Thinking: The Case Of Talia, Kien H. Lim
Kien H Lim
This paper presents the case of an 11th grader, Talia, who demonstrated improvement in her algebraic thinking after five one-hour sessions of solving problems involving inequalities and equations. She improved from association-based to coordination-based predictions, from impulsive to analytic anticipations, and from inequality-as-a-signal-for-a-procedure to inequality-as-a-comparison-of-functions conceptions. In the one-on-one teaching intervention, she progressed from the sub-context of manipulating symbols, to working with specific numbers, to reasoning with “general” numbers, and eventually to reasoning with symbols. Three features were identified to account for her improvement: (a) attention to meaning, (b) opportunity to repeat similar reasoning, and (c) opportunity to explore.
Students' Epistemological Beliefs Of Mathematics When Taught Using Traditional Versus Reform Curricula In Rural Maine High Schools, Glenn T. Colby
Students' Epistemological Beliefs Of Mathematics When Taught Using Traditional Versus Reform Curricula In Rural Maine High Schools, Glenn T. Colby
Electronic Theses and Dissertations
This study compared students’ epistemological beliefs of mathematics after completing 3 years of a reform-oriented curriculum developed by the Core-Plus Mathematics Project (CPMP) versus a more traditional curriculum developed by Glencoe Mathematics. The Conceptions of Mathematics Inventory (CMI; Grouws, Howald, & Colangelo, 1996) was administered to 11th-grade students in four rural Maine high schools (n=102) to measure student beliefs of mathematics. CPMP was used as the primary textbook series in 2 of the schools, while the other 2 schools used Glencoe Mathematics. A variation of the Reformed Teaching Observation Protocol (RTOP; Piburn & Sawada, 2000) and teacher questionnaires were used …