Characterizing the Nature of Students' Feature Noticing-and-using With Respect to Mathematical Symbols Across Different Levels of Algebra Exposure
Open Access
Author:
Sullivan, Patrick
Graduate Program:
Curriculum and Instruction
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
February 28, 2013
Committee Members:
Mary Kathleen Heid, Dissertation Advisor/Co-Advisor Mary Kathleen Heid, Committee Chair/Co-Chair Glendon Wilbur Blume, Committee Member Rose Mary Zbiek, Committee Member Mark Levi, Committee Member
Keywords:
Noticing Features Algebra Algebraic Symbols Symbolic Representations Student Learning
Abstract:
The purpose of this study is to examine the nature of what students notice about symbols and use as they solve unfamiliar algebra problems based on familiar algebra concepts and involving symbolic inscriptions. The researcher conducted a study of students at three levels of algebra exposure: (a) students enrolled in a high school pre-calculus course, (b) college students enrolled in a second semester calculus course, and (c) prospective secondary mathematics teachers enrolled in a mathematics teaching methods course and who have completed three semesters of calculus, linear algebra, an introduction to proof and several upper level mathematics courses.
Six students from each level of algebra exposure were asked to reason about a series of novel algebra problems that involved symbolic inscriptions and content typical of a second-year algebra course. Data were analyzed for instances of recognizing, reasoning, and linking. One of the outcomes of the research was the development of a feature noticing-and-using taxonomy. The researcher found that students’ feature noticing-and-using was characterized by three different strategies: manipulative, relational, and linking. Most students reasoned from a manipulative strategy, but it was found that students faced challenges reasoning from each of these strategies. Students at the highest level of algebra exposure were much more likely than the other two levels of algebra exposure to use multiple strategies in their reasoning.
