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A Study of Proof Conceptions in Algebra

Lulu Healy, Celia Hoyles 

July 2000, Volume 31, Issue 4, Page 396

Abstract:
After surveying high-attaining 14- and 15-year-old students about proof in algebra, we found that students simultaneously held 2 different conceptions of proof: those about arguments they considered would receive the best mark and those about arguments they would adopt for themselves. In the former category, algebraic arguments were popular. In the latter, students preferred arguments that they could evaluate and that they found convincing and explanatory, preferences that excluded algebra. Empirical argument predominated in students' own proof constructions, although most students were aware of its limitations. The most successful students presented proofs in everyday language, not using algebra. Students' responses were influenced mainly by their mathematical competence but also by curricular factors, their views of proof, and their genders.

Keywords:
Article
Calculus and Higher Level Mathematics
Grades 9-12
Curriculum
Math Coordinator / Coach
Teacher
Manipulatives
Problems
Problem Solving / Problem Posing
Survey Studies
Professional Development / Teacher Education
Representation