A Study of Proof Conceptions in Algebra
A Study of Proof Conceptions in Algebra
复制标题
DOI：
10.2307/749651
复制
发表时间：
2000-07-01
影响因子：
2.8
通讯作者：
Hoyles, Celia
中科院分区：
文献类型：
--
作者：
Healy, Lulu;Hoyles, Celia
在对成绩优异的14岁和15岁的学生进行了关于代数证明的调查后，我们发现学生们同时持有两种不同的证明概念：那些他们认为会得到最好分数的论点和那些他们会为自己采用的论点。在前一类中，代数论证很流行。在后一种情况下，学生们更喜欢他们可以评估的论点，他们觉得有说服力和解释性，这种偏好排除了代数。经验论证在学生自己的论证结构中占主导地位，尽管大多数学生都意识到它的局限性。最成功的学生用日常语言来证明，而不是用代数。学生的回答主要受其数学能力的影响，但也受课程因素、他们的证明观和性别的影响。
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.