Using Errors as Springboards for Inquiry in Mathematics Instruction

这个项目将探索利用学生的数学错误的策略，检查错误的潜力，以激励和指导涉及问题产生、问题解决和批判性思维的活动。这与目前只注重尽快获得正确答案和消除错误的做法形成了鲜明对比。将采用概念性和经验性调查相结合的方法。这一方法将包括深入研究几个错误，以揭示它们激发创造性活动的潜力；开发利用这种潜力的教学材料；对将错误作为动机和手段与不同受众进行探究的可能性进行概念性分析；分析学生在中学教学环境中对实施该策略的反应，无论是在自然课堂环境中还是在小组教学实验中。这项研究的发现应该有助于理解错误在教育中的作用，并导致在数学教学中进一步开展关键活动，如解决问题和批判性思维。虽然该项目将侧重于在中学数学教学中使用错误，但它将为在其他受众和其他学科领域应用重新构建的错误教育作用的观点奠定基础。该项目旨在通过探索性研究和开发一种新的战略，认识到试错在数学思想和算法的历史发展中的认识论价值，来实现提高数学教学质量的总干事的主要目标。它还将生成原型教学材料，将这种方法与课堂教师可能使用的方法结合起来；因此，共同出资由教学材料开发计划提供。PI是一名年轻的研究员，他非常有资格进行这项研究。

This project will explore strategies for using students' mathematical errors that will examine the potential of errors to motivate and direct activities involving problem generating, problem solving, and critical thinking. This is in contrast to the current practice that focuses solely on obtaining correct answers and eliminating errors as quickly as possible. A combination of conceptual and empirical investigations will be employed. This approach will include the in-depth study of several errors to unravel their potential to motivate creative activities; the development of instructional material which makes use of such potential; a conceptual analysis of the possibility of using errors as motivation and means for inquiry with different audiences; the analysis of students' reactions to implementations of the strategy in instructional contexts at the secondary level, both in natural classroom settings and in "teaching experiments" with small groups. Findings from this research should assist in understanding the role of errors in education and lead to further occasions in mathematics instruction for crucial activities such as problem solving and critical thinking. Though this project will focus on the use of errors in mathematics instruction at the secondary level, it will create the basis for the application of a reconstructed view of the educational role of errors with other audiences and in other subject areas. This project addresses the Directorate primary goal of advancing the quality of mathematics instruction through exploratory research and development on a new strategy that recognizes the epistemological value of trial and error in the historical development of mathematical ideas and algorithms. It will also generate prototype instructional materials that will incorporate this approach with the potential for use by classroom teachers; consequently, co-funding is being provided by the Instructional Materials Development Program. The PI is a young researcher who is well-qualified to conduct this research.