Using Errors as Springboards for Inquiry in Mathematics Instruction

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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.