Title

Promoting uncertainty to support preservice teachers’ reasoning about the tangent relationship

Department

Secondary and Middle Grades Education

Document Type

Article

Publication Date

10-9-2018

Abstract

Including opportunities for students to experience uncertainty in solving mathematical tasks can prompt learners to resolve the uncertainty, leading to mathematical understanding. In this article, we examine how preservice secondary mathematics teachers’ thinking about a trigonometric relationship was impacted by a series of tasks that prompted uncertainty. Using dynamic geometry software, we asked preservice teachers to compare angle measures of lines on a coordinate grid to their slope values, beginning by investigating lines whose angle measures were in a near-linear relationship to their slopes. After encountering and resolving the uncertainty of the exact relationship between the values, preservice teachers connected what they learned to the tangent relationship and demonstrated new ways of thinking that entail quantitative and covariational reasoning about this trigonometric relationship. We argue that strategically using uncertainty can be an effective way of promoting preservice teachers’ reasoning about the tangent relationship.

Journal

International Journal of Mathematical Education in Science and Technology

Journal ISSN

0020-739X

Volume

50

Issue

4

First Page

527

Last Page

556

Digital Object Identifier (DOI)

10.1080/0020739X.2018.1527405

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