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

• David Glassmeyer ^[1] ; Aaron Brakoniecki ^[2] ; Julie M. Amador ^[3]
  1. [1] Kennesaw State University

     Kennesaw State University

     Estados Unidos

     
  2. [2] Boston University

     Boston University

     City of Boston, Estados Unidos

     
  3. [3] University of Idaho

     University of Idaho

     Estados Unidos

     

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• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 50, Nº. 4, 2019, págs. 527-556
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.