Investigating the transformation of a secondary teacher’s knowledge of trigonometric functions

• Published in: The Journal of mathematical behavior Vol. 62; p. 100869
• Main Author: Tallman, Michael A.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.06.2021
• Subjects: Enacted knowledge; Mathematical knowledge for teaching; Pedagogical content knowledge; Reflected abstraction; Trigonometric functions; Pedagogical content knowledge; Mathematical knowledge for teaching; Trigonometric functions; Reflected abstraction; Enacted knowledge
• ISSN: 0732-3123; 1873-8028
• DOI: 10.1016/j.jmathb.2021.100869

•A teacher’s awareness of her mental activity affects her learning goals.•Uncoordinated mathematical schemes have instructional implications.•Reflected abstraction can support mathematical knowledge for teaching. Shulman (1987) defined pedagogical content knowledge as the knowledge required to transform subject-matter knowledge into curricular material and pedagogical representations. This paper presents the results of an exploratory case study that examined a secondary teacher’s knowledge of sine and cosine values in both clinical and professional settings to discern the characteristics of mathematical schemes that facilitate their transformation into learning artifacts and experiences for students. My analysis revealed that the teacher’s knowledge of sine and cosine values consisted of uncoordinated quantitative and arithmetic schemes and that he was cognizant only of the behavioral proficiencies these schemes enable, not the mental actions and conceptual operations they entail. Based on these findings, I hypothesize that the extent to which a teacher is consciously aware of the mental activity that comprises their mathematical conceptions influences their capacity to transform their mathematical knowledge into curricular material and pedagogical representations to effectively support students’ conceptual learning.