The significance of mathematical knowledge in teaching elementary methods courses: perspectives of mathematics teacher educators

Abstract

Our study investigates perspectives of mathematics teacher educators related to the usage of their mathematical knowledge in teaching "Methods of Teaching Elementary Mathematics" courses. Five mathematics teacher educators, all with experience in teaching methods courses for prospective elementary school teachers, participated in this study. In a clinical interview setting, the participants described where and how, in their teaching of elementary methods courses, they had an opportunity to use their advanced mathematical knowledge and provided examples of such opportunities or situations. We outline five apparently different viewpoints and then turn to the similar concerns that were expressed by the participants. In conclusion, we connect the individual perspectives by situating them in the context of unifying themes, both theoretical and practical.

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

“…J. Dougherty, Bryant, Bryant, Darrough, & Pfannenstiel, 2015;Sangwin & Jones, 2017;Simon, Kara, et al, 2016;Vilkomir & O'Donoghue, 2009). Likewise, with investigations about inverse functions, most focus more on errors made by students in solving problems (Carlson et al, 2015;Kontorovich, 2017;Paoletti et al, 2018;Zazkis & Kontorovich, 2016;Zazkis & Zazkis, 2011). In this section, the researchers conclude reversible reasoning during the process of solving inverse function problems.…”

“…It is in accordance to the findings of the previous study ( Paoletti et al, 2018;Wasserman, 2017), which suggested that researchers need to survey to assess teachers' mathematical knowledge in interpreting inverse functions. So the factors that cause students to experience confusion in the rank -1 (Kontorovich, 2017;Zazkis & Kontorovich, 2016;Zazkis & Zazkis, 2011) and students interpret functions and inverses analytically and graphically (Carlson et al, 2015) can be described in detail.…”

“…One of the barriers to solving these mathematical problems is the confusion to understand "superscript −1 " as a reciprocal or inverse function. Zaskis and his colleagues (Kontorovich, 2017;Zazkis & Kontorovich, 2016;Zazkis & Zazkis, 2011) have revealed that when a number is followed by an exponent (superscript −1), it will involve inverse (usually appears in the context of dividing or multiplying fractions); negative superscripts (associated with exponential operations); and inverse functions (associated with function compositions). In addition, Zazkis discovered two interpretations of superscript −1 suggested by students: (1) students considered □ "# as a homonymous symbol in different contexts (fractions or functions), different terminologies (inverse), different procedures and symbols; and (2) students perceived □ "# as a polisemy focused on general words or acts implied from the words.…”

A study of future physics teachers’ knowledge for teaching: A case of a decibel sound level scale

“…Moreover, descriptions of K4T often highlight topics related to the current state of affairs in the field of education, such as contemporary advances in educational technologies, ethical challenges, student engagement, and unsolved problems. Researchers appear to agree that subjectspecific K4T is paramount for effective teaching and this pertains to teaching all subjects, including elementary or secondary mathematics (e.g., Zazkis & Zazkis, 2011) and science (Campbell et al, 2014;Depaepe et al, 2013).…”

Towards exploring expertise in mathematics education research: What are the requirements and duties of the researchers?

“…In teacher education, the relations between mathematical knowledge and pedagogical knowledge are explored and discussed extensively (e.g.,Jaworski, Wood & Dawson, 1999;Zazkis & Zazkis, 2011).…”