Abstract
The aim of this study was to determine the how pre-service mathematics teachers respond to unexpected questions from students about the second derivative. A qualitative research method was used for this purpose, applying a case study framed as an in-depth analysis of how pre-service mathematics teachers respond to students’ ideas. The participants were 39 pre-service mathematics teachers who were in their final year of their mathematics teacher education program. The pre-service teachers, who participated voluntarily, were asked to respond to open-ended questions relating to a scenario that included a teacher, as well as her 12th-grade students. The written responses that the participants provided constitute the data of this study. The results revealed that most of the participants could not effectively answer an unexpected question from students. Nearly half of the participants stated that they could not answer the question. Others ignored it, while some acknowledged the question and attempted to give an answer. Moreover, a small number of the participants made an effort to explain and demonstrate the concept of concavity by drawing the graphs of the function and relating them to the first derivative.
Highlights
Mathematics teachers’ knowledge and its role in enhancing students’ mathematical thinking and learning plays an important role in mathematics education; as Even (1993) points out, teachers’ professional knowledge is the most critical influence on students’ learning
This theory emphasizes the observation, analysis and development of mathematics teaching, with a focus on teachers’ subject matter knowledge and pedagogical content knowledge, and it has been regarded as an important theory in mathematics education (Breen, Meehan, O’Shea, & Rowland, 2018)
The current study focuses on the first code relating to the Contingency unit of the Knowledge Quartet (KQ), responding to students’ ideas, or teachers' responses to the thoughts produced by students in order to provide their mathematical development (Kula & Bukova Güzel, 2014)
Summary
Mathematics teachers’ knowledge and its role in enhancing students’ mathematical thinking and learning plays an important role in mathematics education; as Even (1993) points out, teachers’ professional knowledge is the most critical influence on students’ learning In consideration of this importance, Rowland, Huckstep, and Thwaites (2005) developed the Knowledge Quartet (KQ) to provide pre-service teachers with content-specific knowledge during the course of mathematics education. The KQ proposes a way of thinking about mathematics teaching in normal classroom settings, with a focus on the mathematics content of a lesson This theory emphasizes the observation, analysis and development of mathematics teaching, with a focus on teachers’ subject matter knowledge and pedagogical content knowledge, and it has been regarded as an important theory in mathematics education (Breen, Meehan, O’Shea, & Rowland, 2018).
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