Examination of Pre-service Mathematics Teachers’ Mental Constructions of Function Transformation

Abstract

Learning and teaching function transformation has a significant place since it provides new opportunities for learners to use, reflect and discover knowledge related to the concept of function. This study's main goals related to the importance of learning function transformation are to examine pre-service mathematics teachers' (PMTs) mental constructions of function transformation from APOS theory perspective and identify their concept images and concept definitions of function transformations. Two frameworks, APOS theory and concept images and concept definitions, were considered in this study. The qualitative study adopted case study design. The participants were three female PMTs. Clinical interview methodology was used to collect the main data. Data were analyzed based on the APOS framework, and the descriptive analysis method was used in the process. The results of the study present PMTs' mental constructions as well as to their concept images or definitions of function transformation. In this study it is found that PMTs had limited knowledge regarding function transformation, but their mental constructions were changed throughout the process and they partially overcame their difficulties related to the families of functions and related function concept images and definitions.

Changes in students’ mental constructions of function transformations through the APOS framework

“…This paper is a part of a wider research, and we focused on the process and results obtained in the last phase (phase 3). The results of the first and second phases were presented in our published paper (Boz-Yaman & Yiğit Koyunkaya, 2019). All three phases are summarized in Table 1.…”

Research on Integrating Mathematical Modeling Thinking into Large, Medium and Small School Teaching

“…Some of these studies primarily explore the methods and effects of integrating mathematical modeling thinking into teaching, aiming to help students better understand and apply mathematical knowledge. Others investigate the application of mathematical modeling thinking in STEM (Science, Technology, Engineering, and Mathematics) education, focusing on nurturing students' interdisciplinary skills and practical problem-solving abilities [14,15]. Additionally, some studies focus on assessment methods and strategies for mathematical modeling, thinking teaching, exploring how to evaluate students' mathematical thinking and problem-solving abilities.…”