STAGES IN PARTIAL FUNCTIONAL THINKING IN THE FORM OF LINEAR FUNCTIONS: APOS THEORY
2020
Purpose of the study: The purpose of this study is to describe students' partial functional thinking processes in solving mathematical problems based on APOS Theory. The problem in this study was formulated into the question, what are the stages of students' partial functional thinking in solving mathematical problems based on APOS Theory?.
Methodology: This study was conducted by with 44 students from the Department of Mathematics Education. The subjects of this study were asked to solve mathematical problems developed from (Wilkie, 2014). Then some of them were interviewed to learn their functional thinking processes. The subjects’ partial functional thinking processes were analyzed using APOS theory.
Main Findings: The results showed that, based on APOS theory, the students’ partial functional thinking consisted of several stages: 1) identifying the problem, 2) organizing the data, 3) determining the recursive patterns, 4) determining the covariational relationships, 5) generalizing the relationships between variations in quantities (correspondence), and 6) re-checking the generalization results. In this case, the students generalized the relationships between variations in the form of functions done partially using the arithmetic formula .
Applications of this study: The findings of this study can help teachers understand the stages in students' thinking processes in solving problems about functions and the difficulty faced by the students in understanding the functions.
Novelty/Originality of this study: The researchers identified stages in students' partial functional thinking in solving mathematical problems in the form of functions based on APOS Theory.
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