Functional Thinking and Self-Esteem: What Mistakes Do Students Make in Solving Growth Patterns and How Do These Mistakes Occur?

Abstract

There is an urgent need to undertake research on identifying the types and patterns of students’ functional thinking errors with regard to their self-esteem levels. Functional thinking impacts students’ learning success in understanding the concept of function, which is a complex aspect of mathematics that requires appropriate approaches and strategies to help students achieve mastery. The present study aims to analyse the types and patterns of functional thinking errors among students with different levels of self-esteem in solving growth pattern problems. Newman’s error analysis was used to analyse students’ errors in functional thinking. The study uses a qualitative descriptive design supported by quantitative categorisation of self-esteem levels, involving two research subjects selected from 34 eleventh-grade high school students with diverse backgrounds, genders and levels of academic ability. A task designed to elicit functional thinking skills was developed as a research instrument. Students who answered incorrectly were then grouped based on similar levels of self-esteem and error patterns. In order to clarify the errors made in solving the growth pattern task, one representative was selected to be interviewed from the group with low self-esteem and one from the group with high self-esteem. By integrating functional thinking, Newman’s error analysis and affective aspects, the research determined differences in errors between high self-esteem and low self-esteem students. Self-confidence, self-regulation and anxiety are all factors that influence student errors. The findings emphasise the importance of learning that balances cognitive and affective aspects.