Examining high school students' conception of the function concept from a theoretical thinking perspective

Abstract

This study explores the conceptions of functions among high school students through the lens of theoretical thinking, encompassing three core components: reflective, systemic and analytical thinking. A case study methodology was employed in this research. The data were gathered through interviews with 11 senior high school students and analysed using deductive content analysis techniques. The findings reveal that students needing more reflective thinking tend to resort to practical methods and quickly gave up when facing challenges. Those who showed limited systemic thinking often relied on incorrect or inadequate criteria to determine if an expression constituted a function and struggled to connect the function concept with other concepts. Students needing more analytical thinking faced challenges in employing mathematical language and representations for functions, verifying if an expression is a function or transforming representations and frequently overlooked quantifiers or logical connectors related to variables in definitional properties. In this study, the theoretical thinking framework, mainly used for university-level mathematical concepts, provided a broad perspective in determining high-school students' understanding of the concept of function. Future research should extend this approach to various educational levels and concepts to enhance our understanding of students' conceptions and enrich the theoretical thinking framework.