Understanding mathematical abstraction: A systematic literature review of its conceptualizations and research practices

Abstract

Mathematical abstraction is a fundamental concept in learning mathematics and plays a significant role in students' mathematical understanding. While this classic topic has been studied by mathematics education experts for a long time, both conceptually and in practice, it has many interpretations. This study aims to systematically review literature published from 2016 to 2022 in the Scopus database on mathematical abstraction. This review focuses on definitions of mathematical abstraction, research methods, mathematical topics, and educational levels in studies of mathematical abstraction. Using a systematic literature review approach, 68 articles and conference papers were initially identified, and after applying the PRISMA flowchart, 23 documents were selected that focused on mathematical abstraction. The studies were then analyzed through content analysis. The results showed that mathematical abstraction is generally understood as a process of constructing students' mathematical knowledge by drawing on prior mathematical expertise or experience. The majority of studies conducted used qualitative research methods at the Junior High School level, aiming to describe the abstraction process among students, including the difficulties encountered. At the same time, the most chosen mathematical topic was geometry. One of the most interesting findings of this research is that research on mathematical abstraction focuses more on assessing abstraction abilities through students' problem-solving performance than on examining how learners construct mathematical concepts. This indicates the need for future research to explore the process of student concept development in greater depth, thereby strengthening theoretical and pedagogical understanding of mathematical abstraction.