Reasoning and proof in mathematics education : a systematic literature review

Abstract

This study presents a systematic literature review of 80 publications on reasoning and proof in mathematics education from 2019 to 2024. This review examined the distribution of the studies across mathematics content areas, educational levels, year of publication, and countries. In addition, it examined the instructional strategies and interventions that promote students’ reasoning and proof, the common challenges students encounter in understanding and engaging with reasoning and proof in mathematics, and teachers’ knowledge, beliefs, and attitudes towards reasoning and proof. The results show that most studies focused on geometry, with an apparent increase in research activity between 2019 and 2023. There were studies from 29 nations, thus signifying that reasoning and proof in mathematics education are internationally important. Türkiye, the United States, and Indonesia were the top three countries where the studies were carried out. Most of the studies were at the pre-service teacher education level, followed by the secondary school education level. The Guide-redirecting Warrant Construction instructional approach was found to be effective in improving students’ reasoning and proof. Furthermore, students have difficulty with reasoning and proof, which is aggravated by teachers’ low proficiency in these areas. The study identified important gaps in the literature and offered recommendations to address them.