The Relationship between Quality of Understanding and Problem-Solving Ability in Mathematics Learning: A Systematic Literature Review

Abstract

The quality of understanding and problem-solving abilities are essential components in mathematics learning. Understanding serves as a foundation for students to comprehend mathematical concepts, while the ability to solve problems allows students to use their knowledge in everyday contexts. The purpose of this study is to explore the relationship between students’ quality of understanding and their problem-solving ability through a systematic literature review. The review focuses on how instrumental and relational understanding influence students’ effectiveness in solving mathematical problems. The search process was conducted using Harzing’s Publish or Perish software with Google Scholar and Scopus as the primary databases, limited to studies published between 2014 and 2025, resulting 30 relevant articles. The findings demonstrate a consistently positive relationship, where relational understanding contributes more strongly to effective and flexible problem-solving than instrumental understanding, especially in non-routine tasks. This review offers a clearer comparison of the relative roles of instrumental and relational understanding in supporting problem-solving, which has not been explicitly emphasized in earlier studies. Additionally, factors such as learning style, prior knowledge, reasoning skills, gender, emotional intelligence, and adversity quotient were identified as complementary influences that shape both understanding and problem-solving performance.