The relative importance of knowledge of discrete facts (e.g., 12 + 5 = 17) or abstract concepts (e.g., mathematical equality) is debated and contributes to the math wars; the different assumptions and approaches of mathematics educators and cognitive scientists who study mathematical learning. Stepping back and approaching the issue using the properties of the controlled semantic cognition system could move the debate forward. The system supports conceptual learning across domains, and represents concepts as common properties of related experiences or things. These properties can be generalized across exemplars, contexts, and time and can be expressed across modalities. The concepts emerge slowly through statistical learning and will be shaped by the frequency and variety of exposures to experiences and things that share common features. The properties of the system help to explain why the ways in which math problems are presented (e.g., in textbooks) lead to conceptual understandings or misunderstandings; why repeated and varied (e.g., different surface structure) solving of problems that tap the same concept are required for concept learning; and, why mathematical concepts can be expressed through gesture, language, or visually. The approach has implications for improving children’s mathematical development.
DAVID C. GEARY (2026) studied this question.