The Psychology of Learning Mathematics [Skemp]

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Richard Skemp’s The Psychology of Learning Mathematics examines mathematics education through both psychological and mathematical perspectives. His central concern is how students actually construct mathematical understanding, rather than simply how they acquire procedures. Skemp discusses the formation of mathematical concepts, the development of mental “schemas,” the role of symbols and imagery, intuitive and reflective intelligence, and the interpersonal and emotional factors that influence learning. He argues that mathematics is particularly revealing because its abstract and hierarchical structure makes weaknesses in students’ conceptual understanding especially visible. 

One of Skemp’s most influential ideas is the distinction between instrumental understanding—knowing a rule or procedure and being able to apply it—and relational understanding—knowing both what to do and why it works, and being able to connect different mathematical ideas. He extends this discussion into a broader theory of intelligent learning, arguing for teaching that helps students construct interconnected conceptual structures rather than rely primarily on rote memorization. 

The book therefore connects mathematical learning with problem solving, communication, motivation, classroom emotions, and constructivist approaches to teaching, making it a significant work in the psychology and pedagogy of mathematics.

BOOK