Teaching Mathematics through Variation Theory: A Systematic Review of Empirical Evidence

Source abstract

Mathematics teaching faces the challenge of promoting an understanding of relationships, properties, and concepts beyond the repetition of procedures. Variation Theory proposes that learning occurs when students are able to discern critical aspects of a mathematical object through the systematic variation of certain elements while others remain invariant. The objective was to analyze how Variation Theory has been applied in mathematics teaching and what contributions empirical evidence reports regarding conceptual understanding and problem solving. The review identified applications in areas such as arithmetic, algebra, geometry, functions, and calculus, mainly through task sequences designed around patterns of contrast, generalization, separation, and fusion. The reviewed studies indicated that the effectiveness of this approach depends on the selection of critical aspects of the content and on the organization of the variations presented to students. It was concluded that Variation Theory provides a didactic framework for designing mathematical learning experiences oriented toward conceptual discernment, although its application requires instructional planning linked to the specific characteristics of each mathematical content.