RETURNING FROM BALANCING TO MODELING: INSTRUCTIONAL RECONSTRUCTION OF DIMENSIONAL ANALYSIS ON ANALOGY

Addressing the issues in dimensional analysis teaching—such as the overemphasis on algebraic calculations over physical mechanisms and the result-oriented approach to formula verification—this paper proposes a physics-led and problem-oriented instructional reconstruction scheme. By introducing high-school chemical equation balancing, which is mathematically isomorphic to the principles of dimensional analysis, as a cognitive scaffold, the study draws on the mechanism-led balancing paradigm to reconstruct the physical logic for selecting involved quantities and determining unit systems. In the selection of involved quantities, universal constants are defined as mechanism converters and a process is established based on physical laws. In the determination of unit systems, by drawing analogies with the chemical concepts of “atomic groups” and “ionic reactions,” the physical independence of dimensions is explored. Operations such as dimensional decoupling and redundancy removal are proposed to establish an “optimal physical unit system” tailored to specific physical processes. Comparative analysis of four typical cases demonstrates the advantages of this physics-led scheme in restoring physical images, enhancing analytical efficacy, and simplifying mathematical operations. This instructional reconstruction aims to guide students from mechanical algebraic trial-and-error back to the exploration of physical essence, improving “scientific thinking” and “model construction” competencies.