DYNAMICAL VIEW OF PROPORTIONALITY: COVARIATIONS.

The article focuses on the concept of proportionality in mathematics education, emphasizing a dynamical view of covariation between quantities within ratios. Using a metal strip problem, it illustrates how changes in one quantity (length) simultaneously correspond to changes in another (mass), highlighting that proportional reasoning involves understanding the mutual transformation of related quantities rather than isolating a single missing value. This covariational perspective aligns with research by Lesh et al. (1988) and Piaget and Inhelder (1975), framing proportionality as a dynamic relationship between two ratios, where variations in one pair correspond directly to variations in the other. The article also references educational tools like the game Prime Climb and puzzles from Math for Love that support collaborative and playful engagement with these mathematical concepts.