Co-variation and Invariance in Proportional and Non-proportional Situations (Pre-print version of "Burning the Candle at Just One End")

Kien H. Lim, University of Texas at El Paso

Abstract

In learning proportions students must understand what makes a situation proportional. If all the missing-value problems encountered by middle-school students involve proportional situations, then there is no need for students to check the equivalence of the two ratios in the proportion they set up. The use of non-proportional situations presents a need for students to analyze the problem situation, determine the manner in which quantities co-vary, and identify the relationship that is invariant.