Co-variation and Invariance in Proportional and Non-proportional Situations (Pre-print version of "Burning the Candle at Just One End")
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.Suggested Citation
Kien H. Lim. "Co-variation and Invariance in Proportional and Non-proportional Situations (Pre-print version of "Burning the Candle at Just One End")" Mathematics Teaching in the Middle School 14.8 (2009): 492-500.
Available at: http://works.bepress.com/kien_lim/11