ABSTRACT
This chapter looks at a framework that was used to facilitate proportional reasoning in four-year longitudinal studies with children from the time they began fraction instruction in grade 3 until they finished grade 6. Proportional reasoning is one of the best indicators that a student has attained understanding of rational numbers and related multiplicative concepts. While, on one hand, it is a measure of one's understanding of elementary mathematical ideas, it is, on the other, part of the foundation for more complex concepts. Proportional reasoning refers to detecting, expressing, analyzing, explaining, and providing evidence in support of assertions about proportional relationships. The term proportional reasoning is used to describe sophisticated mathematical ways of thinking that emerge sometime in the late elementary or middle school years and continue to grow in depth and sophistication throughout the high school and college years.
