Students often struggle with mathematics and many teachers feel that they are spending too much time “re-teaching” math rather than teaching new mathematical concepts to their students. Researchers at the AIMS Center for Math and Science Education turned to the research of Dr. Leslie Steffe to find out why. The difficulties students experience are related to their conceptual understanding of number whether they can think about numbers in more than one way at a time. Students perceive mathematical situations differently than adults and their ways are meaningful and powerful. Students don’t have misconceptions, they have understandings built on prior experiences that have (so far) worked. The process of coming to understand whole number is far more sophisticated than adults may realize.

This team explores Dr. Steffe’s research on how children develop a sense of whole number in additive situations, which progress along a continuum from concrete material toward a completely abstract concept of number, and Dr. Steffe has identified specific stages of this development. Our goal is to design student experiences that teachers can use to adapt their instruction to the mathematics of their students in an effort to advance their students along this continuum as they begin to form an understanding of additive reasoning.

Observing and recording students at different places along the continuum and identifying specific indicators of the stages has allowed us to collect a video library of children demonstrating the different stages as identified by Dr. Steffe. These videos are used to help us share the research findings with classroom teachers. Information gained as a result of this project will be used to continue our pursuance of research that can address the difficulties students and teachers have in mathematics.