Multiple Solutions: More Paths to an End or More Opportunities to Learn Mathematics

Abstract

Similarities and differences among multiple solutions to two different problems (How much skin covers the human body? and How many melon balls in a melon?) and how thinking about the differences among problems and their solutions can be used to extend students' understanding of mathematical concepts and skills. The article discusses the teachers' questioning skills as they focused on the conceptual and procedural aspects of the alternative solutions. The authors noted that when the solutions differ conceptually, the conceptual diversity of solutions helps students refine their understanding of definitions and nuances of underlying concepts.