Barbara J. Dougherty

Multiplicative reasoning (MR) is a central focus of elementary-grade mathematics. Students develop MR as they learn multiplication and division, which according to most standards (e.g., Common Core State Standards in Mathematics [CCAA-M; NGA Center & CCSSO, 2010]; California Common Core State Standards for Mathematics [California Department of Education, 2013]), begins in Grade 3 and continues through Grade 5.

Many rules taught in mathematics classrooms “expire” when students develop knowledge that is more sophisticated, such as using new number systems. For example, in elementary grades, students are sometimes taught that “addition makes bigger” or “subtraction makes smaller” when learning to compute with whole numbers, only to find that these rules expire when they begin computing with integers (Karp, Bush, and Dougherty 2014).

By Terry Crites, Barbara J. Dougherty, Hannah Slovin, and Karen Karp; Barbara J. Dougherty, Volume Editor; Barbara J. Dougherty, Series Editor, Putting Essential Understanding into Practice Series Do your students suppose that if the perimeter of a shape increases, the area also increases? Do they think that area is the product of base and height, without understanding that this applies only to parallelograms?