ABSTRACT
Students who are successful in mathematics have a rich sense of what numbers mean and can engage in quantitative reasoning. Students can use concrete objects to demonstrate mathematical concepts, as when they use toy blocks to model an addition problem or cut a pizza into eight equal pieces to illustrate fractional parts of a whole. The process of representing their ideas helps students construct meaning, as well as organize and clarify their thinking. When students lack a foundation in concrete and visual representation, their attempt to perform symbolic operations often becomes a rote execution of meaningless procedures. Provide opportunities for students to model the same concept using a variety of different manipulatives and visual representations. The ability to represent mathematical ideas in multiple ways is a critical component of quantitative reasoning.
