Making Connections for Learners

Students enter classrooms with prior understandings and preconceptions. New understandings develop through engaging these prior understandings and experiences. Adults and children alike possess an inherent ability to develop strategies and mathematical reasoning. These informal understandings and abilities serve as a link to new understandings.

Certain mathematical preconceptions are counterproductive. Students need to know that mathematics is more than computations and procedural rules; mathematics is about solving problems. Importantly, all students need to know they have the ability to do math. Preconceptions can also include misconceptions about mathematical concepts. If misconceptions are not exposed and challenged, mathematical understanding can be impeded (Fuson, Kalchman and Bransford 2005).

Mathematical concepts become meaningful when they are embedded in socially and personally constructed contexts. Concepts are intelligible when they are decontextualized and uni-dimensional (Wilensky 1997). Engaging prior understandings and experiences can form a bridge between informal and formal understandings of mathematics.

Instructional approaches for engaging prior understandings and preconceptions include giving students opportunities to use their informal problem-solving strategies, building on these informal strategies to guide mathematical thinking into the formal mathematical discipline, encouraging students to discuss their strategies with themselves and others, and designing instructional activities that can effectively guide common conceptions into targeted mathematical understandings (Fuson, Kalchman and Bransford 2005).