Expert's Corner: Conceptual Foundations in Math

Thom O'Brien has been with ExploreLearning for eight years in a variety of roles, including working with teachers to integrate Gizmos into more effective teaching in Math and Science. Thom has a Master's degree in Instructional Mathematics and he taught 7th grade math before joining EL.

Have your students worked through math problems, performing the mechanics of each step, but not having the foggiest idea why that procedure works? Some students have become masters at solving problems just by mimicking steps, rather than by really understanding what they're doing, and why. This disconnect can be the result of a lack of a deep conceptual understanding of the topic. Providing students opportunities to visualize the concepts, discuss their thinking, and work in small groups can help students build these conceptual foundations.

Today's mathematics teachers can infuse lessons with practice that supports conceptual learning. A great way to do this is with visual models of mathematical concepts and problems. Obviously, Gizmos are a great support for visual learning. Try just about any math Gizmo — for example Comparing and Ordering Fractions. This Gizmo helps students develop a visual representation of least common denominator and gives them a basis for understanding how to add and subtract fractions with unlike denominators.

In addition, teachers can move math classrooms towards conceptual problem solving with the language used in the room. Mathematical communication is saturated with "doer" verbs; write, draw, build, graph, multiply, for example. Simply adding in some "thinker" verbs such as think about, decide, explain, reflect on, and consider, help teachers take students down the road toward more complex mathematical thinking. As an example, try the Quilting Bee Gizmo. As a warm up activity, ask students to reflect on symmetry by having them find it in the world around them or in magazine pictures. Then with the Gizmo, ask them to extend their thinking by considering additional lines of symmetry in the quilts they have been working with.

Read the research behind Gizmos for more information on how simulations can be powerful tools for improving student learning.

Go go GIZMOS!!!