For many people, the mention of math manipulatives calls to mind cute little bears used for counting, or craft sticks tied in bundles to illustrate place value. Once those concepts have been learned, these people see little use for hands-on math tools. However, educators have discovered that using manipulatives helps students of all ages learn new concepts, deepens understanding, increases retention, and makes mathematics more interesting. This is especially important for students who may not yet be ready for unsupported abstract thinking. Being able to see, touch, and build a problem with manipulatives is vital for these students. Of course, you don’t want to give your middle or high school student a handful of bears to count. The manipulatives that are appropriate for older students have been carefully designed to bridge the gap between simple arithmetic and more abstract concepts in a developmentally-appropriate way.
Math Manipulatives for Everyone
Here are some of the advanced concepts that can be demonstrated with appropriate manipulatives:
- operations with fractions
- operations with decimals
- area, volume, and surface area
- operations with negative and positive numbers
- square roots
- place value in algebraic equations
- algebraic properties
- polynomial factoring
- operations with polynomials
- solving equations
Many adults who are shown polynomial factoring with place-value blocks or algebra tiles are astonished to see the abstract concepts so clearly represented. If older students are resistant to using manipulatives, take some time to model the process. Your involvement and attitude is critical to their success.
Once your student is convinced that the use of manipulatives is not just for “little kids,” he may make other objections to using them. Some students grasp new concepts quickly and don’t need manipulatives to solve a problem. It is still important for the student to be able to demonstrate the concept to the instructor using the manipulatives. Doing this successfully shows understanding rather than just the ability to follow a rote procedure. It also enables students who have difficulty verbalizing abstract ideas to demonstrate how they thought through a problem.
Other students need to spend more time building problems but are irritated by the extra time required. The key here is to insist on the necessary practice, but not to bore the students by requiring more than is needed. A successful student understands the concepts behind each problem and knows how to solve the problem efficiently.
You may be familiar with the Math-U-See manipulatives, which provide a foundation for many mathematical concepts. They include base-ten blocks, fraction overlays, and algebra/decimal inserts. Did you know that Math-U-See now offers an app that features all the manipulatives in an easy-to-use format? The app is a wonderful tool for students on the go who want their math lessons to be more portable. For more information, go to www.mathusee.com.