Marilyn Burns is a teacher and a leading math innovator. Here she answers the pressing question: What are math manipulatives and why is my child using them in school?
Manipulatives in Today's Classroom
Have you ever visited a new city and felt confused about finding your bearings, even if you had a map and directions? After a few days, you probably got a feel for the area, and even if you became lost from time to time, you could count on familiar landmarks to help you on your way. And with enough exploring, most likely you ventured with more confidence wherever you needed to go.
We can think of the value of firsthand experiences for learning mathematics in a similar way. Math has many areas — patterns, measurement, geometry, statistics, probability, and more — and they're often unfamiliar, abstract, and confusing to students. We need to help children develop the ability and confidence to find their way around in each of these areas, see how they connect, and know what to do should they forget a fact or procedure. Here are five reasons manipulative materials do just that.
- Manipulatives help make abstract ideas concrete. A picture may be worth a thousand words, but while children learn to identify animals from picture books, they still probably don't have a sense about the animals' sizes, skin textures, or sounds. Even videos fall short. There's no substitute for firsthand experience. Along the same lines, manipulatives give students ways to construct physical models of abstract mathematical ideas.
- Manipulatives lift math off textbook pages. While we want students to become comfortable and proficient with the language of math (everything from the plus sign to the notations of algebra), words and symbols only represent ideas. Ideas exist in children's minds, and manipulatives help them construct an understanding of ideas that they can then connect to mathematical vocabulary and symbols.
- Manipulatives build students' confidence by giving them a way to test and confirm their reasoning. One goal of the National Council for the Teachers of Mathematics Standards is to build students' confidence with mathematics. If students have physical evidence of how their thinking works, their understanding is more robust.
- Manipulatives are useful tools for solving problems. In searching for solutions, architects construct models of buildings, engineers build prototypes of equipment, and doctors use computers to predict the impact of medical procedures. In the same way, manipulative materials serve as concrete models for students to use to solve problems.
- Manipulatives make learning math interesting and enjoyable. Give students the choice of working on a page of problems or solving a problem with colorful and interestingly shaped blocks, and there's no contest. Manipulatives intrigue and motivate while helping students learn.