Strong math skills provide the foundation for a wide variety of careers, such as computer programming, law, design and medicine. To really learn math, kids need to move beyond memorization to understand how the concepts behind the formulas work in real-world situations. Manipulatives help them make that leap by bridging the gap between concrete objects and abstract math ideas.
With a little creative thought, any small object can be used as a manipulative. You can use marbles, toy foods or toy animals to sort into sets or to demonstrate the quantities different numbers represent. Use small puzzles or food-to-cut toys to teach fractions or geometric shape tiles to help teach spatial concepts. As long as you understand the concept you are trying to teach, you will be able to find objects that your child can use to learn it. Allow her to play with the manipulatives and experiment with the ideas so she can learn that there are many ways to solve problems.
It’s relatively easy to visualize early math concepts, such as quantity and simple proportions. As math becomes more abstract, however, concrete visualization becomes more difficult. Try to imagine how the angles of different shapes combine or what the number “a” in an alegebraic equation actually looks like. Manipulatives help bridge that gap. Children can arrange shapes to manipulate angles, or sort things into sets labeled “a” and “b” which can then be added or subtracted into new sets to make abstract equations more concrete. The National Council of Teachers of Mathematics have consistently recommended the use of manipulatives since the 1940s because of their effectiveness in helping kids move beyond memorization toward a deeper understanding of the underlying math concepts.
Children learn in different ways. Although some children learn best through visual or auditory presentations of ideas, others learn best by touching or manipulating objects. These learners are called tactile or kinesthetic learners, respectively. Manipulatives work within those modalities so that children who are less able to process purely visual text or auditory lectures can utilize their strengths to learn math. When manipulatives are used in the classroom, they typically supplement visual and auditory lessons so that all children are taught in their preferred modality. You can reinforce those lessons by providing your own manipulatives at home to help with homework or to play math games.
Children who used manipulatives showed both better retention for math concepts and reduced math anxiety when compared with peers who did not learn with them, according to a variety of studies summarized by Matthew Boggan, Ed.D., et. al., in a 2010 analysis for the Journal of Instructional Pedagogies. Manipulatives help because in addition to providing concrete links to abstract ideas, they allow kids to be active learners, and activity fosters a deeper understanding of difficult ideas. As your child masters concepts, her confidence increases which reduces any anxiety she might feel.