## What are math manipulatives?

Math manipulatives are objects learners can use to represent abstract pieces of  mathematical information, providing a hands-on way to explore and understand math problems so children can better visualize the concept. For example, when you use fraction strips to show your child visually that 1/2 is larger than 1/3, the concept of fractions gets a whole lot easier because he can now “see” it with his brain. Denominators can be confusing until kids can really see that a fraction is just a piece of a whole, and that the denominator tells you about the size of the piece and the numerator tells you how many pieces you have. In addition to helping children “see” math problems, manipulatives also provide valuable tactile understanding. Tactile learning builds a deeper, more profound understanding of math concepts. The more of your child’s senses you can involve in learning, the better.

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As a kid, I loved school and I would always finish my work quickly and then my teachers would ask me to help the other kids. Even back then, I intuitively knew that manipulatives (although I did not have the terminology) were the best way to help all of my little friends “see” math the way I did. So I would drag everything out of my desk and show my classmate how addition and subtraction worked with pencils or erasers. I’d group crayons into tens with hair ties to explain place value. I’d trade my classmate a bundle of ten for ten ones when she had too few in the ones column to subtract the number below (borrowing). Do you know how I knew the value in “seeing” and “touching” math? I used it constantly myself — counting, adding and subtracting with my fingers, toes and whatever I had on hand. I knew my little tricks had helped me, so I taught them to my classmates and friends.

Over the past four decades, studies conducted in many countries across multiple grade levels indicate that math manipulatives substantially improve mathematical understanding and ability. Math manipulatives help children to understand abstract concepts by equating them to something concrete. Young children think of their world in concrete, tangible ways.  They collect information about objects they experience in daily life and organize those facts as they classify objects into categories. Abstract thinking, on the other hand, typically doesn’t develop until children are about age twelve or older. As children develop the skill of abstract thinking, they learn to deal with concepts they haven’t directly experienced, learning to draw their own conclusions from previous experiences.

That’s not to say that younger kids can’t understand advanced math concepts. Just take the extra effort to use math manipulatives to make those concepts tangible and concrete. A good example is my eight-year-old who has spent a good part of this year learning Algebra. When I first introduced it, I used an actual, physical balance scale to demonstrate that I could only keep the scale balanced (which is what the equal sign signifies) by doing the same thing to both sides of the balance. I also demonstrated that she would never be able to quantify an unknown (variable) unless she could get it by itself on one side of the equation. Because she understands that concept in a concrete way, she’s never struggled with Algebra concepts. You can make seemingly abstract concepts concrete with the right visuals. That, my friends, is the beauty of math manipulatives.