Using Manipulatives In Math Class

The book chapter "Tools For Learning Mathematics" by Van de Walle describes various physical and digital manipulatives to aid in the teaching and learning of mathematics and the benefits of using them. Math is about understanding complex patterns and concepts about numbers, being able to visualize complex ideas helps people to better understand them.

My strongest memory of math in Grade One is using place value blocks. These are a memorable physical tool for teaching the idea of thousands, hundreds, tens, and ones. Physical representations of math concepts makes it fun, memorable, and easier to understand. Instead of just meaningless numbers on a page, place value blocks help children understand what these numbers represent. I think they could also be used to help children understand what is really happening when they add, subtract, multiply, and divide three digit numbers. The methods are more memorable when it is understood why they work.

The chapter discusses the use of calculators. I was always taught in school to think the use of calculators was basically cheating, which it is if you're doing basic addition, but by high school they were commonplace. The chapter describes neat things that can be done with a calculator even in the younger grades, for instance, helping to understand counting by fives or other numbers.

I find math much easier to understand when I can picture it in my head or draw it. This is why some more complex concepts, like I learned in high school, elude me. I can't fully conceive of an imaginary number because I can't visually represent it. I do not understand how imaginary numbers can be used because I do not fully understand what they are. I feel that the more complex a math concept is, the less it lends itself to visual and tactile representation, and therefore harder to make sense of. Perhaps higher level math needs to find ways to keep grounded in visual and tactile representation. Is it harder to represent or does it just seem that way because of how it's taught?