The Power Tools of Mathematics

When we think of mathematics we often think of numbers, shapes, graphs, equations, adding, subtracting etc. We often see math as “representing” items, equations or situations. Take for example representing five. We could represent it with the word “five” the symbol or digit “5” and the quantity of five using manipulatives. (Manipulatives are any object that helps us represent our thinking for example: blocks, unit cubes, pencils, counters etc.) Have you ever stopped to think about if we are using manipulatives enough?  My answer is “no we are not using manipulatives enough.”

When we use manipulatives we are striving to make things clear for the students. Manipulatives provide that hands-on experience where students define and defend their own understandings of each situation.

Within some of our classes there is the misconception that if the teacher draws the representation then a student will gain an understanding. That's simply not always true. When a teacher is using the manipulatives, drawing the picture or representing the situation with base-ten blocks or counters then the teacher is the one in control of the learning. Students have to be able to construct their own meaning. They do this through representing their thinking. Students may be a drawing a graph or 3D shape. They could be using different blocks, using different tools, whatever works for them. It's not a one size fits all.

If you're wondering if a student really understands the concept that you're trying to instill in them ask them to represent their thinking. Then look at what they represented and better yet talk to them about how they represented it. What this representation means to them? Why did you choose to use these manipulatives/tools? Would these tools/representation work in every situation?

Using manipulatives in the classroom is not as easy as just getting them out and saying here some tools get to it and do it. As teachers we need to model what we expect. We need to allow students time to understand what each manipulative can and should be used for. There are times when base ten blocks are not the right tool to use maybe we need a ten frame and two sided counters.

We need to think about how our students to tackle the problem. We need to purposely plan and know our students. We need to ask ourselves more questions: How might my students struggle with this situation? What specifically are they going to struggle with? What ways can represent their thinking?  How can using manipulative in this situation clear up those struggles or clear up those misunderstandings? What are the possible manipulatives to use to allow students effectively and efficiently represent their thinking? Manipualtives are a way for ALL students at ALL levels to show us what they understand and how they understand it.

By taking the manipulatives off the shelves and showing your students how they can use them to represent their thinking will change what you know or think you know about your students understanding.