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The other day I heard about a sad math situation. A group of children had graduated from kindergarten and had begun first grade. When it came to math time, the teacher told the students that they could no longer use math manipulatives. “Math manipulatives are toys for babies,” she said. “It is time to grow up.”
What?!?
In certain circles, there seems to be a misconception regarding manipulatives and math. I have heard people say that the progression of learning goes something like this:
- Children in kindergarten through second-grade use manipulatives.
- Children in third-grade through fifth-grade draw pictures.
- Middle and high school students use algorithms with paper and pencil to “show their work”.
This is incorrect! Every time a student learns a new concept, they should be shown with actual objects or manipulatives if possible.
Everyone Benefits
Unfortunately, when it comes to math and manipulatives, sometimes the tools of the trade are reserved for the “slower” student when in reality, everyone can benefit. In fifth grade, I struggled with the concept of area. It would have helped me tremendously to build arrays with place value blocks or tiles, and count the squares myself until I trusted the formula that area is length times width. Drawing it out on graph paper would also have been helpful. Instead, when I stayed after class to ask the teacher questions, I was told that I did not need to understand; I just needed to use the formula.
It wasn’t until I began to teach my own children that I discovered why some of the procedures I had used all my life to solve math problems actually worked. Time and again, I have watched students (and even adults) have that “ah-ha moment” when they break out the manipulatives and see why a specific math algorithm works.
Use the Tools of the Trade
Think about it. Would you teach someone to sew without allowing them to hold the needle and thread? Would you teach your child to cook without actually letting them add ingredients? It is the same with math as it would be for sewing or cooking. Using the appropriate tools builds understanding. It follows a natural progression to move from an actual item like fraction tiles, to drawing a picture of a fraction, to labeling fractions on a number line.
Often a math manipulative is something you already have on hand. Counting can be taught with buttons, cars, stuffed animals, beans and popsicle sticks. A clock can be the one on the wall, a toy, or you can make a clock out of a paper plate.
For teaching place value I like to use place value disks, with a homemade place value chart. I have also utilized popsicle sticks, leaving some as singles and others rubber-banded into groups of ten. Likewise, pennies and dimes work well and students learn the value of the coins at the same time.
Loose change is great for counting by 1’s, 5’s, and 10’s. When my child was in Kindergarten, we set up a little store. I marked empty cereal boxes etc. with prices under $0.50 and we played “store”. He learned numbers 1-50 in a fun, non-threatening way.
Other tools you might want to have on hand are dice, a tape measure, measuring cups, pattern blocks, and geometric solids. Older students should add fraction tiles, a protractor, and a scale to what you already have on hand.
Teaching Math With Manipulatives
Teaching math with manipulatives doesn’t need to be daunting. Let me reassure you with some simple suggestions to get you started.
Step One: Free Play
The first time I bring out a manipulative, I give my students a few minutes for appropriate play. For example, if I was using teddy bear counters, students spread them out for a few minutes and play with them before we begin to use them as “tools”.
Once the formal lesson begins, the manipulatives are no longer toys but become tools of the trade.
Step Two: Explore
As students work with the tool, ask questions that lead to discoveries. For example, if children were exploring with a meter stick, I would ask, “What in this room is bigger than a meter?” Then, “What is smaller?” I would show the students how to put the meter stick against the table to see if it was bigger or smaller to check their guesses.
Step Three: Teach
The following steps work with any new manipulative or concept.
- Explain how the tool is to be used.
- Demonstrate how it is used.
- Assist the child in working with the tool. If instructing at home, this could be done one-on-one. In a classroom setting, students could partner up with someone to practice. During this phase, the teacher should be involved, making corrections and giving feedback. Students can share their strategies, explain their reasoning, and ask questions.
Step Four: Practice Solving Problems
Students in this phase are solving problems independently. As they develop understanding, you may see the manipulative fall to the side. This is fine if they comprehend the concept.
The best textbooks will guide and explain how to introduce a lesson with the manipulatives. Directions can be found in the Teacher’s Edition of the text. Instruction should show a progression similar to the one I am describing.
Don’t Skip Manipulatives
So here’s the bottom line. If the text calls for putting coins into a cup to count, then don’t short change them (pun intended). Even if there are pictures of coins in the textbook, using actual objects reinforces the concept like nothing else.
Don’t be one of those parents or teachers who shuns manipulatives and moves directly into textbook independent practice mode. Students need background knowledge to comprehend why an algorithm works. You won’t need to use manipulatives every day, but bringing them out regularly will benefit your student or child. Watch their excitement as they catch on to sophisticated math concepts in a fun, non-threatening way that really makes sense.
