Using Manipulatives in the Classroom

One of the hardest things about teaching math to children is the fact that you're an adult. We don't think about numbers in the same way our students do because we've learned Algebra. Most of us were never taught using math manipulatives, or if we were, it was only in early elementary. Most of us were not taught in our college courses how to incorporate them into our teaching. We might have them in our classroom cabinet gathering dust because we're either afraid they will become weapons of mass chaos or we have no idea what to do with them. After this blog post, I hope your views on manipulatives will have changed and you'll be inspired to pull them out of the dark and use them with your students!

Why are Manipulatives Important?

Manipulatives help make math more concrete for students. Numbers always relate back to some amount of things, and allowing students to move those things around will help them understand what is happening when we apply different operations to them. Now, I know that most state tests do not allow for use of physical manipulatives, but students don't start the beginning of the year ready for those state tests. These are tools to help students build conceptual understanding of the math. Worst case scenario, the students use their scratch paper to draw representations of the manipulatives they used in the classroom throughout the year. Manipulatives also make math more engaging for students, and help them build their mathematical confidence. I know that in the beginning, it can seem like you're spending a lot of time trying to set expectations about how they should be used in class and trying to help students make connections between the math and the object, but in the long run the use of manipulatives in your classroom will cut down on the amount of remediation and re-teaching you have to do later on. This is because the students' understanding of the math will be more complete once they (and you!) get the hang of using the manipulatives in the classroom!

Classroom Management

Let's get the big scary stuff out of the way first. Children have a natural inclination towards playing. This is fine, as long as we are able to pull them back to the reality of the lesson and get them working. It's even better if we can trick them into thinking they're playing the whole time, while we're secretly teaching them. When you first give manipulatives to your students, allow them time to examine them and explore what they can do. You can structure this by including a question or two on their recording sheets asking them to describe the manipulative or write down things they observe.

Some students need a little help with organization, so providing a workspace for them is often very beneficial. This can be a piece of construction paper on their desk that their manipulatives need to stay on. You can extend this and require only the manipulatives that are part of their answer to be on the paper while the rest are on their desk. This will help you see what they are seeing, as well as keep things a little more orderly.

Some teachers have their students put both hands on top of their heads when it's time to listen to instructions. This will only work if you sell it to them, but even middle school students will buy into it if you believe in it. Having some sort of attention grabber and signal from the students is important, but make sure it fits with your personality and the personality of the class.

If the manipulatives end up in the air or on the floor in manners that are unacceptable, give a warning to the offender, and make it very clear that if it happens again, they will have to do their assignment without the manipulatives. If it happens again, take the manipulatives away for the day. Let them try it again the next time the manipulatives get pulled out with a clean slate, but repeat the process if necessary. Being firm about this at the beginning of the process will save headaches down the line.

At the end of the class, make sure you've scheduled time for the students to put everything away properly. You can enlist student helpers if necessary, but it is not your job to clean up after them. No matter how old the student is, they are old enough to put things back!

When Should We Use Manipulatives?

Manipulatives should not only be used during Centers or Stations. They should not be used sparingly. They should be available to students as often as humanly possible. Students will wean themselves off of the manipulatives when they start making the connections between the object, the symbol, and the mathematical idea both represent. Additionally, students will begin to realize there are faster, easier ways to solve the problem that do not require using the manipulatives once they become comfortable with the concepts. If you are familiar with the 8 Standards for Mathematical Practice, you'll recognize what I'm about to say next. Our students need to learn which tools are appropriate to use in each situation. One way to help them with this skill is to provide students with multiple types of manipulatives and allow them to choose which one to solve the problem. Sometimes their choices will surprise you and you'll learn a new way to approach not only the problem, but the manipulative as well. Sometimes they will choose a manipulative that is not the most efficient, but that's ok. They will learn.

[Anecdote Time: I had my 6th graders measure their heights so we could calculate the mean height for their period as well as the entire grade. I provided them with a bucket of different tools to use that included rulers, measuring tapes, meter sticks, and calculators. As I circulated around the room, I noticed one student lying down on the floor with another student moving a small object along the length of his body. While I thought it was incredibly strange, I let it go because they were working well together. As I collected the recorded heights, we had a great conversation about different units. One student was 5 feet 8 inches. Another student was 150 centimeters. Finally, the student from the floor told me proudly that he was 183 paperclips tall. I wrote it down, because it was technically correct. We got to extend our conversation about units to include nonstandard units, and the efficiency of standard vs. nonstandard units. The moral of the story: just because on the surface it seems wrong, doesn't always mean it is!]

Which Manipulative Do We Use?

Be careful about only using manipulatives for one concept and one concept only. Sometimes it seems as if a certain type of manipulative is only good for one type of skill, but that's rarely the case. For example, while Linking Cubes might seem like they are only good for geometrical models and exploring area and perimeter, they are also excellent for place value lessons, as well as exploring fractions and ratios. Algebra Tiles at first might seem like they should only be used for Algebraic purposes. If you compare the unit tiles to a Two-Color Counter, the only real difference is their shape. I'm in the process of creating a Google Doc with descriptions and activities for each of the more common (and some uncommon) math manipulatives to help in this particular area. If you have any suggestions for additions, please send them my way!

How do you use manipulatives in your classroom? If you don't use them, what are some reasons you don't? Share in the comments!