# Making Math Meaningful with Manipulatives!

If you’re not a teacher, you may not be familiar with the term manipulatives, but you can probably infer what they are. Manipulatives are models that help children think and reflect on new ideas in math. They include resources that allow children to explore, question, guess and check, but more importantly, to play with the problem. Counters, toys, linking cubes, abacuses are just a few examples.

#### Why use manipulatives?

We all know the old adage: we learn better by doing and math is no different! Manipulatives give students, of all ages, opportunities to have a hands-on approach and develop deeper understanding of concepts. Research has shown benefits to using manipulatives all through life! That means, don’t be in a rush to move your child into more abstract ways of solving problems. There is a natural progression to manipulatives and you need to assess your child’s readiness before pushing them to a more abstract level. When choosing materials, they should be sequenced from concrete to abstract and from 3-D to 2-D. See the chart below for more information.

#### Transitioning from concrete to abstract manipulatives (Charlesworth, 2000)

 1) Start with real objects. Sensorimotor stage. 2) Move to real objects supplemented by pictures. Pre-operational stage 3) Once the first two are mastered, you can use cutouts of real objects. This is the transition from 3-D to 2-D, but the objects can still be manipulated. Pre-operational stage. 4) Now move to pictures. Transitional stage 5) Finally (and much later!) use paper and pencil. Concrete operations stage

So where do virtual manipulatives fit on this spectrum? Good question! I’m not sure! My guess is that they act like real objects because you can move them, but because they are 2-D, they might be more on par with the cut-outs level, in terms of concreteness (see step 3 above). Let’s see what Rory thinks. I’m going to get Rory to do a task with real objects and then do the same task with on-line manipulatives. Then we’ll see what he has to say! This task is an introduction to addition but it would also be great to use for lessons on one:one correspondence, decomposing numbers, counting on and  cardinality.

Well it looks like Rory prefers virtual manipulatives. It may have been the novelty of it or the fact that the computer images acted more life-like than the real objects! He claims that the boat was more real compared to my egg carton version and he liked that the bears kept looking at him (in case you couldn’t tell)! The important thing is that children are given the freedom to choose their own manipulative so that they aren’t restricted to one method. That way, they can discover their own way to reach a solution that makes sense for them. If he likes the on-line tool, on-line tool it is! But I’ll make sure he has the real objects on stand-by in case he’d like to use them as well.

Looking for manipulatives? Look no farther!

Click here for a list of manipulatives that teachers often use with this age group!

Are you a parent? The great thing is that anything can be a manipulative! You don’t need to run to a teacher supply store in order to help your child.

Click here for a list of great things to use at home!