How to Teach math Hands-on

What is CRA or Concrete Representational Abstract teaching? It's a hands on, research based strategy for teaching math concepts. It also happens to be my go-to strategy for teaching math topics. It especially works well with students that are struggling with a concept. 

So how do I teach using this strategy? I'm going to use a pretty simple topic to show you but it can be used with more complex standards also. ​

The first step to learning a new math concept is by doing it. It's called the concrete stage. This would be kids picking up objects and counting them. They are physically moving objects. There are a LOT of great math manipulatives out there to help with this. When we are learning anything that is adding or subtracting we use base-10 blocks in my groups. 

In the example above the student has 12 blocks and then added 3 more. They are physically moving the blocks. 

After my students are able to use the manipulatives well we move onto the next stage; representational. That's when they use a drawing to represent the concrete object. In our example above we used circles, but you could use hash marks or something else. 

The last step or stage is abstract. That's actually where a lot of our worksheets, or assessments are. They are at the abstract level and if a student's brain doesn't understand the concreate and representational stages then they will be less likely to be successful at the abstract level. 

When I see students in my groups making mistakes at the abstract level (like on a pre-test lets say) they almost always make the same mistake with the hands-on materials.