The most meaningful Mathematics instruction begins when kids have the opportunity to touch, manipulate, and physically move things. So many times I have seen teachers... (Myself included... Guilty!) of beginning instruction by teaching an algorithm! We soon realize that starting there gets us very far from where we ultimately want to be, because our angels have no understanding of the algorithm... From now on as you are planning your mathematics instruction I want you to think...
and no... Not Certified Public Accountant.
Ok so the "C" Stands for "Concrete"
Those are your hands-on, manipulative type of activities. I love using my base-tens or other counter types of items to complete concrete problems.
This picture shows how we would set up a subtraction problem using base-tens. Students especially need this hands-on approach when they are first learning how to regroup and when doing basic operations.
Next.... the "P" stands for "Pictorial"
That is simply having your student draw a picture to model what they did with their hands-on materials.
Here is a slightly different subtraction problem shown in the pictorial model.
Finally with enough exposure and manipulating the first 2 methods, students will come to the third or the "A" which we call the abstract. You could also call it the "algorithm.
Here again we have that same subtraction problem from above using the Abstract model.
CPA is not just for basic operations. But can be used with all of your mathematics concepts. Give your students that hands-on experience and they will amaze you with just how fast they catch on!