Concrete/Pictorial/Abstract - Makes Math Make Sense

One of the key principles in Singapore Math is the concrete - pictorial - abstract approach, sometimes referred to as the CPA approach. In a nutshell, this principle accepts that young children need a lot of hands-on manipulation of objects, before going on to paper-pencil tasks. I'm sure many of us learned to do "math" without a true understanding of what was going on. This can lead to real frustration later on, when the math gets more complex and a deeper, truer math understanding is necessary. We often need to slow down, and make sure that we aren't just rushing children through math books.

Children are first introduced to a skill by acting it out with real objects. In my math group, we will be using Base Ten Blocks and other manipulatives often. In this way, children understand numbers and place value much better - that a 10-stick is really made up on 10 units. After using and getting comfortable with materials, then children can relate the skill to representations like pictures or diagrams. Finally, they reach the symbolic stage, and are now ready for doing equations using mathematical notations.

Today, for example, we worked on subtraction with renaming. I gave children a number to build using the base ten blocks, like "43". Once they built it with 4 10-sticks and 3 unit blocks, I then told them to show me what happens when they subtract 27, for example. We talked about how we would need to trade in one of the sticks for 10 units, thereby giving us 3 10-sticks and 13 unit blocks. Then we could easily take away the 27. More practice is needed, but the children enjoyed the exercise.