You may have seen this video making the edu-blog rounds:
There’s a Place for Everything…
Manipulatives are a great tool for teaching elementary math concepts. Converting the blocks to pictures makes it easy for kids to sketch their ideas. But blocks and pictures should be steps along the way to abstraction, and no student should be forced to use them any longer than necessary. Fourth grade addition is MUCH longer than necessary!
Our goal as teachers is to help students progress from concrete (manipulative blocks) to pictorial (like this student’s sketches or the Singapore math models I call bar diagrams) and from there to abstract work (numbers and variables).
If a student understands place value — that the order we write numbers indicates the size of “block” they represent — then drawing pictures like these is mere busywork. It distracts the student from the important goal of solving problems.
[Hat tip: I first saw this video at Out In Left Field.]