# Make a Change for Good: Part 3

## Adopt a Piagetian approach to teaching mathematics concepts and skills

### Piaget Stages and A Piagetian Approach to Mathematics

Piaget is a name we don’t often read about these days. He proposed that children move through four stages of learning:

• His first stage (Sensorimotor) really only applied to children up to two years of age. But the next two stages are highly relevant to the elementary grades.

• Piaget’s Stage 3 (Concrete Operational) begins around Grade 2. In these grades students become more sophisticated in their thinking and begin to mentally visualize the concrete and pictorial manipulations as they apply them to more abstract problems. For example, if they have a strategy for 9 + 4, they can then continue to think quantitatively and apply the same thinking to 29 + 15. In the same way that “nine plus four has the same value as ten plus three,” then “twenty-nine plus fifteen has the same value as thirty plus fourteen.”
• The same thinking can be applied to 298 + 56, which removes the need to apply a traditional paper-and-pencil algorithm.

See this ORIGO ONE video for more on extending the make-ten addition strategy.

Not only does it make sense to use basic fact strategies as the foundation for computation with greater numbers, but due to Hattie’s study (see Part 1 of this series), we now know that this really works. The “effect” size of using this Piagetian approach is 1.28. As the average is 0.40, this represents more than three years of growth for each year of school! Perhaps it’s time to revisit Piaget’s classic thinking on how young children develop mathematical meanings and make it the mainstream approach to teaching mathematics in today’s classrooms.