Reinventing Arithmetic: Implications of Piaget's Theory

A Revolutionary Approach to Teaching Math

In "Reinventing Arithmetic: Implications of Piaget's Theory," Constance Kamii and Georgia Declark present a groundbreaking approach to teaching mathematics that is based on the constructivist theories of Jean Piaget. This book challenges traditional methods of math instruction and offers a new way of understanding how children learn math.

Key Concepts

Piaget's Constructivist Theory

Piaget's theory of cognitive development emphasizes the importance of children's active exploration and construction of knowledge. According to Piaget, children do not simply absorb information from their environment; they actively construct their understanding of the world through their interactions with it.

The Three Stages of Cognitive Development

Piaget identified three stages of cognitive development:

1. Sensorimotor stage (birth to 2 years): During this stage, children learn through their senses and motor skills. They explore their environment by touching, tasting, smelling, and listening.
2. Preoperational stage (2 to 7 years): During this stage, children begin to use language and symbols to represent their thoughts. They can think about things that are not present in their immediate environment, but they are still egocentric and unable to see things from another person's perspective.
3. Concrete operational stage (7 to 11 years): During this stage, children develop the ability to think logically about concrete objects. They can understand cause-and-effect relationships, and they can solve problems by using trial and error.

Implications for Math Instruction

Kamii and Declark argue that Piaget's theory has profound implications for how we teach math. They believe that traditional math instruction, which is based on rote memorization and drill-and-practice, is not effective because it does not take into account the way children actually learn.

Instead, Kamii and Declark advocate for a constructivist approach to math instruction that is based on the following principles:

• Children should be actively involved in their learning. They should be given opportunities to explore math concepts through hands-on activities and investigations.
• Children should be allowed to make mistakes. Mistakes are an important part of the learning process. They help children to identify their misconceptions and to develop new strategies for solving problems.
• Children should be encouraged to collaborate with others. Learning math is a social process. Children can learn from each other by sharing their ideas and strategies.

Benefits of a Constructivist Approach to Math Instruction

A constructivist approach to math instruction has many benefits, including:

• Increased student engagement: Students are more likely to be engaged in math when they are actively involved in their learning.
• Improved student understanding: Students who learn math through a constructivist approach have a deeper understanding of math concepts.
• Increased problem-solving skills: Students who learn math through a constructivist approach are better able to solve problems.
• Increased confidence: Students who learn math through a constructivist approach are more confident in their math abilities.

Conclusion

"Reinventing Arithmetic: Implications of Piaget's Theory" is a must-read for anyone who is interested in improving math education. Kamii and Declark provide a compelling argument for a constructivist approach to math instruction, and they offer practical strategies for implementing this approach in the classroom. This book is a valuable resource for teachers, parents, and anyone else who is interested in helping children learn math.

Call to Action

If you are interested in learning more about a constructivist approach to math instruction, I encourage you to read "Reinventing Arithmetic: Implications of Piaget's Theory." This book is available in print and online.