# Process dimensions of mathematics

## Overview

Includes information to help learn and facilitate the learning and use of the process dimensions of mathematics.

## Problem solving Tools to facilitate mathematical problem solving

• Problem solving Concepts, misconceptions, & outcomes by levels in the mathematical knowledge base

## Reasoning and proof

• Reasoning & proof Concepts, misconceptions, & outcomes by levels in the mathematical knowledge base

## Representation

Representation Concepts, misconceptions, & outcomes by levels in the mathematical knowledge base

### Area representations

Lynne Outhred and Michael Mitchelmore asked learners to illustrate the area of a rectangular shape. They found learners demonstrated four different strategies: incomplete covering, visual covering, concrete covering, and measurement. The drawings below show samples from each.

### Representation of relative position of objects

Illustration of Internal Representation

Actual object, real world, or external representation

### Representation of external objects with points on an other external object

What does this have to do with mathematical representations?

## Communication

Communication Concepts, misconceptions, & outcomes by levels in the mathematical knowledge base

## Connections & perspective

Connections & perspective Concepts, misconceptions, & outcomes by levels in the mathematical knowledge base

### Information to facilitate literacy in connections & perspective & tools to achieve it

• Mathematical ideas build upon each other.
• Mathematical ideas are connected to other mathematical ideas.
• Mathematical ideas are connected to the world.

### Activities to facilitate reasoning & proof

Other math knowlege base &

activity pages

Content dimensions

1. WIn
2. NOnBA
3. THABTHIn
4. DUBA
5. SATOn
6. SHAPE
7. PETHOnBA
8. PETHABTHIn
9. SHOnKA
10. GTHEBOn

### Interesting book

The Power of Logical Thinking: Easy Lessons in the Art of Reasoning... and Hard Facts About Its Absence in Our Lives, Marilyn Vos Savant (1996) ISBN 0-312-13985-3 Saint Martin's Press: New York.