Hob fantasy image banner image Hob icon

Processes for the practice of mathematics

Problem solving Tools to facilitate mathematical problem solving

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

Information to facilitate literacy in problem solving & tools to achieve it

Activities to facilitate problem solving

 

Representation

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

Information to facilitate representation & tools to achieve it

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.

area image

Lynne Outhred & Michael Mitchelmore. Young Children Intuitive Understanding of Rectangular Area Measurement, JRME. 2000. Vol 31, #2. 144-167.

Representation of relative position of objects

image

Illustration of Internal Representation

 

image

Actual object, real world, or external representation

 

Representation of external objects with points on an other external object

image

What does this have to do with mathematical representations?

 

Activities to facilitate representation

 

Communication

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

Information to facilitate literacy in communitation & tools to achieve it

Activities to facilitate reasoning & proof

 

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.

 

 

 

 

Common sense & knowledge

Common sense Vs Knowledge

 

Counting in Winnebago

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

 

Interesting book

book cover

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.