Representations of Mathematical Ideas

Concepts

• Representations help organize, record, and communicate mathematical ideas.
• Representations help solve problems.
• Mathematical ideas are represented externally and internally.
• Mathematical ideas are represented with object and actions with those objects.
• The representation, null and zero are special representations of the lack of objects or ideas.
• All mathematical representations are connected to physical entities.
• When representing values graphically the use of a scale and units helps to visualize that representation and to do so more accurately and proportionally. For example the difference between six feet and ten feet is four. The difference between 72 inches and 120 inches is 48. How each are represented makes a difference as to communicating the equality or not.

Teacher tools

• Mathematical representations with language as nouns and verbs. Examples

Some representations

Area representations

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

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?