Archive for October 5th, 2012

Multiple Representations of Math Problems Increase Understanding

Posted on October 5, 2012. Filed under: Assessment, Common Core, Mathematical Proficiency | Tags: , , , , , |

It is important to have your students model their ideas in several ways.  Lesh, Post & Behr (1987) have proposed 5 different representations for concepts (cited in Van De Walle, 2006 p. 10).


1. Pictures

2. Written symbols

3. Oral Language

4. Real World Situations

5. Manipulative Models

Researchers have found that when students can represent ideas in various ways “there is a better chance of a concept being formed correctly and integrated into a rich web of ideas” (Van De Wahl (2006 p.10)


Let’s use a decimal example.  Ask the students “What is 4 x .25?”

Oral Language (reason it out and explain your thinking): First have them reason out the answer.  Think 4 quarters.

Real World Situations: Then have them tell you a real life story where you would use this equation.

Manipulative Models: Next have them represent it with decimal squares.

Abstract Model: Then have them show it on a numberline.

Pictures: Then have them draw it out with a pictorial representation such as circles or squares.

Written Symbols: Finally, solve the equation with numbers.

Do this with your students on a regular basis.  Think about your current unit of study and the concepts you are teaching.  Are you emphasizing multiple representations that require thinking beyond just “getting the answer.”  How do the anchor charts in your classroom support this type of thinking?  How does your Problem of the Day support this type of thinking?


Happy Mathing,

Dr. Nicki

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