## Monday, October 24, 2016

### Because My Teacher Told Me To

My students know that my favorite question to ask them is "Why?"  Any time they "explain" their work by telling me the math steps they use, I always dig deeper.

• Tell me more about that?
• Why are those the steps you used?
• How did you know to multiply and not divide?
In a middle school math classroom, I find that more often than not students only response to these questions is "Because that is how my teacher told me to do these problems."

It is disappointing to me because I know that the teachers in previous years used visuals, manipulatives, and concrete examples to help students understand these concepts.  The fact of the matter is by the time they get to middle school the only thing that stuck with them was a rule, a trick, or steps to follow.

Some teachers feel very strongly about removing any tricks or shortcuts from math because they deprive students of this deeper understand of numbers that is essential to being able to apply math to unique situations.  So how do you know if it is sound math method or a trick?

• Is doubles +1 just a trick for adding 6+7?
• Is finding a common denominator a trick for adding fractions with unlike denominators?
• Is cross canceling fractions before multiplying just a trick?
Some teachers may see only the third one as a trick, however, the answer to all three could be yes or no.  It depends on how the students receive and retain this information.

• Are you simply outlining steps for them to follow?
• Telling students how to use a unit rectangle to solve 1/3 times 2/5 does not give any deeper understanding than telling them to multiply across.