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.
• Do you jump too quickly to formalizing their understanding?
• I am guilty of this.  "Ok kids.  We just did 2 problems. What patterns do you notice? Yep, we just multiply across. Let's do that from now on."  It's no wonder students don't remember why we do things in math.  They latch onto that algorithm because it is time to move on.
• Do you give time to explore? 
• This one I am focusing on this year and find myself struggling. We use manipulatives and eTools, but are the students exploring?  Again, it depends on how we approach things.  Giving students some direction is ok:
• adjust values to see what happens
• try drawing visuals
• create patterns
• look for common attributes or differences
• Is there time for discourse and sharing strategies?
• Don't pigeonhole students into one approach.  If it isn't the most efficient method or the one you were hoping for it is ok.  Continue the conversations and do purposeful activities (think about activities/questions where they can't use their go to strategy) to move students in their understanding.  

While I see the shift in math instruction towards deeper understanding, I think it still falls short.  Many students are now just memorizing different strategies.  There is still too much spoon feeding of information (I know because I am still doing it.  If I don't want to and it still happens imagine how much is going on in classrooms where teachers are not even aware).  The Breaking the Cycle Video by Tracy Zager highlights the need for professional development and a shift in teacher mindset.

I encourage all of you to continue to ask the question why and when students can't answer think about what you can do to help build math sense and deepen their understanding.