- Tell me more about that?
- Why are those the steps you used?
- How did you know to multiply and not divide?
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?
- 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.
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.