Look for and Express Regularity in Repeated Reasoning… in Math!

My class was working on coming up with the "rules" for multiplying integers.  First, they used what they know about repeated addition (and rules for adding integers) to answer these problems.

Next, they cut apart the cards and sorted them into 3 categories… those that resulted in a positive answer, negative answer, and answer of 0.  Then I had them look at each category (one at a time) and report out anything they noticed in the problem that they could use to predict if the answer would be positive, negative, or zero.  My goal was to have them discover the rules that I used to just tell them:

positive x positive = positive
negative x negative = positive
negative x positive = negative
positive x negative = positive
anything x 0 = 0
0 x anything = 0

In the past, I might have just wrote this on the board, talked a lot, and expected student to apply the rules.  Having students do this "card sort" and come up with the rules themselves really helped them to make sense of the rules.  I thought this is a great example of  CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.

Then, I was thinking, how can I give my students more experiences to look for regularity in repeated reasoning in math.  How interesting that I want to encourage this in the mathematics context but discourage it in the social/emotional context because that leads to stereotypes of people and cultures!  I wonder if this contradiction could be confusing to students.  In math we are saying, "What do you notice is the same here?  Go ahead and try applying it to all situations that are like this."  But then in social/emotional settings we are saying "You notice something you think is the same here? Well, don't apply that to every situation!"  As teachers, I think it is important for us to look outside of our own content and be mindful of misconceptions that can arise when students apply what they learn in our class in their lives.  While we might not explicitly teach a lesson about how stereotypes develop and why they are harmful in our math classes, we can make sure that we are always modeling being kind, thoughtful, and considerate.  We can also reinforce this by having expectations and reinforcing these behaviors in our students when they work in partners or groups or even in class discussions.