Communication In Math Class

I once had a parent very upset with me because I gave her son a math assignment to do with a partner.  “Are you trying to teach my child math or are you trying to teach them social skills?”  Well, both.

Times have changed since I was a student and since many of today’s parents were students.  It is true that my middle school math class was silent.  No talking was allowed.  We all sat in rows alphabetically.  I sat behind the same boy for all of 6^th, 7^th, and 8^th grade.  I never talked to him or any other students in class nor did we ever share our ideas in front of the class.

If one talks to adult mathematicians, however, it is clear that the work of a mathematician is social work.  Solutions are rarely arrived at on one’s own.  It is through collaboration and discussion that solutions are found. 

The new Common Core Math Practices reflect this.  One of them reads: “Construct viable arguments and critique the reasoning of others.”  Students need to learn to clearly explain their thinking to others.  They also need to learn how to disagree with and question the work of others in a tactful manner.

My husband and I recently remodeled our 50 year-old kitchen.  He was very invested in the color of the new floor.  He really wanted a deep reddish color.  I wasn’t focused on the floor at all and was ready to go with the first color suggested by the contractor.  I was focused on the backsplash and what kind of tiles to use there.   My husband wanted the backsplash to be plain white.  By bringing our two different perspectives together, we were able to create a finished product that is more complete and more elegant than we could have done on our own. 

I know you have had this experience too.  You worked on a work project, a house project, or had a discussion with someone.  By bringing your ideas together the final result was much stronger.

A math problem flows in the same way.  Yes, we can often solve a problem by using algorithms to get the solution but another person might have a more elegant way of getting to the solution.  Their path might take into account patterns or ways of grouping numbers thus making the problem so much simpler than you originally thought.  They might have attended to a piece of the problem that you hadn’t considered carefully enough, making the final solution more complete.  In addition, the sharing of ideas makes each person reconsider their perspective in light of new information and either reject their first idea or add to it.

By talking about math with our children, we can also help them see new connections in math and think about concepts in ways that may be different or new to our children.  We also help them learn that math is part of the real world.  It is not just something that is done inside of a math classroom.  We can work together on sudoku puzzles on an airplane or play Blockus together in the evening.  It is more enjoyable if it is shared.

It is funny to think back to my middle school math classroom.  In addition to regular math class, I was on the math team.  The same teacher practiced with us after school, solving complex problems together as a group but during our regular class time we were in those rows.  Why did the teacher teach the two groups so differently?  The implication was that kids who were good at math should talk about it and those who weren’t should listen quietly to the teacher’s ideas.  Maybe those of us on the team got better at math BECAUSE we talked about it after school.

Common Core directs all students today to be doing math like mathematicians.  We want them to talk and share ideas and learn from each other.  Not only will this prepare them better mathematically but it will make math feel like math is a part of their whole lives, not just their school lives.