Increasing Mathematical Discussion

  According to both math standards and research, mathematical discussion is important to students learning mathematics because if they can clearly explain their thinking, it means they understand the concept.

Unfortunately, many of us do not include as much discussion as we'd like because of all the things we are mandated to accomplish in a 45 to 55 minute period.

When we listen in on various discussions, we are able to assess student understanding of the material.  Furthermore, we can tell how well they listen to others while being able to express their ideas, something they will need in the future.  In addition, it gives students a chance to develop the ability to construct arguments designed to defend their point of view.

It is important to create safe atmosphere in class so students feel as if they are creating a community.  It is a place where students are recognized for their questions while being encouraged to comment on ideas.  One part of this is for students to become active listeners so they are able to follow someone's argument and be able to counter it, should it become necessary.

Furthermore, it is important to encourage student interaction because it is the interaction which helps develop discussion.  This discussion should happen equally well in pairs, small groups, and whole class.  Unfortunately, one cannot jump directly to whole class discussions without allowing students the chance to become comfortable discussing math topics in pairs and small groups.

One way to encourage pairs discussion is to provide conversation starters such as:
#1 What answer did you get for problem______?
#2  I got____________.  Did you get the same answer?
#1 Yes.  How did you do it?
#2 Explains how he or she got it.
Continue with #2 taking the lead.

Another way is to set up prompts which hold students accountable for listening to what is being said.  For instance, a student might restate the point another student made when speaking.  A way to keep things interesting is to use Popsicle sticks with names or dice to select the next student.  It might also be necessary to ask the student speaking to repeat what they just said if they are too quiet.  In order to comment on someone's ideas, they have to hear them.

Finally, once students have learned to be active listeners and are able to restate the points, they can then agree or disagree with what was said by providing support for their stand. Although it can be a slow process, it is worth the time investment to help students become comfortable in expressing their ideas.

Let me know what you think, I'd love to hear.  Have a great day.