Mathematical Communication, What?, How? Why?

As teachers, we tend to spend more time teaching students content and  process than we do to communicate so when we ask them to explain their thinking, we get those blank looks, or I don't know, or shrugs.  We need to spend more time on this but if you are like me, teaching students to communicate their mathematical ideas was not part of my teacher training.  It has been shown that effective communication is needed for rigor and deeper understanding but most teachers have never taken time to instruct students in how to do it.

In addition, mathematical communication helps improve learning but gives students some real life experience similar to what they might face once they are out of school.  When asked to explain, it helps if they can formulate their thoughts into words or representation necessary to express them to others in a coherent, understandable manner.

Furthermore, mathematical communication helps deepen their conceptual understanding while expanding and refining it and it allows them to meld their ideas with others and it requires careful thought.

 

The process requires that students need to express themselves orally, using representations, and in written form.  One way to do this is through the use of literacy strategies usually used in English such as word walls, modeling, revision, shared writing, and examples.  All ways to show students how they need to talk and write math.  

As they prepare to share their thoughts, they end up reviewing what they know about the topic, make new mathematical connections, are able to organize their ideas, become able to decide how important the idea is to the topic, are able to share their ideas with others, learn and use the appropriate vocabulary, create a cohesive idea to share their ideas, and express the ideas verbally, written, or through some form of representation.

At the same time, they have to listen to others ideas, compare those ideas with what they know and believe, create new knowledge and add it to their own, decide how to respond and with what information, then deliver the response.

This is an ongoing process that repeats to refine their understanding continually.  During the process, students often discover their own weaknesses and misunderstandings.  Furthermore, teachers can use these communications as a form of assessment to help pinpoint student deficit. 

One important step is to create a classroom that invites communication.  Arrange the classroom so students can face each other because it encourages communications and have a carpeted area where students can gather in groups.  Place whiteboards so students can use them to illustrated their ideas.  Make sure students understand that errors are a normal part of the learning process.  Let them know your expectations for verbal, written, and representative forms of communications so they know what to do.  Finally provide lots of opportunities for mathematical communications using authentic contexts.

If you are not integrating communications into your daily class, you should start.  le me know what you think, I'd love to hear.  Have a great day.