Levels Of Communication In Mathematical Discourse

 

As math teachers, we know we need to encourage mathematical discourse but as is often the case, we are told to do it but are not given the training to accompany the mandate.  I usually end up doing a bit more research to learn more about the topic so I can do a better job.  

Mathematical discourse is about helping students learn to talk about mathematics.  The discourse can involve six different forms of conversation but the choice of form indicates their level of mathematical literacy.  In the first level, they might use ordinary language which uses non mathematical language and vocabulary to convey ideas.  Instead of numerator, they might talk about the number on the top or division with the house. They use the language they have to communicate their ideas.

Next, they might use mathematical terms when they write or speak about ideas such as the cubed root of eight is two.  It is as if they can speak or write sentences that could be translated into symbols.  The third type of communication involves writing down the mathematical sentence using the proper symbols such as "x < 3" and are able to state that a number is less than three.They understand the connection between the symbols and the mathematical sentence.

The fourth type is the one where students are able to create models, diagrams, pictures or other visual representation to share mathematical ideas.  This connects abstract and concrete. Next is the ability to share unspoken assumptions or know what the non mathematical parts of a problem are such as when calculating the amount of sod needed for a 6 by 8 foot rectangular area and knowing what sod is.  Finally is the quasi-mathematical language are students who are missing certain words in their vocabulary, making it harder for them to express themselves mathematically.

Furthermore, the teacher can use these levels of communication to assess where the student is on the spectrum and to determine what they know or understand. It is the perfect opportunity to provide scaffolding to help students move from using non-mathematical language to using the proper terms and the associated representations.

As students develop mathematical literacy, their ability to engage in higher level discourse increases so they are better able to communicate their ideas, thoughts, and understanding.  For fluency students need to be able to create illustrations, drawings, or use manipulatives to provide a visual representation along with symbols, words, and correct vocabulary.

Next time, I'll look at ways to help students improve their literacy.  Let me know what you think, I'd love to hear.  Have a great day.