Communication in Mathematics


If students communicate their thinking in a variety of ways orally, visually and in written form when problem-solving in mathematics, then students will have a better understanding of the concepts and be able to explain their thinking.

Students that participate in gallery walks and receive descriptive feedback from the teacher are more apt to explain their thinking with justification.

My inquiry evolved as I collaborated with teachers to assist students in being able to communicate their thinking in mathematics. I began to wonder "how can students communicate their thinking in a variety of ways and how does this communication assist students to fully understand the concepts being taught?"

Mathematical Processes

The Mathematical processes align with the Ontario curriculum as shown in the gears above. These processes are integral to problem solving. Students deepen their knowledge and understanding as they develop, refine and use these processes in doing mathematics.



  • I worked in four schools in total, two from October to January and two from February to June
  • School visits were twice a week
  • Worked with students in grades 1, 2, 3, and 6
  • Used the co-learning model at some locations
  • Evidence was collected and shared through the triangulation of data (field notes, interviews and video recordings)

Literature Review


Student Voice

SWST When you do math, do you prefer talking about it or just working on your own?

Malika and Aryan both say at the same time Talking about it.


Malika If we need help we can talk about it.

Aryan We can share our ideas and plans.

SWST Do you learn from one another?

Aryan Yes, we learn from one anothers’ habits and ideas.

Malika How we can improve.

Aryan How we think and can correct our mistakes.

SWST Do you ever find that you can learn from others and that you can teach something too?

Malika and Aryan Yes!

SWST Do you ever teach someone else the strategies you’re using?

Malika Yes, we discuss them and then we tell them our strategies.

Aryan They tell us their strategies too.

SWST Does that help you?

Aryan and Malika Yes.


Malika It helps us understand their way of thinking.

Aryan Yes, so we understand what’s going on in their mind and our mind and we combine our thoughts and answers.

Key Learnings

The key learning for me as an educator is that one cannot assign a level 4 only to students that are able to communicate their thinking in written form. As educators we need to honour multiple forms of communication. The author Marian Small outlines in her book Making Math Meaningful to Canadian Students, different forms of communication.
  1. Oral Communication (speaking and listening)
  2. Written Communication (reading and writing)
  3. Symbolic, graphical, or pictorial communication
  4. Physical communication through active involvement with manipulatives.

Historically, we as educators have given more credit to written communication than any other form.

I have also learned that students need time to discuss their ideas, strategies and solutions when problem-solving in mathematics. This allows them to justify their thinking and reflect on what they've learned. Through these discussions teachers can identify what students are thinking and determine what instruction students need to move their thinking further.


If students communicate their thinking in a variety of ways orally, visually and in written form when problem-solving in mathematics then students will have a better understanding of the concepts. My inquiry has lead me to believe that when students participate in gallery walks they are more apt to communicate their solutions to their peers clearly. Students listen to one another’s mathematical thinking. Oral communication allows students to use mathematical vocabulary and explain why something is correct or incorrect. Written and pictorial communication provides students with the opportunity to show their thinking. Students stated that gallery walks allow them to “see the answer”.

The purpose of academic discourse in the mathematics classroom is to determine what students are thinking. Asking open ended questions, using “talk move” strategies and providing students with descriptive feedback all contribute to allowing students to communicate their thinking clearly. It is through effective questioning that allows the teacher to determine how students arrive at a conclusion. Once teachers understand student thinking then they provide the necessary feedback to expand their thinking and what is causing the confusion in their thought processes. ( Small, 2009, pg.70)

When students work in learning environments where purposeful talk is present and the teacher facilitates discussions and asks further questions then students will communicate their thinking clearly and with justification.

Student Work Study -Monograph- June 2013

If you wish to read a more detailed version of the monograph please contact Shannon Beach.