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Using language purposefully when teaching mathematics

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It is important to encourage positive communication in a mathematics classroom to enhance understanding and engagement.

This can be done two main ways: by giving the students more voice and active participation in class and by altering your own communication style to be more conducive to learning.

Giving students more voice and active participation

Allowing students to openly communicate and share their understanding is an important strategy in fostering their understanding with mathematics.

It is suggested that teachers should implement two strategies to involve the students more in their learning. The first is to use more group work where there is an opportunity for peer to peer learning, and the second is where students are encouraged to share their findings to the class before the teacher summarises the learning obtained (Sullivan, 2011) .

graphic showing the advantages that come from adopting these strategies

Note: there is a description of this image in the downloads section.

Walshaw and Anthony (2008) identify that one-way delivery from the teacher does not provide “students with opportunities to engage in mathematical discourse” and thus stops “students from expressing what they were learning” (p. 531).

This quote from research by Hine et al. (2004) articulates that students need to be able to express mathematical language:

I do think it’s important that they’re able to communicate with other people and their peers. They will learn at least as much from each other as they will with me. To be able to do that they have to talk to each other. It’s also… one of the reasons I often… force them to say things because they need to be able to use the language because language itself carries very specific meanings; and unless they have the language to be able to, obviously communicate, but I think it also has something to do with their understanding as well (p. 52).
These strategies give students the opportunities to engage more with mathematical language and will therefore increase their understanding.

Altering teacher communication style to be more conducive to learning

The way teachers communicate about mathematics has a profound impact on the students’ capacity to learn. In this section, we will explore some strategies for purposeful language use in a mathematics classroom.
At times teachers can create barriers to learning through making simple language mistakes.
Here are some commons mistakes that teachers make:
  • Using the word “equation” rather than “expression”
  • Using “timesing” rather than “multiplying”
  • Using “minus” and “negative” interchangeably
  • Inaccurately using the term “apples and oranges” when discussing like terms (such as the cost of something)
  • Mixing up unknowns, variables, and parameters
Another way to use language purposefully when teaching maths is to ask good questions. The way questions are framed or communicated to students is a key part of them being able to understand and communicate maths ideas.
There are two types of questions: closed and open. Closed questions have a single correct answer and typically have less emphasis on the strategies and processes to get to the right answer. On the other hand, an open question cannot be answered with a yes or no, and therefore leaves more room for the student to explore the question and their answer.
Open questions offer a number of advantages including:
  • Bringing inactive students into the discussion
  • Allowing teachers to assess in real time whether a student has mastered a particular concept or what particular strategies they are using to solve a problem
  • Eliciting group work and discussion
Here is an example open question:
Your teacher asks you to cut triangles out of a square. How many triangles might you cut? Draw a diagram and explain your answer.

Using this open question, the teacher is able to check:

  • If the student recognises a shape within shapes
  • If the student recognises that the triangles keep repeating
  • If the student can explain how they found the triangles

The last way you can altering your own communication style to be more conducive to learning is to use visual mathematics.

Communicating concepts visually can be advantageous given the often abstract nature of mathematics. Indeed, some students may prefer working with visual representations of mathematics concepts rather than mathematics in written form e.g., a visual representation of an equation or formula. As Boaler and colleagues explain (2016), neuroscience suggests that our brains may be configured to think about mathematics ideas more visually than conceptually.

The below picture demonstrates the visual ways students represented the problem 18 x 5.

different visual representations of how six students solved 18 x 5. Each representation is very different and shows the different ways students problem solve.

This demonstrates how students can develop very different ways to solve the same problem using visual representations. Using visuals in mathematics “facilitates higher-level thinking, enables communication and helps people see the creativity in mathematics” (Boaler, 2016).

Boaler, J. Visual Math Improves Performance [Internet]. Stanford (US): Youcubed; 2016. Available from:
Hine, G., Anderson, J., Reaburn, R., Cavanagh, M., Galligan, L., Ngu, B., and White, B. Teaching Secondary Maths. Second Edition. Cambridge (UK): Cambridge University Press; 2021.
National Curriculum Board. Shape of the Australian Curriculum: Mathematics [Internet]. (AU): National Curriculum Board; 2009. Available from:
Sullivan, P. Teaching Mathematics: Using research-informed strategies. Melbourne (AU): Australian Council for Educational Research; 2011.
Watson, A., and Sullivan, P. Chapter 5: Teachers Learning about Tasks and Lessons. The Handbook of Mathematics Teacher Education: Volume 2: Tools and Processes in Mathematics Teacher Education. Rotterdam (NL): Sense Publishers: 2008; p. 109-134.
Walshaw, M., & Anthony, G. (2008). The Teacher’s Role in Classroom Discourse: A Review of Recent Research Into Mathematics Classrooms. Review of Educational Research, 78(3), 516–551.
© University of Southern Queensland
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