What does maths engagement look like?

In December 2017, I attended the Maths Association of Victoria conference at La Trobe University, Melbourne, which provided an opportunity to learn more about engagement in maths. The topic of student engagement in mathematics (or lack of) is a cause for concern among maths educators. A lack of maths engagement can “limit one’s capacity to understand life experiences through a mathematical perspective” (Attard, 2012a, p. 9).

I gained inspiration particularly from sessions led by Catherine Attard (an Australian researcher and maths educator), and Dan Finkel (a researcher and maths educator from Seattle, USA). In this blog post, I share with you some key insights and tasks from those sessions.

Catherine Attard

Attard immediately captivated us, as we got busy (and totally engaged!) folding a paper circle in many ways. The task involved us in rich discussion of the mathematical language associated with geometry and the attributes of 2D and 3D shapes, and engaged us in some deep thinking and mathematical reasoning. Take a look at this great task (and others) located in Attard’s excellent website: http://www.engagingmaths.com   https://engagingmaths.com/teaching-resources/

Attard cautions us, however, that although we might think students are engaged when they appear to be busy working and are on task, ‘it is only when students are experiencing cognitive challenge, are actively involved and are enjoying and appreciating mathematics, that they are truly engaged’ (Attard, 2012, p.23).


Engagement with mathematics (Attard, 2012b, p.23)

Attard also reminds us how important it is that we as teachers of mathematics are engaged if students are to be truly engaged. In her view, engaged teachers are ‘fully invested in teaching mathematics, work collaboratively with colleagues to design meaningful and relevant tasks, go beyond the minimum requirements of delivering curriculum, and genuinely enjoy teaching mathematics in a way that makes a difference to students’ (Attard, 2017, para. 5). In other words, teacher engagement in mathematics is critical for student engagement in mathematics!

number grid

In her session, Attard also challenged us to promote ‘substantive discussion’ in our classrooms, as a strategy for engagement. One suggestion for doing this was to use images for ‘Which One Doesn’t Belong?’ Discussing one of these images would make a great maths starter in a classroom, offering students the opportunity to think mathematically and to articulate and justify their thinking to classmates.

Dan Finkel

Dan Finkel’s session, ‘Playful Explorations to Deep Questions’, also captivated and engaged us. Finkel’s goal is ‘to give everyone the chance to fall in love with mathematics’. His website https://mathforlove.com/ is well worth a look – or better still, sign up to regularly receive informative emails and great maths teaching ideas.

You might also like to spend a very valuable 14 minutes watching Dan’s inspirational TED talk ‘Five Principles of Extraordinary Maths Teaching’. https://www.youtube.com/watch?v=ytVneQUA5-cI

He promotes these five principles to engage students in mathematics:

  • Start with a question
  • Students need time to struggle
  • Teachers are not the answer key!
  • Say yes to students’ ideas and questions
  • The willingness to play

Finkel suggests that the first job of teachers is to provide a rich environment for students to play, as often that play has deep mathematical thinking attached. Challenging play produces a state of ‘productive struggle’.

Like Attard, Finkel recognises the importance of student dialogue and building numerical conversations with students. Two questions in particular Finkel loves to use for promoting deeper discussion and thinking are ‘What if…?’ and “How many?’ Images such as the one below are particularly useful for discussing ‘How many?’


Follow this link for more ‘unit chat’ images (with teaching explanations) that make for great discussion based on the ‘How many?’ question in particular. Try some in your classes and enjoy the numerical conversations that result. https://www.dropbox.com/s/81ju3nei20543zv/Unit%20Chat%20Images%20by%20Dan%20Finkel%20-%20Math%20for%20Love.pdf?dl=0%3Cbr%20/%3E

Some final questions to consider:

  1. How might you enhance your own engagement with the teaching of mathematics?
    2. How might you adapt your own maths teaching practices to ensure that mathematics in your classroom is engaging for your students?
    3. How might you foster productive mathematical conversation in your classroom?

Lynn Davies
May 2018


Attard, C. (2012a). Engagement with mathematics: What does it mean and what does it look like? Australian Primary Mathematics Classroom 17(1), 9-13.

Attard, C. (2012b). Applying a framework for engagement in the primary mathematics classroom. Australian Primary Mathematics Classroom 17(4), 22-27.

Attard, C. (2017). Are you an engaged teacher? (Blog Post). Retrieved from https://engagingmaths.com/2017/05/23/are-you-an-engaged-teacher/

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