This is the second in a series of three blog posts exploring effective mathematics pedagogy, drawing on the insights of the Australian Association of Mathematics Teachers (AAMT) 2025 position on pedagogy in mathematics and Maths Australia’s ‘I-CRAVE Maths’ methodology. In this post, we will delve into strategies for developing mathematical proficiency in students.
1. The Power of Clarity: Clear Explanations in Mathematics
A cornerstone of developing mathematical proficiency is ensuring that mathematical concepts and procedures are taught with clarity. Maths Australia’s ‘I-CRAVE Maths’ emphasises the importance of explicit instruction and the use of clear mathematical language that is congruent and accurate for both current and future applications. This aligns with AAMT’s focus on making mathematical thinking visible and accessible through clear explanations.
When teachers provide clear explanations, they make the underlying structure of mathematics more apparent to students. This helps students to not only understand what to do, but also why it works, fostering a deeper and more robust understanding.
2. Making Maths Tangible: Representations and Manipulatives
Mathematical proficiency is also enhanced when students have opportunities to engage with mathematical concepts in a variety of ways. A core element of the ‘I-CRAVE Maths’ methodology is the use of concrete manipulatives and visual representations to support mathematical understanding. This directly implements AAMT’s emphasis on the value of representations and manipulatives at all stages of learning.
Manipulatives and representations provide students with tangible ways to explore abstract mathematical ideas. They can be used to model concepts, visualise relationships, and solve problems, making mathematics more accessible and engaging.
Maths Australia encourages teachers to critically consider the manipulative used however, to ensure that the tool is accurate and that it progresses the student mathematically, not being a mere time-filler that keeps them stuck in counting by units, for example.
It’s worth noting that while manipulatives are widely used with younger learners, their use is often discarded as students get older. This is a missed opportunity, as manipulatives can be valuable tools for learners of all ages to explore complex mathematical concepts.
3. The Value of Talk: Mathematical Dialogue and Discussion
Developing mathematical proficiency is not a silent endeavour! Maths Australia’s ‘I-CRAVE Maths’ encourages student interaction and discussion throughout the learning process, enabling students to articulate their thinking and reasoning. This aligns with AAMT’s emphasis on engaging students in mathematical dialogue to make their thinking visible and build understanding.
When students have the opportunity to talk about mathematics, they deepen their own understanding and learn from the perspectives of others. Mathematical dialogue and discussion foster a collaborative learning environment where students can share ideas, challenge assumptions, and refine their mathematical thinking.
Researchers have also shown the value in students hearing their own voice as they explain concepts, organizing information to be spoken and also retaining this knowledge more thoroughly as they engage this sense.
4. The Right Level of Challenge: Maintaining Appropriate Challenge
Mathematical proficiency grows when students are appropriately challenged. Maths Australia’s ‘I-CRAVE Maths’ advocates for differentiated instruction and the use of varied tasks to cater to different learning styles and levels, which supports maintaining appropriate challenge. This aligns with AAMT’s focus on ensuring all students are appropriately challenged and supported.
Providing tasks that are too easy can lead to boredom and disengagement, while tasks that are too difficult can cause frustration and anxiety. Effective teachers strive to find the sweet spot where tasks are challenging enough to promote growth, but not so challenging as to be discouraging.
Developing mathematical proficiency requires a multifaceted approach. By prioritising clear explanations, utilising representations and manipulatives (for all ages), fostering mathematical dialogue, and maintaining appropriate challenge, teachers can create a learning environment that empowers students to become confident and capable mathematicians.
We trust you have enjoyed this series of blogs that relate to AAMT’s position paper on Pedagogy in Mathematics (2025). We look forward to the opportunity to work with you, implementing all aspects of their recommendations into your numeracy instruction with fidelity for transforming numeracy outcomes for teachers and students alike. Contact us…..book a call with Esther White.
To learn more about our training, visit mathsaustralia.com.au/training