Teaching for Mastery Sustaining Workgroup: A Professional Development Journey

By Swapna Agarwal and Aditi Rudra

Aditi and I have been attending the Teaching for Mastery Sustaining Workgroup, a professional development initiative led by the National Centre for Excellence in the Teaching of Mathematics (NCETM). This program aims to support teachers embed the mastery approach into everyday teaching practices, focusing on helping students achieve a deep and sustainable understanding of mathematical concepts.

Fluency 

In our first session, we explored the core mastery principle of fluency in learning. Fluency is more than just knowing the "right answer"—it’s about combining efficiency, accuracy, and flexibility to solve problems with confidence and adaptability. To develop fluency, we focused on designing tasks that push students beyond traditional memorization and procedural thinking. Here’s an example: 

3 x 0.5 x 8

Most students approach this calculation from left to right. While this method works, it isn’t the most efficient. A more fluent approach leverages the commutative law of multiplication to reorder the numbers. Instead, multiplying 0.5 x 8 first, allows the calculation to be completed more efficiently. This approach not only simplifies the process but also demonstrates flexibility in thinking—students recognize that the order of multiplication can be adjusted to make calculations easier. Students were then able to take this exercise forward when looking at more complex calculations such as calculating the volume of a cuboid or multiplying numbers in standard form. 

This led to our first key takeaway: the vital role of question design in developing fluency. Carefully crafted tasks can challenge students’ conventional thinking and encourage them to explore more efficient and flexible strategies. This, in turn, deepens their understanding and builds a more robust foundation for problem-solving.

Mathematical Thinking

In our second session, we delved into the idea of mathematical thinking. This principle shifts the focus from passive learning to active engagement, where students are encouraged to not just receive information but to work with it, reason through it, and discuss it. Our work at the session looked at how visual representations can be used to support students in identifying patterns, making connections and embed long term-memory of the concept, displayed in the image below. 

Following the session, Aditi and I facilitated an INSET session for all colleagues teaching Year 8, focusing on developing students' understanding of proportional relationships through multiple representations. We explored three key approaches to proportional reasoning: ratio tables, double number lines, and graphs. During the session, colleagues collaborated to examine the similarities and differences between these representations and identified key characteristics, such as the function multiplier and scalar multiplier, within each approach. The discussion also emphasized drawing connections not only between the representations themselves but also within different areas of mathematics.

This led to our second key takeaway: the power of using multiple representations to deepen understanding. Representations such as ratio tables, number lines, and graphs allow students to draw on their familiarity with concrete models while exploring the connections between different approaches. By linking these representations, students can develop a more comprehensive and interconnected understanding of mathematical concepts.

Application to Other Subjects
The principles of fluency and mathematical thinking, explored through this mastery CPD, are highly transferable across the curriculum. For instance, in English, fluency can be seen in developing students' ability to craft sentences that balance efficiency and nuance—moving beyond rigid structures to adapt language for specific contexts. By designing tasks that require students to rearrange sentences for emphasis or clarity, teachers can foster a flexible understanding of syntax and style, much like rearranging multiplication for efficiency in maths.

Similarly, multiple representations can be employed in science to deepen conceptual understanding. Consider teaching energy transfer: using diagrams, equations, and physical models side by side encourages students to connect theoretical principles with practical observations. These methods ensure students not only memorise facts but also develop the ability to reason and explain their ideas, creating a rich, interconnected understanding akin to exploring proportional reasoning with varied visual tools in mathematics. By extending these approaches beyond mathematics, we can enrich teaching practices across the curriculum, cultivating learners who are confident, flexible, and ready to tackle complex problems. 

Participating in the Teaching for Mastery Sustaining Workgroup has been incredibly beneficial. It has given us practical strategies that can be applied in the classroom to promote a deeper understanding of mathematics. We look forward to continuing this journey and sharing these practices across the department to ensure that teaching for mastery becomes a standard approach in our school. If you like to explore Teaching for Mastery and related workgroups, visit www.ncetm.org.uk.