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.

The Power of the Do Now language

By Ruhina Cockar

In this blogpost we’re going to revisit one of the 5 Quick Wins we spoke about on INSET day - the Do Now!

Why do we call our starters, “Do Now”’s at Westminster Academy?

We don’t often talk about the rationale behind the language we use so let’s talk about Do Nows versus Starters. 

The term "Do Now" originates from the Teach Like a Champion (TLAC, 2010) framework, developed by Doug Lemov. At the time, TLAC was a groundbreaking book detailing deliberate pedagogical practice and has made a huge impact in education in the UK since. 

As educators, we understand the importance of the first few minutes of a lesson - it is crucial for setting the tone, engaging students, and ensuring a purposeful start to learning. The “Do Now” is a short, focused activity that students begin immediately upon entering the classroom. The key here is that the Do Now is ready, written on the board or given to students as they enter. At WA we expect the Do Now in its entirety (including going through answers) to be no more than 10 minutes of the lesson structure. We want to prime students for the learning to come, not take time away from progressing the learning.

“While you are greeting students at the door, or finding that stack of copies, or erasing the mark-ups you made to your overhead from the last lesson, students should already be busy, via the Do Now with scholarly work that prepares them to succeed. In fact, students entering your room should never have to ask themselves, ‘What am I supposed to be doing?’ That much should go without saying. The habits of a good classroom should answer, ‘You should be doing the Do Now, because we always start with the Do Now.’” - TLAC, Doug Lemov

The language of “Do Now” as opposed to “starter” is deliberate to promote a sense of urgency - students begin the work straight away, reducing idle time and maximising the time on the task and their learning. 

The language is designed to transition students from entering the classroom into the learning mindset required for the current lesson. As the teacher, you can then align this with other evidence-based strategies such as retrieval practice or reviewing previous learning/prerequisites required for the lesson to engage and support students with the new concept/knowledge being taught. 

The “Do Now” is also designed to promote self-management through building routines and predictability in the classroom. This in turn fosters independence and focus - students know the expected behaviour at the start of every lesson. This ensures that the teacher is then able to manage other tasks, like taking the register or addressing individual student needs.

We know from the EEF Improving Behaviour in Schools Report that Consistency is Key (recommendation 6) so all staff, every lesson delivering Do Nows in this way adds to the power of the Do Now to support maximising learning time in lesson.

Working with Quick Win 1: Meet and greet at the door, together with Quick Win 4: Do Nows should be short, these are powerful, practical strategies to transform the way lessons begin! 

Reflective Questions for you:

1. How often do you speak to students about making every minute of their learning count? How do you foster that sense of urgency?

2. How purposeful are your Do Nows currently?

3. Do your students start their work independently, or do they often rely on you for direction during the first few minutes? What can you do to change this?

4. Is a predictable routine that helps students transition smoothly into learning established?

5. How do you gauge the effectiveness of your Do Nows? What evidence do you use to decide if they’re working?

6. What adjustments could you make to ensure your "Do Now" activities better meet the needs of your students?

7. It might be helpful to revisit the guiding questions from the INSET on how to think about your Do Now activity:

1. What do they need to remember in order to make sense of today’s learning? From last lesson? From any time before?

2. What are the misconceptions arising when I’ve taught this lesson/topic before?

3. What is a question that all students can answer on this? (This should help devise the first activity in particular)

Sources:

• Lemov, D. (2014). The Do Now: A primer. Doug Lemov’s Field Notes. https://teachlikeachampion.org/blog/now-primer/

• Ensuring a smooth and successful start to the lesson - Evidence Based Education - Blog post 

• EEF - Improving Behaviour in Schools Guidance Report