CPD Workshop: An example of a Teaching for Mastery lesson for KS3

On Saturday 11 June, I was fortunate to attend the ‘An example of a Teaching for Mastery lesson for KS3’ workshop delivered by Simon Mazumder in Birmingham. 

The participants experienced a sequence of lessons aimed at developing a deep understanding of maths as opposed to encouraging students to resort to rote learning. Simon demonstrated how he informally introduces advanced ideas like Pythagoras’ theorem, irrational numbers, and operations with surds in year 7, whilst also developing fluency with more basic skills like cartesian coordinates, finding areas and properties of 2D shapes.

The session started with the classic question of finding the missing length of a cuboid with the same volume as a given cube. To everyone’s surprise, this question was part of a KS2 assessment, and we explored solutions accessible to primary students.

We were then provided with squared paper, which we were instructed to fold to form a set of axes. We plotted the vertices (-7,5) and (-3,5) of a square, after which we had to find the possible coordinates of the other two vertices. From Simon’s experience, no year 7 would typically spot the pair (-5,3), (-5,7), which he would use as an opportunity to intrigue them and conduct exploratory group work. 

A discussion about areas would then reveal that despite pupils’ beliefs, the side length of this square cannot be 2. Hence, the next task was to find the best approximation to 2dp of the side of a square with an area of 8 square units. Once students would be happy with an approximation, Simon would ask them to type √8 into their calculator and find the area of a square with this side length, following with a classroom discussion about the meaning of these results.

By looking at similar shapes, results like √8=2√2 would be deduced. Simon would then repeat the exploration starting with the points (-2,-6) and (4,-6), in order to consolidate the newly developed skills and to generalise the previous discoveries. He ended the session with an extension on finding the third vertex of an isosceles right-angled triangle with vertices (3,8) and (3,4), which beautifully links with the thinking developed in the whole investigation. 

In Simon’s lessons, mathematics was portrayed as a network of interconnected logical ideas. Concepts like operations with surds gained meaning and value as they were built naturally on previously explored mathematics. The teacher did not mechanically transmit abstract ideas, but rather connected students’ intuitive understanding to the formal machinery of maths.

In a system of standardised tests where teachers often feel the pressures of accelerating rather than going deeper, it was refreshing to experience a connectionist approach to teaching. I am looking forward to incorporating what I have learnt from this session into my own practice.

By Andreea Rotaru