MATHS ADVANCE BLOG

Why do so many able students feel disengaged in mathematics classrooms despite their potential? One related question discussed in this post is when should teachers move students from mastery-based learning to higher-order thinking and problem-solving?

Statement 1 from Chat GPT:

Mastery is the cornerstone of a solid mathematical education. It requires that students not only understand key concepts but can apply them fluently and flexibly across various situations. The Teaching for Mastery approach emphasises depth of understanding before moving on to the next topic, ensuring that students are not merely memorising methods but internalising them deeply. This model is grounded in the belief that a strong foundation prevents students from later difficulties in problem-solving, a belief that is supported by research in cognitive science.

Statement 2 from Chat GPT:

For schools to successfully implement extended thinking opportunities, there needs to be a cultural shift in how challenge is perceived and integrated into the curriculum. It’s not enough to treat stretch and challenge as an afterthought or as something that only happens in extracurricular settings. Instead, schools need to create an environment where challenge is embedded in everyday lessons.

Of course the prompts that produced these two statements were markedly different, but the two statements demonstrate a dilemma faced by departments and teachers: how and when should learners transition from structured routine practice into problem-solving and extending thinking? There is a strong consensus amongst MATS, and a variety of organisations that state precedence should be given to mastery over problem-solving. This is consistent with research, and the weight of evidence suggesting mastery to be an essential tool in tackling higher level problems. It follows that preferencing mastery is sensible at the level of the school or MAT as it makes it more likely that teaching is well adapted for the majority of learners. 

However, while the importance of mastery is widely accepted, there is growing evidence that more needs to be done to challenge the most able learners. The policy of mastery before challenge, therefore, needs to be reconciled with statistics such as those below: 

A report from Ofsted revealed that in around 40% of schools visited, the most able pupils were not making the progress they were capable of, especially during Key Stage 3 (ages 11–14), when foundational skills are being reinforced. Many schools failed to provide challenging tasks, leading to stagnation for high-ability students​(GOV.UK).

The Education Endowment Foundation (EEF) also reports that Key Stage 3 progress is often slow, particularly in subjects like mathematics, where students are not consistently being challenged to deepen their understanding. This reflects a broader issue with how teaching strategies at this stage fail to build on prior knowledge​(EEF).

There are certainly no easy answers to this quandary, and what is true in some educational settings will not be true in others. It occurs that achieving an appropriate balance between mastery and problem-solving/extension is difficult within individual classrooms, never mind across sets or multiple institutions. The timing of when to introduce problem-solving and challenge opportunities is key. If students are rushed into complex problem-solving without achieving mastery, they may struggle and become discouraged. On the other hand, delaying opportunities for stretch and challenge can result in disengagement for more able students who are ready to move ahead. Finding this balance is complex, and later in this post, I’ll explore my own solution to address these challenges.

One aspect here that often goes unmentioned is the role of feedback in motivating pupils. Research shows that feedback focused on effort and improvement, rather than purely on attainment, encourages students to develop a growth mindset. This is key in fostering resilience, particularly in problem-solving, where initial failure is often a part of the learning process. For example, Carol Dweck’s work on the growth mindset emphasises that when feedback celebrates effort, students are more likely to embrace challenges and persist in the face of difficulties, which is crucial for engaging in higher-order thinking tasks​(GOV.UK).

Providing feedback on problem-solving tasks that focuses on effort and improvement encourages students to take risks and engage more deeply. This gives learners the space to attempt complex problems without the fear of being penalised for failure. Offering optional extended problems across year groups also gives students autonomy over their learning, helping them embrace difficult tasks as opportunities for growth.

To address the challenges discussed, I believe schools need resources that support both mastery and meaningful problem-solving opportunities. Such a resource should cover the full curriculum and offer flexibility to be integrated into lessons for students at various levels. After four years of development, I created Maths Advance, a platform designed to help schools bridge the gap between routine practice and deeper challenge. For those familiar with the platform, I appreciate your continued support. If you’re new and curious, feel free to explore it here. As a thank you for reaching the end of the blog post, I am happy to offer a one sixth discount (usual price £120) to anyone interested in subscribing. Just mention this post when you get in touch!

As always, I would greatly appreciate any feedback, and I look forward to sharing more insights in future posts.

Coming soon.

George.