MATHS ADVANCE BLOG

The Value of Unseen Development in Maths

In a data-driven age, where metrics and outcomes often dominate, the idea that some types of progress are immeasurable is often sidelined. Yet, development that defies easy measurement is both real and significant. Perhaps it is a consequence of the easy measurability of attainment in mathematics, or the psychology of its practitioners, but there is a systematic risk of overlooking skills that are less measurable yet just as important to learners’ medium and long term progress. 

Unseen Growth in Mathematics

In my first teaching job, I shared an A-Level class with the Head of Mathematics. As mentioned in a previous post, she was a first rate practitioner, and gave an interesting piece of advice to one of our year twelve learners who had underperformed in a recent test. The advice was not to revise the various rules for differentiation, or to complete the mixed exercise on logs and exponentials, rather it was to only hand in homework where every single line of working was to begin next to the left hand margin, no line was to contain more than one equals sign, and no line was to deviate from a horizontal alignment. This bit of advice worked wonders as this learners’ working was soon decipherable (with a bit of stubborness on our part), and in the following assessments method marks were easy to award. One suspects that this adjustment facilitated more frequent breakthroughs in understanding for this learner. Unfortunately though, this is an expectation of learners that is being lessened over time, and not part of the vast majority of mark schemes. Much else is not, and will not ever be, adequately measured by assessments: 

How do you measure resilience?

Edison required over one thousand attempts to create the lightbulb.

How do you quantify confidence to have a go at a problem?

For all his shortcomings, the below quote from Henry Ford still resonates today.

What is the value in thinking flexibly?

Florence Nightingale applied statistical methods to a domain that no one had thought to do so previously, with incredible success.

In teaching mathematics, it is easy to focus on measurable outcomes—grades, test scores, and the number of correct answers. However, these often prioritise short-term achievements over lasting understanding. To draw an imperfect analogy: it is like Edison dedicating himself to perfect the recipe for the long lasting candle, or Ford enhancing the performance of horse-drawn carriages. Similarly, emphasising measurable outcomes can miss the chance to spark intrinsic motivation and curiosity, the most powerful drivers of deep, enduring learning.

As we reconsider the goals of maths education, we might ask: what should departments prioritise at different key stages? What does leadership look like if it looks beyond exam readiness?

My own philosophy is to promote mastery, whilst embedding challenge, but this is not without hurdles. For one, educators face the pressure to quantify all progress, even when such assessment might undermine student curiosity, and when the data being produced is of questionable value. A friend recently asked me whether I had read the new Yuval Noah Harari book Nexus, in which he makes the argument that an overflow of data, without discernment, can obscure genuine insight. This is something I have thought for many years about progress data in schools when it is based on short term-testing: It is something that school leaders need to acknowledge and have courage to look beyond. 

At this point, I will surrender to my own better intentions by mentioning my own platform. I have been developing https://mathsadvance.co.uk/ since the first COVID lockdown as it was apparent to me then that schools did not have access to a resource that could provide challenge for their learners across the KS3/4 curricula. After years of considerable toil, and many valued contributions, I now think it meets the criteria to be a highly effective tool enabling schools to embed challenge across their provision. All questions are free to access, so I urge you to explore the site at your convenience, and consider how it might be used at a department level to provide opportunities for extending learning. 

I would greatly welcome any feedback.

Another blog post, coming soon.

George Bowman

Founder, Maths Advance.