MATHS ADVANCE BLOG

The ultimate aim of this blog post is to address the idea that maths should cover topics relevant to adult life. Typically given as examples are money management, tax returns, and various aspects of business mathematics. Whilst I sympathise with these suggestions and recognise their potential usefulness, I argue that they overlook some fundamental truths about engagement.

To make my case, I will first consider why people, especially learners, engage with narrative fiction. I will then draw parallels to the learning mathematics, and explain why the demand for more practical aspects may not align with key motivations for learning.

The topics of this blog post can accommodate a range of expert opinion. Whilst I cannot cover the full range of opinion in this post, I welcome any feedback. 

Engagement with Literature:

Years ago, I had an intriguing conversation with an ex-colleague, Teacher of English. She said that learners were more likely to engage with characters they can relate to. Indeed, a substantial body of research suggests that learners are more likely to engage deeply with characters and narratives that reflect their lived experiences. One might then suggest that the insistence on reading classic works from the literary canon is not always the most sensible approach.

This relatedness, however, is only one of the motivations for engaging with a specific text. During my research for this post, I encountered four established models of reader engagement: Reader-Response Theory (Louise Rosenblatt), Self-Determination Theory (Ryan and Deci), Transport Theory (Melanie Green and Timothy Brock), and Uses and Gratifications Theory (Katz et al.). While these models vary slightly in how they categorise motivations for engaging with literature, they convey a similar core message: readers engage for a limited number of key reasons. 

Drawing on the framework from Uses and Gratifications Theory, these reasons are:

• Entertainment: Reading for pleasure or as a form of escapism.
• Information: Gaining knowledge or understanding from the text.
• Personal Identity: Connecting with characters or themes that reflect the reader’s identity.
• Social Integration: Sharing the reading experience with others or feeling part of a reading community.

Engagement with Mathematics

This brings me to an intriguing question: can the reasons people engage with mathematics be analogous to the reasons they engage with literature? The connections may not be immediately obvious, but I invite the reader to explore this idea with me:

Entertainment:

There is potentially much to say about the ‘entertainment’ of mathematics: 

One aspect is the element of wonder often attached to concepts such as Fermat’s Last Theorem (below), Euler’s identity, and Gödel’s incompleteness theorems. The higher one studies mathematics, the more opportunities one has for such appreciation. Whilst it may be the case that KS3 learners have moments that might be categorised similarly, it is surely not one of the primary factors for the engagement of the majority of younger learners? 

In contrast to the awe experienced with complex theorems, younger learners encounter moments of clarity that bring about personal satisfaction. While these moments could be categorised as entertainment, they more closely align with the acquisition of knowledge and understanding.

Information:

Mathematics, at its core, is a tool for understanding the world. Similar to how literature provides knowledge and insights into different cultures and human experiences, mathematics offers a framework for making sense of patterns, data, and structures in the world around us. Beyond academic curiosity, this knowledge can also be useful for learners’ future employment or personal circumstances. This is perhaps the primary motivator for the majority as it might reasonably be said to derive from parental expectations. Information as a motivator for engaging with mathematics is often driven by parental expectations and societal norms. Mathematics is widely regarded as a critical subject for future success, whether in higher education or career prospects in fields such as engineering, finance, and technology. The pressure to acquire this ‘useful knowledge’ can be a strong motivator. 

If a learner is not driven by this underlying motivation, however, other motivation(s) will need to be found. A significant proportion of learners will often ask in mathematics, ‘When am I going to use this in real life?’ Even when the long-term value of a mathematical concept is evident, however, students may struggle to stay engaged if the material feels disconnected from their immediate interests and lacks relevance to their current lives. I will return to this point in the final section when considering functional mathematics specifically. 

There are also the aforementioned ‘lightbulb’ moments. For instance, a KS3 learner might be convinced of why any number to the power zero is equal to one when presented with a convincing demonstration, or a GCSE learner might see that the difference of two squares is just factorising a quadratic where the x-term is equal to zero. These moments are often enjoyed by the learner, but one might also reasonably categorise these as ‘personal identity/social integration’ in that the learner is keen to feel a sense of progress rather than a need for information.

Personal Identity/Social Integration:

Unlike in literature, where social integration can stem from shared cultural understanding, mathematics often fosters social engagement through competition and relative achievement. This dynamic shapes the way learners perceive their progress, with enjoyment often tied to their relative attainment.

The charts below show a noticeable trend: a sharp decline in the proportion of students who report enjoying mathematics upon entering secondary school. This shift often coincides with the introduction of ability-based grouping, which can influence how students perceive their aptitude and enjoyment of the subject. While the trends may not be immediately obvious, a comparison of the starting and finishing positions or the addition of trend lines clearly shows a general decline in enjoyment of mathematics. 

*One reason older primary learners may enjoy mathematics less is the transition from exploratory, play-based learning to more structured, formal instruction. As the curriculum becomes more rigid, focusing on abstract concepts and assessments, the enjoyment of discovery can diminish. This shift may be compounded by the introduction of standardised testing, which places pressure on performance over creative problem-solving. Such shifts will not be reversed in secondary school.   

The key point here is that learning for social purposes in mathematics is driven more by individual competition than by some form of group dynamic. 

Functional Mathematics and Engagement:

One common criticism of mathematics education is its perceived focus on abstract concepts at the expense of practical, real-life applications such as taxes, mortgages, and personal finance. Many adults lament that their secondary education did not adequately cover these areas of financial literacy. However, this criticism overlooks an important point.

Although concepts like compound interest have clear, practical applications, they often fail to capture the interest of learners. This is because, while undeniably useful, such topics lack the intellectual excitement that sparks curiosity and engagement. Nor do they have the immediate relevance necessary to motivate engagement from learners. Unlike abstract mathematical concepts which may challenge learners’ thinking, functional topics may feel distant or irrelevant to their current lives. To truly motivate learners, maths lessons need to go beyond practicality and offer moments of discovery: opportunities for students to challenge themselves and experience a sense of progress. 

Another blog post, coming soon.

George Bowman, Founder, Maths Advance.

https://mathsadvance.co.uk/