What chess really teaches us about the path to mastery

Play is so often shunned in formal learning environments. The standard maths curriculum, for instance, is like a purgatory for student-novices; before they are given the chance to do mathematics proper, they have to consume a years-long diet of facts and procedures. ‘Play’ is the bit that comes after (if at all), once these supposed prerequisites are embedded.

Arguments against play centre on the idea that novices think differently to experts. There’s a large extent to which this is true. In a series of studies half a century ago, subjects were asked to memorise and recall chess board configurations. …


A quick guide to problem solving by analogy

Here’s something to puzzle over.

A patient presents with a malignant, inoperable tumour. The doctor can use a particular type of ray to destroy the tumour. Unfortunately, the ray will also destroy healthy tissue in the process. The rays cause no damage to healthy tissue at lower intensity but, of course, they will not destroy the tumour at that intensity either. Can you describe a way to destroy the tumour without causing damage to healthy tissue?

We’ll return to our patient shortly. Before that, let’s play a game.

Sum to 15 is a two-player game in which players take turns…


What magic(ians) and math(ematician)s have in common

I took up card magic last year after spending time on YouTube in thrall of Shin Lim (if you’ve never heard the name, now is the time to get acquainted). I’d had fleeting experiences with magic before. As a child I once scuppered a magician’s act by accidentally destroying his prop (two interlocking Polos). In later years I would teach mathematically-inspired tricks to groups of schoolchildren. But this was my first plunge into the craft proper. It was in the early stages of the pandemic, after I had been reliably informed that an effective coping mechanism for lockdown is to…


The BBC has announced it is “to deliver the biggest education offer in its history”, featuring hours of daily content for primary and secondary students across its channels.

For its part, the BBC deserves credit for delivering a public service at a time of desperate need. For many families, television will be the only means of accessing educational content during the coming period. It’s better than nothing — but only marginally.

Television-based lessons, however well produced, still leave no room for interaction, feedback or self-paced learning. That’s what computers are for. They generate the ‘thousands of forms of functions’ that…


My most cherished correspondence dates back to December 23, 2002: an offer letter from St Anne’s College, Oxford, to pursue a degree in mathematics. The dream subject at the dream university, and the catalyst for my development as mathematician and educator. I sat my exams, earned my grades, gleefully took my place. I didn’t realise it then, but that made me one of the lucky ones.

If history does not repeat itself then surely it rhymes. At around the same time I was preparing for my A Levels and looking ahead to Oxford, the SARS coronavirus emerged. I knew little…


What an EdTech CEO ignores about learning and teaching

Football simulation, yes. But learning? (source)

Did you hear the one about the EdTech CEO who thinks all learning activities should cater to low attention spans?

It would read as satire, except that Mohit Midha appears deadly serious. The boss of Mangahigh, an online maths platform, claims that video games offer a blueprint for the future of education, citing football simulator FIFA as an example for educators to follow.

Digital maths content is at the heart of my work and FIFA football is at the heart of my play. The article hints at little understanding of either.

(Full disclosure: I work on a product in the…


Mathematical thinking spans multiple worlds

My work keeps me in touch with maths educators from across the world. Recently, I have noticed a renewed emphasis on problem solving in the classroom. It is refreshing to see problem solving embraced as a core tenet of mathematical thinking, rather than simply an enrichment activity that resides at the edges of the curriculum.

One problem still lingers, however: the insistence that problem solving must be situated within real world contexts. Apparently, it is only in the real world that students can find mathematics useful and relatable. …


It is so much more than a formula

Why do we have to learn Pythagoras?

It’s a question that stretches back almost as much as the Greek maestro himself, and one that hip-hop artist and activist Akala recently challenged educators with. For maths education to find relevance and resonance with students, we have to interrogate the stock response of ‘because it’s useful’. Is utility really the goal of mathematical study and, if so, is the current brand of school maths even serving this purpose?

As currently taught, the usefulness of Pythagoras’ Theorem is far from obvious. The procedural diet of the curriculum elevates the Theorem as a…


We’ve just relaxed our human ambition

Photo by Ethan Miller/Getty

Am I the only one who feels a tad underwhelmed by Google Duplex? My social media feeds are filled with gushing platitudes over the virtual assistant’s handling of a simple haircut appointment. Some are even claiming the Turing Test has been passed. Putting aside the ethical ramifications of abdicating such tasks to the robots (a topic worthy of its own post), I’m left wondering: is this how low we’ve set the bar for human conversation?

Google Duplex may score top marks for authentic tone and delightful mannerisms, but the topic of conversation was hardly riveting. …


Where Paul Erdös got it wrong

I seem to keep encountering the following quote:

It appears on my Twitter feed every few weeks, is quoted in several maths books and, just this week, I found the words emblazoned on the office wall of a mathematician colleague.

The quote is attributed to Paul Erdös, the twentieth century Hungarian mathematician who was so prolific that mathematicians hence have identified themselves in terms of an Erdös number, a value that reflects their “collaborative distance” to the man himself. …

Junaid Mubeen

Mathematics. Education. Innovation. Views my own.

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store