Metacognition

I'm going to suggest a way of looking at mathematics you may not have heard of. It became completely normal for me, and everyone I've watched make enormous gains in maths in a short window understands its importance. After some practice it'll be normal for you too. I didn't always think this way — but it matters more than almost anything else.

The word "metacognition" gets badly misread. The clean definition: thinking about your thoughts. After going through every resource out there for UK admissions prep, I haven't found a single person or institution treating this as the core skill it is. Honing it has helped me far beyond maths.

Metacognition is the awareness and understanding of your own thought process. It feels hard to initiate, and hard to picture in practice. Watch my videos and pay attention to what I say and write out — you'll see empirically what it looks like. (Even if you never take my one-on-one mentoring, I run free demo calls for anyone who reaches out, so come ask.)

The way you build it: verbally journal your thoughts, then dissect them as if you were reading someone else's diary — grading someone else's thinking, not your own. It's a skill of low supply and exponential demand. Once you've mastered and embedded it, it lets you plan, monitor and evaluate your own learning and problem-solving. I attribute nearly every fast gain I've made — well beyond maths — to obsessively practising this.

P.S. If you're applying to these degrees, I'll assume you've got some interest in quant finance, maths or STEM research. The ability to dissect your own process and fix your own cognitive pipeline is compulsory later — backtesting stochastic models, statistical work, the whole game. Prepping properly for the TMUA pays off long after the exam.

How does this help me prepare?

Because you need a data log of the cognitive procedure that led to the wrong answer. Picture crossing a moat to reach a castle — the correct answer — and laying stepping stones as you cross. Even if you don't reach the castle, you need to know exactly what your attempt looked like. That's why journaling what happened inside your head is how you backtrack your procedure.

What was the cognitive procedure I followed to reach my conclusion, and what was the procedure the model answer used to reach the correct one? Do it for the questions you got right, too — surprisingly often you'll find your process was cleaner than the model answer's.

So journals matter. But what exactly do you write? Just long entries of everything you thought? No. That's where command terms and reaction circuits come in.