How I Think About Teaching
Teaching is mostly a listening problem.
The instinct, when you know something well, is to explain it. To find the clearest path from where you are to where the student needs to be and then walk them down it efficiently. That instinct is wrong often enough to be worth examining. The clearest path from your vantage point is rarely the path the student is actually standing at the start of.
What tends to work better is finding out what the student already knows — not just the content, but the mental models, the analogies they reach for, the places where their intuition is good and the places where it quietly misfires — and then building from there. This takes longer at the start and saves a lot of time later.
Difficulty and confidence
Most of my students at QQI Level 5 and 6 arrive with some version of the same history with mathematics: they were told, somewhere along the line, that they weren't a maths person. The category got fixed early and the evidence since then has mostly been interpreted through that lens.
What I've found is that the category is almost never accurate. Most of these students can do the mathematics. What they can't do — yet — is tolerate the particular kind of not-knowing that mathematical work requires. When a problem doesn't immediately resolve, when you have to sit with something unclear and keep working, the learned response is often to conclude that this confirms the original story: I'm not good at this.
A large part of what I'm doing in the first weeks of any course is working on that response directly. Not by reassuring students — reassurance is cheap and doesn't stick — but by designing problems where the experience of getting there is available quickly enough that the students get to find out for themselves that they can do it.
Programming helps with this more than almost anything else I've tried. When a piece of code works, it works. The feedback is immediate and unambiguous and not filtered through someone else's judgment. Students who have been failing mathematics for years will stay up troubleshooting a program because the problem feels solvable in a way that abstract algebra didn't. That feeling is correct: it is solvable, and so was the algebra.
Integration
I teach programming and mathematics as integrated subjects wherever the curriculum allows it. This isn't purely a pedagogical position — though I think it's correct pedagogically — it's also just accurate. The separation between the two is a historical and administrative artefact, not a feature of the subjects themselves.
The practical argument is that students who encounter a mathematical idea in a programming context tend to understand it differently than students who encounter the same idea in a pure mathematics context. The abstraction arrives after the concrete experience rather than before it. The notation is motivated rather than arbitrary. This changes what students are able to do with the idea later.
The harder argument — the one worth taking seriously — is about what it actually means to understand something. A student who can reproduce a derivation under exam conditions but cannot use the underlying idea to solve a problem they haven't seen before has not, in any meaningful sense, understood the thing. Integration creates more opportunities for that second kind of understanding, because the contexts multiply.
Assessment
I try to design assessments that are hard to game by memorising and reproducing. This means fewer closed-book exams on isolated skills and more extended tasks where the student has to apply knowledge across a problem they haven't seen exactly before.
This is more work to mark. It also produces more accurate information about what students can actually do, which is the point.
I take the QQI standards seriously as a framework — the learning outcomes are usually sensible — but I try to design toward the spirit of the outcome rather than the easiest way to demonstrate it. There's a difference between a student who has met a learning outcome and a student who can produce evidence that they've met a learning outcome in a controlled setting.
Further reading
The consulting page describes how this thinking translates into curriculum design work with institutions. The teaching materials on this site give concrete examples of what these ideas look like in practice — resources, briefs, and worksheets from actual courses.
