Understanding how students develop mathematically — their prior knowledge, misconceptions, motivations, and social contexts — is fundamental to responsive teaching. Standard 3 asks us to use knowledge of our ākonga to genuinely differentiate. The evidence on this page demonstrates deliberate design for three distinct learner profiles: ākonga at risk of not gaining NCEA numeracy, ākonga who disengage from traditional teaching, and ākonga who need extension beyond the standard curriculum.
NCEA Numeracy CAA Prep — Mr Gee's Maths Emporium
A comprehensive, self-paced CAA preparation programme built specifically with low-achieving ākonga in mind. Covers all three CAA outcomes (Formulate, Calculate, Justify) across all 6 domains. Module 7 addresses the single most-failed component — Outcome 3 written justification — using AI feedback on student responses. Includes a guided onboarding tour explaining what the CAA is and why it matters, written in plain, non-threatening language.
Mr Gee's Maths Emporium — Gamified Learning Hub
A full gamified mathematics platform built from scratch to address a clear pattern: students who switched off during traditional instruction but would voluntarily work on mathematics if it felt like a game. Features include XP, leaderboards, avatar customisation, streak tracking, and a teacher dashboard. Had a measurable impact on voluntary engagement — particularly among reluctant learners who had not previously engaged with mathematics work outside the classroom.
Extension Assessment Tools — AlgebraLand & Beyond
A suite of over 30 fully interactive extension lessons for Year 10 students on the NCEA Level 1 algebra pathway. Each lesson includes slides, direct teaching, and an infinite randomised question generator so no two students work on identical problems. Four difficulty tiers (Mild → Spicy → Extra Hot → Inferno) and a Codebreaker extended-abstract task at the top of each topic. Designed explicitly so that high-achieving ākonga are never sitting waiting — they can always go further.
Additional lesson plans and classroom resources will appear here.
- How do I find out what my learners already know, can do, and care about?
- How does knowledge of individual ākonga shape my planning decisions?
- What do I know about my ākonga beyond their mathematical ability?
- How do I design differently for different types of learners — not just different levels?
Three types of learner, three different responses
When I look at my classes, I don't see a single spectrum from "low" to "high." I see different kinds of learners who struggle for different reasons and who need different things from me. This has been the most important insight of my first year of teaching — and it's what drove me to build the resources on this page.
The CAA resource came first. I had a group of Year 10 ākonga who were at genuine risk of not gaining NCEA numeracy — not because they lacked ability, but because they didn't understand what the CAA was testing or why Outcome 3 kept catching them out. Standard programmes explained the content but not the exam logic. So I built something that started with "here is exactly what this exam wants from you" before a single question was practised. The AI feedback on Outcome 3 responses was the part I was most unsure about — I didn't know if students would engage with it seriously. They did.
The Emporium came from a different problem: students who were capable but who had already decided that maths wasn't for them. Traditional practice sets were being ignored. I noticed these same students would spend 45 minutes on a mobile game — competing, trying again after failure, chasing points. I built the Emporium to redirect that energy. The leaderboard was the detail that surprised me most: students who rarely spoke in class became vocal about their ranking. One student who had produced almost no written work in Term 1 had 1,800 XP by Week 6 of Term 2.
The extension tools addressed the third problem: high-achieving ākonga who finished tasks quickly and had nothing meaningful to do. I don't think "do more questions" is good enough as extension. The Codebreaker tasks at the top of each AlgebraLand topic require algebraic reasoning and generalisation at NCEA extended abstract level — they give genuinely capable students something worth thinking hard about. Having infinite randomised questions also means extension students aren't waiting for me to print more.
What I am still developing: while I have built good resources for these learner profiles, I am not yet confident I am always identifying the right resource for the right student at the right time. I sometimes default to giving students the Emporium when they need more direct teaching from me. Knowing the learner is not just about building the resources — it is about the ongoing professional judgement of when to use them.