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 four distinct learner profiles: ākonga at risk of not gaining NCEA numeracy, ākonga who disengage from traditional teaching, ākonga who need extension beyond the standard curriculum, and ākonga capable of being accelerated ahead of the standard timeline altogether.
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 across all 6 domains. Module 7 addresses the most-failed component — Outcome 3 written justification — using AI feedback on student responses. Includes guided onboarding written in plain, non-threatening language explaining exactly what the CAA tests and why.
Mr Gee's Maths Emporium — Gamified Learning Hub
A full gamified mathematics platform built to address a clear pattern: students who switched off during traditional instruction but would voluntarily work on mathematics if it felt like a game. Had a measurable impact on voluntary engagement — particularly among reluctant learners who had not previously engaged with mathematics work outside the classroom. One student who produced almost no written work in Term 1 had 1,800 XP by Week 6 of Term 2.
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. Four difficulty tiers and a Codebreaker extended-abstract task at the top of each topic. Designed so high-achieving ākonga are never waiting — they can always go further.
Knowing this particular group of ākonga meant recognising that the standard Year 10 pathway would not stretch them. I extended a Year 10 connected class and entered them into NCEA 1.4 (Mathematical Reasoning) a full year early, supporting them beyond class time with regular mathematics tutorials to bridge the gap between Year 10 and Level 1 content and reasoning demands.
Powers & Roots — NCEA 1.4 Revision Deck
A full revision deck built specifically for this accelerated cohort ahead of their NCEA 1.4 sitting: index laws, negative indices, fractional indices and roots, common-base simplifying, and solving exponential equations. Structured across five parts with worked examples, an explicit common-mistakes slide for every law, quickfire checks, and a graded exit ticket — pitched at the reasoning-and-justification standard the external assessment demands, not just procedural fluency.
"The Ozone Layer & CFCs" — an independent statistical investigation from a student in this connected class, examining how the type and reliability of scientific evidence changed between the first 1974 warnings about CFCs and the 1985 discovery of the Antarctic ozone hole, and reasoning about why politicians and chemical companies were slow to act on the earlier evidence. The work correctly distinguishes primary from secondary and observational from experimental data, reads real historical ozone/CFC datasets, and connects the scientific timeline to social and economic barriers to action — the kind of reasoning this acceleration was designed to make possible.
📄 View Student Project (PDF)- 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. 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. 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. 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. The Codebreaker tasks require algebraic reasoning and generalisation at NCEA extended abstract level — something worth thinking hard about.
The fourth group pushed me further than any of the others. Extending a Year 10 connected class into NCEA 1.4 a year early was a genuine risk — it meant these ākonga would sit an external standard designed for a year above them, with reasoning demands well beyond anything in the Year 10 curriculum. Knowing them as individuals told me they could handle it; the tutorials were where I found out where the actual gaps were and closed them one at a time rather than guessing. A 90% Exceeding rate — the highest band at Rolleston — and most of the cohort now electing into Scholarship Calculus tells me the initial judgement about these learners was right, but I'm conscious that judgement carried real stakes for the students involved, and I want to be similarly rigorous before accelerating a group again.
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. Knowing the learner is not just about building the resources — it is about the ongoing professional judgement of when to use them.