Symmetry
Is nature really symmetrical?
Find the pattern. Then find where it fails.
Approximation, angle, transformation and variation begin with looking closely.
Try it →Etain Kiely · mathematics, learning & human judgement
Noticing Maths
Mathematics is a practice of attention.
We notice patterns, measure change, question evidence and decide what matters.
What catches your attention first?
eˣ — Grow at your own rate.
A public notebook for learning to look, check and judge more carefully.
Try it
Start with something ordinary.
Noticing Maths is a way of working, not a slogan. Take a small question into your own context and let the mathematics sharpen — or overturn — what you first thought.
Scale
What would you measure first?
Height? spread? branching? rate?
The right measurement depends on the question you are actually trying to answer.
Try it →Change
When does a model stop describing the real thing?
The pond did not read the textbook.
Models help us predict. Reality reveals assumptions.
Try it →Notice.What is actually here?
Measure.How could I know more carefully?
Question.What does the evidence support?
Decide.What am I prepared to conclude?
Return. Look again.
Something may have changed — including what you know.
Qualities worth developing
More than getting the answer.
The aim is not simply higher confidence or faster calculation. It is pride in becoming a more attentive, evidence-aware and independent mathematical judge.
Attention
Notice structure, pattern, difference, scale and anomaly.
Evidence
Measure, compare, represent and ask what the data can legitimately support.
Judgement
Check assumptions, uncertainty, AI output and apparently authoritative answers.
Agency
Know what to do next when the first approach does not work.
Research
Can we see these qualities developing?
The research underneath Noticing Maths asks how we can understand learners more richly than through final marks alone — while refusing to turn people into another set of scores.
Before the calculation
Does a learner predict sign, scale, range or graph shape before using a tool?
After difficulty
Can they locate the first invalid step, respond to feedback and choose a useful next action?
When support disappears
Can they transfer the mathematics independently and defend what the evidence supports?
Selected research
A research arc, not a list of topics.
From personalised feedback and learner voice to self-regulation, intelligent assessment and time-series modelling, the recurring question is what evidence allows us to notice — and how human judgement should act on it.
HEA · 2026
REAL Analytics: Making Learning Trajectories Visible, Measurable and Responsive at Scale
Detection is inseparable from care.
National progression exemplar describing learner-facing trajectories, early support and responsible analytics.
Read exemplar ↗StudentSurvey.ie · 2024
NLP for Sentiment Analysis and Topic Modelling of Postgraduate Engagement Data
What does learner language tell us that activity traces cannot?
A commissioned national report bringing qualitative student voice into the analytical picture.
Read report ↗ACM ECSEE · 2025
Soft Skills as Predictors of Success in Software Engineering
Capability is more than technical performance.
Research with Ontiretse Ishmael and John Healy on confidence, adaptability and time management.
Open DOI ↗
Real places · real people · all kinds of weather
REAL Living Lab
Take the questions outside.
REAL Living Lab is where students, communities, researchers and practitioners can test ideas in the places where people actually live and learn.
Care enough to notice. Measure enough to know.
Enter REAL →Creative Ireland · My World
Attention can come before measurement.
My World is a distinct creative strand in which pattern can be noticed, arranged, moved, repeated, refused, changed or returned to. Here, return is not repetition for its own sake: it can be choice, communication and influence.
Open My World →Students can build possibilities. Children retain ownership of meaning.
Who is this for?
Anyone willing to look closely.
Mathematics should not belong only to people who already feel good at mathematics. Attention, evidence and judgement are useful wherever we make decisions in an uncertain world.
learnersteachersparentsgardenersscientistscodersartistscommunitiesdecision-makersthe merely curious
Citizens of Earth — and beyond, should the opportunity arise.