Windows into Practice: Teaching Mathematical Reasoning Across Language Contexts
10 Nov 2026
At a time of curriculum reform across Ireland, primary teachers are looking for practical ways to move away from procedural routines and give children greater agency to think, talk, and reason mathematically.
As part of the MeasEolMata research project—and featured at the NCCA Primary Mathematics Shared Learning Day— a collaborative cross-border team of academic researchers and four teacher-researchers—working across three English-medium classrooms and one Irish-medium Gaelscoil—engaged in an iterative Lesson Study. Together, we explored how open-ended, qualitative tasks can reveal authentic mathematical reasoning across diverse primary settings.
The Task: Sharing Brownies
To anchor our collaborative inquiry, we used Susan Lamon’s qualitative Sharing Brownies task.
Unlike traditional fraction problems, the task introduces sharing scenarios without explicit numbers (e.g., comparing Monday's share with Thursday's share when more friends arrive but the number of brownies stays the same).
Why This Task?
Stripping away explicit calculations forces children to reason about quantities, spatial shares, and relationships rather than jumping straight to formulas. This placed decision-making squarely on us as teachers: do we preserve conceptual freedoms by holding space for pupil reasoning, or do we restrict the task by introducing quick algorithms?
How We Worked
Our professional learning journey unfolded in three connected phases:
Phase 1: In-Person Lift-Off Day | Phase 2: Enactment 1 & Online Debrief | Phase 3: Enactment 2 & Final Reflection |
We met with the academic research team to analyse the task, align it with the PMC Progression Continua, and co-design our first lesson plan. | We recorded our classroom enactments using fixed video cameras, met online to analyse video excerpts, and refined our pedagogical strategies. | We re-taught the revised lesson to a new cohort and gathered in person for a joint synthesis of our learning. |
Key Windows into Practice & Pedagogical Insights
Allowing Thinking Time Before Intervening: In initial enactments, we noticed a natural urge as teachers to step in quickly with numbers or formulas when children experienced struggle. Extending wait times allowed children space to draw their own informal area models and double number lines, self-correcting through partner talk.
Scaffolding Language in Immersion (CLIL) Contexts: In our Gaelscoil setting, supporting reasoning required explicit language pre-teaching. For instance, clarifying terms like cothrom ("fair" vs. "equal") ensured pupils could access core proportional concepts and justify their thinking in Gaeilge without lowering cognitive demand.
Addressing Concept Bounds: Video analysis revealed that pupils consistently constrained their number lines between 0 and 1, struggling to represent shares greater than 1 whole. Identifying this in real-time enabled us to adapt task constraints on the spot.
Resources & Digital Artefacts
You can access all project materials and digital artefacts directly on Mathscify.org (Search: reasoning / réasúnaíocht):
Conference Poster
Watch the Video Digital Artefact
Bilingual Lesson Resources
Project Team: Dr Marie Brennan (Drumlease NS, Leitrim), Ms Caitríona Horgan (Ballyheada NS, Cork), Mr Jarlath Brennan (Kilglass NS, Sligo), and Mr Dara Ferriter (Gaelscoil an Mhuilinn, Westmeath).
In Collaboration With: Dublin City University (DCU), St Mary’s University College Belfast, Ulster University, and Trinity College Dublin.
Kindly Funded and Supported By: SCoTENS, the Teaching Council, and COGG.