Institution

University of Galway

Description

Matamaitic don Inbhuanaitheacht (Mathematics for Sustainability) is an Irish-language module which teaches students from a wide range of backgrounds useful mathematical and computer skills for modelling and analysis, nested in a Sustainability context.

This interdisciplinary module teaches students mathematical and computer skills relevant to Sustainability, equipping them with the ability to analyze and model Sustainability initiatives, and to critically evaluate reports in the media and elsewhere, skills which are more relevant now than ever in this misinformation age.

Arising as part of a University of Galway initiative to promote the Irish language within the College of Science and Engineering, the initial aims of this module were to:
(1) Provide an opportunity for STEM students to undertake some of their studies through Irish.
(2) Offer something novel which wasn’t simply a translation of an existing module.
(3) Stand alone as a module—to be accessible to students with no mathematical background post-second-level, and not be a prerequisite for any later modules, as this would disadvantage students without Irish.
(4) Be enjoyable!

STEM offerings through Irish at third-level are currently extremely limited, and it is important for a language’s survival not only that it be used to discuss culture, heritage, and historical topics, but also allow for work on, and discussion of, technological advancements, medical treatments, approaches to climate change and interconnected global challenges, and other future-oriented points of interest.

This module represents one of the very few opportunities for students to study STEM through Irish, even in the University of Galway, with its commitment to its status as a bilingual university. The University’s strong support of this module is a testament to its dedication both to the Irish language and to championing Sustainability, and highlights its vision for celebrating our heritage and preparing for the future.

Upon entering third-level, students who choose to study STEM are often forced to forsake the Irish language, or vice versa. This is detrimental to the Irish language, as it leads to a systemic decline, where there is a paucity of appropriately qualified STEM graduates with Irish to work as teachers in the increasing number of primary and secondary Irish-medium schools. Further, there are a great many companies in the biomedical, technological, sustainability, audiovisual, etc industries with bases in the Gaeltacht, and if graduates are not provided with the skills to work through Irish in such companies, it will be to the detriment of the Gaeltacht itself.

Taught through Irish, the module “Matamaitic don Inbhuanaitheacht” offers students of Irish the opportunity to engage with STEM and Sustainability, and also offers STEM students the chance to continue using their Irish.

The module introduces students to new mathematical concepts, such as matrices, and also builds on second-level material such as calculus and statistics, and applies these to problems in a Sustainability framework.

Both Sustainability and Mathematics are very broad areas, and lend themselves well to devising interesting practical examples.

To account for the students’ wide range of mathematical backgrounds, extensive use is made of interactive Jupyter-notebooks, where students learn to implement models and conduct analyses in Python, saving themselves computational `heavy-lifting’, but enabling them to analyse and discuss effects of parameter-adjustment and interventions in real-world scenarios, such as disease spread, travel network optimisation, heat distribution, population modelling.
These Jupyter-notebooks allow the instructor to share notes which look like pdfs, but contain editable computer code which students can edit and execute, giving them opportunity to experiment with the models and providing a wealth of opportunities for further study for students who are so inclined.
Further, students can similarly share their documents and code with the instructor for marking or discussion.

Decolonising the curriculum is an important facet of this module – it seeks to recognise and validate the Irish language within the university, it uses local and relevant data and knowledge within the learning system, and provides equality of access to education through the Irish language. This module encourages students to consider a range of issues concerning language and sustainability as well as the more obvious mathematical analysis and modelling techniques, and hopefully is of some assistance in enabling them to address interconnected global challenges by drawing on diverse knowledge systems and creating new ecologies of knowledge.

The attached figures illustrate: a simple example of a Jupyter-notebook, an example from the module of correlation analysis based on University of Galway’s Travel Survey data, an example of SIR disease spread with zombies incorporated at the students’ behest.

Intended Learning Outcomes

Students gain mathematical skills (in the areas of matrix algebra, differential calculus, graph theory, and probability and statistics) and an understanding of how to apply these in sustainability contexts; creating and analysing models for areas such as SIR infection modelling, transport network optimisation, population dynamics, and data analysis.

Students develop programming skills, and the ability to use software to perform calculations and analysis, and to visualise models and data.

They learn to critically evaluate models they are presented with, and to draw their own conclusions from data.

The module also gives STEM students the chance to use their Irish, and Irish students the chance to engage with STEM, opportunities which they would otherwise likely not be afforded.

Students gain an increased awareness of Sustainability issues in some cases, through experimentation and analysis, and consideration of potential interventions or possible scenarios.

Teaching and Learning Approach

Lectures highlighted Sustainability issues motivating whichever new material we intended to cover, introduced the basic mathematical techniques, and then applied them to the Sustainability examples.

For more complex modelling and analyses, to avoid computational difficulties, we held weekly computer labs, where students learned to implement the techniques they had learned using Jupyter-notebooks and build on this to generate more comprehensive and useful models and analyses.

(Jupyter-notebooks are an open-source web-based application that allows users to create, share, and execute interactive documents containing live code, visualisations, text, equations, and more. They are an excellent resource for teaching, documentation, or report-writing, in fields such as mathematics, computer science, data science. They allow the editing and execution of code – Python was used for this module, but there are other options – allowing students to, for example, verify their calculations, or run calculations which are infeasible to do by hand.)

Assessment Strategy

The course was broken into three larger independent “topics” centred, broadly, on matrices, calculus, and data analysis. Each topic involved a class test and a homework lab Jupyter-notebook.

The class tests (3 x 5\%) involved simpler computations and more closely resembled the summer exam (50\%), to ensure students weren’t relying overmuch on AI etc. Homeworks (3 x 5\%) required students to utilise Python for more in-depth modelling or analysis; writing or adjusting code, or discussing effects of tweaking parameters.
There was also 5\% for participation.

For ’25/’26, very short class tests will be administered each class (~20 x 1\%) (allowing students the marks for their best ~20 tests to account for unavoidable absences etc), as attendance for ’24/’25 was poor across the College of Arts. This will ensure attendance, and avoid AI.

For this course, the small class makes marking pen and paper tests feasible, but for larger classes an online test could be administered on a closed wifi network. This is a technique we are currently investigating for efficiency, to avoid AI use, and would also be more sustainable, avoiding the use of paper tests!

Impact and Outcomes

On an individual student level, students acquired quantitative, programming, analysis, modelling, and language skills, and awareness and knowledge of how they might in future use these for work in sustainability and other contexts. They developed critical skills to analyse information they are presented with rather than relying on others’ interpretation.

The winner of the Christofides Prize is now teaching in the Gaeltacht, with this having been her only Irish-language module in the degree.

On an institutional level, the introduction of this module required developing workarounds for introducing interdisciplinary modules, serves as an example of how Irish-langugage modules in STEM can be a success,
and re-introduced the Christofides Prize – an important step in acknowledging the importance of Irish, within the School of Maths and within the College of Science and Engineering more generally.

The module provides students with hard skills for dealing with Sustainability issues, enabling them to perform concrete calculations, both in modelling more precisely the effect of proposed initiatives, and in analysing data, skills relevant to addressing complex and ‘wicked’ challenges.

Collaboration, Partnerships & Student Participation

The School of Mathematical and Statistical Sciences awards the Christofides Prize to students with the highest marks in this module, named after Tony Christofides, a lecturer from Greece who learned Irish before moving here, and then taught Maths through Irish. He also became a staunch advocate for language rights, and was a founder of Cinegael in the 1970s, from which grew the Gaeltacht’s audio-visual industry.

For the data analysis component, the Sustainability Office provided local-interest suggestions, and data from the university’s Travel Survey for students to experiment with.

The module is taught by the School of Maths, but is also available through other Schools in the Colleges of Science and Engineering and of Arts, Social Sciences and Celtic Studies.

Students provided feedback on suitable topics and examples chosen for the course, and were offered the opportunity to highlight any particular sustainability topics they would be interested in studying the mathematics of.

Student Engagement

6 students in the cohort for the pilot year (’24/25) of this module.
Challenges to overcome included issues with cross-disciplinary registration leading to some students missing out on enrolling.
Module has also been added as an option for BSc in Mathematical Sciences and BSc in Marine Science for ’25/26, and to be added for BSc in Agricultural Science for ’26/27

Disciplines

• Arts and Humanities
• Education
• Engineering, Manufacturing and Construction
• Generic programmes and qualifications
• Health and Welfare
• Information and Communication Technologies
• Natural Sciences, Mathematics and Statistics
• Teaching and Learning

Programmes

BSc Science, BA Arts, BA Mathematics and Education

Best Practices & Resources

Top Tips

• In STEM subjects where calculations or programming are involved, Jupyter-notebooks are an excellent tool, allowing students to combine notes with editable and executable code in a convenient format. Ensure students are comfortable using Jupyter-notebook early.
• Give students the freedom to develop their own ideas, and just be on hand to help them therewith. During our discussion on SIRD (susceptible, infected, recovered, dead) disease modelling, the students proposed introducing zombies to the model, and then themselves developed the appropriate changes, which both entertained them and led to a better grasp of the concepts. Assign marks for attendance, as different departments’ attendance rates differ and it can be disruptive.
• Use local data and examples where possible. Students were more invested when relatable examples were used, such as when we used the University of Galway’s Travel Survey data for our data analysis topic.

Useful Resources

• https://www.dataquest.io/blog/jupyter-notebook-tutorial/
• https://www.learnpython.org

Funding Details

The development of this initiative was supported as part of a strategic fund from the University of Galway to promote the Irish language within the College of Science and Engineering, as is the reintroduced Christofides Prize.

The course, now developed and with the various frameworks in place, will be taught by the School of Mathematical and Statistical Sciences, with some support from Acadamh na hOllscolaíochta Gaeilge.