An important new empirical evidence-based report on Irish post-primary students’ knowledge of algebra identifies strengths and weaknesses in their knowledge of the subject and proposes recommendations to address the weaknesses.
The report finds that students have good knowledge of equality, proportional reasoning, patterns, and comparing and ordering numbers, but that they are struggling with key skills such as fractions, decimal numbers, order of operations, and indices.
A total of 555 pupils, and their teachers, from 29 classes in 19 post-primary schools around Ireland took part in the study over one school year, prior to Covid-19.
The report, A profile of Irish second year post-primary students’ knowledge of initial algebra, by GMIT engineering mathematics lecturer Dr Aoife O’Brien and UCC lecturer Dr Máire Ní Ríordáin, is based on Dr O’Brien’s doctoral thesis.
“I’d like to thank all the teachers and secondary school pupils who took part in this study, algebra is challenging for students to learn and for teachers to teach at primary and post-primary level, and this study provides the first in-depth examination in the Irish context,” Dr O’Brien said.
“Algebra may not be seen as important in daily life – and this is often joked about – however a lack of knowledge of algebra today is likened to not being able to read or write at the beginning of the 20th century. It is an essential foundation for many third level courses as it is a component of all engineering, science, business, and many other courses. Helping students to develop a strong basis in algebra early in post-primary education ensures equality in their education, allowing for all students to progress into third level and therefore into well-paid employment.
“Many people think that children begin to learn algebra in post-primary school, but this is not true and children as young as five can understand algebraic concepts," she continued. "The foundations for algebra are laid down throughout primary school, however algebra is introduced more formally in first and second year in post-primary school at which point students should be ready to meet it. However, post-primary teachers have reported issues with students’ foundational knowledge, for example, a lack of understanding of fractions.
“My study provides the empirical evidence to support what teachers have been saying and are reporting on from their experiences in the classroom. Students at age approximately 14 are struggling with their fraction knowledge, along with other areas such as decimals, order of operations, indices, integers, variables, and equations.”
Dr Máire Ní Ríordáin believes students’ struggles with algebra may be heightened by the present context, given that current second-year students were in sixth class when the pandemic first forced closures of Irish schools. “There is a requirement to address students’ needs through targeted supports for teachers and students,” she said.
“Such supports will require funding and investment by key stakeholders in education. The attention on students’ strengths and weaknesses in algebra provides an important baseline from which to start the process of building these supports.”
There is much to be gained by improving students’ understanding of algebra and accordingly maths in schools, given it underpins all the STEM and numerate disciplines. As Professor John O’ Donoghue writes in his foreword to the report: “The stakes are very high and the rewards for individuals and society are great: significant improvement in algebra learning and teaching will lead to better outcomes in their mathematics education for post-primary students, better preparation for STEM disciplines and other numerate disciplines in higher education (HE ), and better numeracy in the wider population. The expected payoff for better outcomes in these areas is better economic outcomes and national prosperity.”
The report is available online at research.thea.ie/handle/20 500.12065/3867.
