OPINION:IN AN opinion article in The Irish Times on August 29th on Project Maths, Prof Jo Boaler, a mathematical educationalist, argued students do better "when teachers cut down on content and choose to teach mathematics with depth".
That same Project Maths, introduced in 2009, is a new secondary level mathematics curriculum. It came about after a review by the National Council for Curriculum and Assessment (NCCA) amid concern over the uptake of higher level mathematics, particularly in the Leaving Certificate.
Its aims were to provide students with a greater understanding of mathematical concepts, with increased use of contexts and applications that enable students to relate mathematics to everyday experience.
However, several academics who have reviewed the course as rolled out believe this initiative is ill-conceived and will be severely damaging not only to mathematics but to engineering, technology and all the sciences. This would adversely affect our reputation, our economy and investment in the country.
In the new syllabus, calculus has been reduced by at least 40 per cent (with most of integration removed), while theory and applications of vectors and matrices have been eliminated. Note that the concept of a vector is one of the most fundamental for any practising engineer. The treatment of sequences and series has been reduced very significantly. Also, the assessment of advanced mathematical techniques in examinations has been considerably reduced.
All this amounts to a major repositioning downwards of the Project Maths curriculum compared to the old Leaving Certificate higher course.
In her piece, Prof Boaler does not refer to any benchmarking exercises of the new Project Maths course to compare it to curriculums in other countries.
In Singapore, an expert in mathematics education, Prof Peng Yee Lee, of the National Institute of Education, is of the opinion that breadth, depth and academic challenge are important, and “whether you like it or not, calculus is the gateway” to advanced maths. Singapore is regarded as having one of the best mathematics education systems globally.
It is accepted that Project Maths and bonus points may have some success in attracting more students to the honours stream, and we would welcome this. However, we cannot accept Project Maths as currently constituted offers the best foundation for students wishing to continue studying engineering, science or mathematics. For those wishing to pursue these areas at third level, the content is not suitable nor challenging enough.
Some of the basics of the language of mathematics have been foregone and, without these, deep understanding is impossible. Could a language be advanced with its alphabet and grammar diluted? Students’ problem-solving abilities, highly dependent on mathematics, are going to suffer.
Many topics that engineers and mathematicians need are completely missing from the Irish mathematics education system at second level in the new course.
In Singapore there is an obligatory syllabus for students wishing to pursue mathematics, engineering and science at third level. It is full of the topics that have been omitted from or considerably de-emphasised in Project Maths.
To study engineering, science or mathematics at a university in Canada, it is compulsory to take very challenging courses in advanced mathematical functions, calculus and vectors – the most demanding of these is the course entitled “Calculus and Vectors”.
When the content of the most advanced mathematics curriculums at upper secondary level in Scotland and England and Wales are examined, they are full of the very topics that have been completely removed from our old top level honours maths curriculum.
In Holland, for the senior cycle, a Project Maths-type syllabus is available at two levels, as rolled out here. The important difference is that Holland offers a more demanding course, compulsory for students pursuing the sciences, engineering and mathematics, at two levels. These have the more challenging topics, covering calculus, theory and applications of vectors, and theory of sequences and series – essential to supporting a seamless advance from secondary level to university for engineering, science and mathematics or indeed applied mathematics at this highest level.
In short, we are competing with countries which insist future potential students of engineering, science and maths take topics being deleted from our Leaving Cert. This should be a matter of major concern for policymakers, the NCCA and for Minister for Education Ruairí Quinn.
So what about our “knowledge economy” and future investment in Ireland? Our concerns are that if Project Maths as rolled out thus far becomes the norm, students entering third level science, mathematics and engineering will not have had exposure to some of the key mathematical topics they will need. That makes for a much steeper and perhaps impossible learning curve.
Ireland’s knowledge economy is centred on science, technology and engineering, and these sectors have an expanding need for people with strong maths backgrounds. People seeking employment in those sectors will need to know more sophisticated mathematics to compete. The sooner students are introduced to such training, the better.
Project Maths appears to be moving in the opposite direction. The possible long-term consequences of neglecting to quickly reform this project will include detrimental effects on the education sectors concerned. Such neglect will severely damage the reputation of our universities and thus Ireland’s international competitiveness. In a country linked to such distinguished theorists as William Rowan Hamilton, George Boole and George Gabriel Stokes – to name a few – we should not deny our best and brightest the curriculum so many of our international peers embrace.
Dr Cora Stack is a lecturer in mathematics at Institute of Technology, Tallaght, Dublin; Prof Margaret Stack is professor of mechanical engineering at the University of Strathclyde; Prof Ted Hurley is former head of the department of mathematics at NUI Galway, and John Brennan is a teacher of mathematics at Ballinteer Institute, Dublin, and textbook author