Sir, – While I agree with the authors of the article on project maths (Opinion, September 10th), that a knowledge of calculus, vectors and matrices and sequences and series is essential for students entering third-level science and engineering courses, I believe that what is even more important is an understanding of and an ability to use the maths they have learnt in school.
As a lecturer in Trinity College for 39 years, my teaching duties every year included a first- or second-year maths course for science, and occasionally for engineering, students, as well as a sophister course in quantum mechanics, which relies heavily on sophisticated mathematics. During my last 10 years as a lecturer I saw a catastrophic decline in the students’ mathematical abilities. This was not associated with a lowering of entry standards, but with the increased emphasis on rote learning in schools. Students facing a simple problem involving powers or the rearrangement of an algebraic formula would say “I don’t remember the rule”. If they had understood this Junior Cert material they would have been able to work out the answer without resort to “black box” formulae. Their lack of understanding of basic maths, in spite of good grades in the Leaving Certificate exam, made it extremely difficult for them to cope with new concepts and to apply maths in physics courses.
The school of physics in Trinity introduced first-year small group tutorials in an attempt to improve the situation. In my experience of taking these tutorials many of the students had not even realised that there was another way to learn than by rote. Even the highly qualified and mathematically inclined theoretical physics students had suffered from a lack of training in using reason and working things out for themselves.
These tutorials had to focus on Junior Certificate material. It should not be the job of a university, nor can the university maintain its standards, if it has to re- teach Junior Certificate maths before its students can cope with university level maths and science.
When I retired in 2007 I devoted myself to writing a book (Maths as a Language) which was based on my experience of these first-year tutorials.
It received some interest, but was often said to be “a new way of teaching maths” whereas it was in fact a return to teaching in a way that used to be common in schools: the book attempts to help the reader to develop an understanding of basic mathematics and the ability to reason mathematically, which are essential for progressing to more sophisticated topics, and for application of maths in science subjects.
Sequences and series, calculus, and vectors and matrices have always been a large part of the syllabus for first year maths for science and engineering students in Trinity. In my opinion, if Project maths can instil understanding and mathematical reasoning in students it will prepare them for maths-based courses at third-level better than the old Leaving Certificate maths, even if certain topics have been dropped from the school syllabus. – Yours, etc,