Leaving Cert: higher maths paper 1 ‘easiest on record’

Leaving Cert maths paper 1 is over. The higher level paper is by far the easiest on record. Strip away the applications and what’s left is on a par with the ordinary level papers of old. Knowledge of actual maths at a high level has plummeted. The syllabus and the paper lack the quality and substance that students embarking on a college education deserve.

The ordinary level paper 1 is egregious. Question 5, on calculating the area of a quadrilateral under a quadratic, is on a par with an honours question. Question 6, on complex numbers, begins with such triviality as to be confusing, but immediately escalates to a level that is as difficult as the corresponding honours maths question! I feel so sorry for those students who worked hard at their maths, only to be confronted with such an impossible paper. We can only hope that paper 2, on Monday, is fair.

Taking stock

Project Maths exams have been with us for several years now; it is time to take stock. Most questions are in the context of an application, which tends to make them convoluted and overly verbose. My experience from teaching large first year classes at University of Limerick is that such questions are disadvantageous to students whose native language is not English, not to mention students with dyslexia etc. We are giving these students a double penalty for their difficulties with the subtleties of English.

Project Maths has meant the evisceration of much of calculus and the obliteration of vectors and matrices from the syllabus. These topics are core subjects taught in first year maths in college, but at a much higher level; students today enter college with a very inadequate preparation in these vital areas. There is clearly some guilt about this, as in recent papers (e.g. question 6 mentioned above), the angle between vectors appears in the guise of a complex numbers question. While this may be doable for an honours student, such a question is out of context for the topic being examined, and is a killer for the ordinary level student.

The vibes are that this guilt may soon extend to replacing of applied maths with a new advanced maths subject that covers the missing material from the old syllabus. This would be maths for the rich and elite. How fair would it be to rural or female students, very few of whom have the option of taking the current applied maths, because smaller and girls-only schools may have fewer subjects on offer?

Other disciplines

Students are now expected to be familiar with concepts from other disciplines, often physics. Question 1 (higher) this year, on the bouncing ball, expects them to know what “vertical distance” means - based on vertical projection of the depicted actual motion. Facility with physical units is assumed throughout. Every maths paper states “You may lose marks if the appropriate units of measurement are not included, where relevant”. Question 8 on the higher paper uses four different units of length, along with a plethora of units of areas, volumes and rates. This is more physics than maths! Even the examiners themselves show unnecessary sloppiness with units; question 2(b)(ii) on the ordinary paper 1, about the volume of the earth, fails to mention the unit of volume. Not to give full marks to any (positive) answer to that part would be an injustice to the already much beleaguered ordinary level student.

Very little has been said about the sea change in the marking scheme, pari passu with the introduction of Project Maths. It is a large rug under which many problems are swept. Last year's honours paper 2, question 4 had a 10-mark question with two parts. A correct answer to the first part got 7 marks, as did a correct answer to the second part. Since when does 7+7=10? This sends out all the wrong signals: do a little on all questions (even if you haven't a clue), but don't waste your time finishing them. Answers, which on the old syllabus would have got 20 per cent or less, routinely today get up to 70 per cent. Why did this happen? It certainly allows the creators of Project Maths to get desired and well-trumpeted results, perhaps attempting to justify the huge additional expenditure on a very misguided exercise, which unfortunately we're stuck with for years to come.

Dr. Eugene Gath has a Ph.D. in mathematics from Massachusetts Institute of Technology and has lectured in mathematics and financial mathematics at University of Limerick since 1990.