The following post is written by John Webb from The Department of Mathematics and Applied Mathematics at The University of Cape Town. With his permission I include it here as an advert for a book which is discussed at the bottom of the post. Mathemafrica receives no payment for including this text. I hope that in addition to being an advert for the book, this may be a chance for students to discuss some of the problems they see with the transition between school and University here in South Africa for maths students.

Why do so many first-year students fail varsity maths?
Thousands of students across South Africa have started their university careers, and many of them have enrolled for a course in Mathematics. Some will be aiming at a maths major, in particular those who hope to teach mathematics at school level. But far more will be doing maths as a requirement for their degrees in a whole range of areas. Computer science, statistics, physics, actuarial science, engineering, economics and many other fields of study all need a solid grounding in mathematics.

Within a couple of weeks of starting varsity many of these students will be floundering in their maths lectures, and after a disastrous performance in their first class test will drop out or move to a bridging or slow-stream course with extra tutorial support. This early failure will inevitably mean taking an extra year to get their degree.
Many of these students will have arrived at university with an A for matric maths, and often they will have six or more subject A’s. Why are these A students failing university maths?

Grade inflation

In the last few years the matric maths syllabus has been severely cut. The trickier parts of the algebra, geometry and trigonometry syllabus have been left out, and the final exams are now much easier.

Achieving a good maths mark is much easier than before. There has been huge grade inflation in matric results. In the past a good school could expect about half a dozen A’s for Senior Certificate Mathematics. Now they are boasting 50 or more A’s, most of whom would have earned C’s and D’s in the past.

Maths is not the only subject to suffer from grade inflation. Under the pre-OBE curriculum, six As would get you into the top ten in the province. Today, a number of schools now boast 30 to 40 students with six or more As.
The problem is, as George Orwell might have put it, that all A’s are equal, but some are less equal than others.

What can be done?

The answer is to offer high school students who are planning to continue with maths at university an opportunity, while still at school, to sharpen their maths skills by tackling problems that are more challenging than those of the matric exam.

Based on many years of lecturing first year mathematics students, I have put together a book of exercises covering areas of maths that are inadequately covered at school but are essential for university maths.

Varsity Maths Prep

The book of problems is aimed to identify weaknesses in a student’s preparedness for university mathematics. Some problems focus on popular algebraic errors. Others were inspired by questions that students would ask during lectures about a simple piece of school geometry or algebra. Full solutions are provided.

Failure to solve any of the problems will indicate a weakness in the student’s background that must be fixed before entering the Maths 101 lecture hall.

Will Varsity Maths Prep help students prepare for the National Benchmark Test?

The exercises in Varsity Maths Prep will certainly be good preparation for the National Benchmark Test (NBT) in Mathematics, but that is not its primary aim. The NBT looks back at what has been learnt at school. Varsity Maths Prep looks ahead to the sort of mathematical skills and thinking that varsity maths lecturers will expect of students in their classes. And it’s not just the maths profs: lecturers in Physics, Computer Science, Engineering and Economics all expect their students to have fluent algebraic skills, numerical ability and good geometrical and spatial perception in two and three dimensions

Dumbed-down maths

A good example of how school maths is dumbed down can be found in
trigonometry. There are six basic trig functions, but when Higher Grade Maths was abolished, only three were left in the curriculum. The array of trig formulas, which have wide application in physics and engineering, was cut down to just a couple, and students are no longer expected to prove, or even know them, since a formula sheet is now part of the final exam.

The same can be said about algebra and the formula for solving a quadratic equation. Since it is on the formula sheet, students don’t know it, and don’t know how to derive it.
Students are also very weak on basic arithmetic, reaching for a calculator even when confronted with the task of adding or multiplying single-digit numbers.

As university students start their studies, those in mathematics courses will be shocked to realize that their matric Maths A symbol does not mean that they can handle varsity maths.
It’s as if a cricket coach showed his novice batsmen only how to play gentle full tosses and longhops, without ever bowling them a bouncer, yorker or googly. With such instruction, ducks in a real cricket match would be inevitable. It’s the same with maths. If you only meet a limited range of simple problems at school, at varsity you will be stumped, caught out or bowled over.

The book is not for high school students who are battling to pass maths. It is aimed at those who are good at maths and will collect a comfortable A in Senior Certificate mathematics. They may get into Science, Engineering, and Commerce degree programmes with ease, but will unexpectedly find varsity maths a serious challenge.

The book costs R95 and can be ordered from
The Answer
50 Imam Haron Road (formerly Lansdowne Road) Claremont 7708
Tel: 021 671 0837 Fax: 021 671 2546 Email: info@theanswerseries.co.za
Website: http://www.theanswer.co.za/shop/varsity-maths-prep/