Mathematical decline

An observation on the changing face of mathematics education in Ireland.

In my lecturing days a few years ago (OK, “few” might be an understatement) we used to complain about having to provide “remedial maths” to each fresh intake of students. It seemed to many of us, charged with the task of producing the next batch of computing experts, that for many of the raw cadets the light of mathematics just had not shone on them. Sure, there were many who had passed their second level tests quite successfully, but a lot of these seemed to have been denied enlightenment. We blamed rote learning, the pressure of the points race, strategic teaching practices (teaching designed to maximize the points but not to promote understanding), fear, a culture that was gradually lowering the value of mathematics, and societal ignorance.

Of course, many of those responsible for our children up to the second level of our education system recognized the problem and promised to do something about it. However, a look at the new “Project Maths”gives the impression that maybe an opportunity has been lost. It would seem that the new syllabus has indeed gone some way to put various branches of maths into proper context, with a strong focus on practical problem solving. This is a good thing. But instead of expanding this to cover the full breadth, some of the key elements have not just been reduced, but in some cases completely amputated.

The syllabus still has many of (what I consider) the important basics, such as 1 & 2 order derivations (linear, quadratic and cubic), rates of change, min/max, differentiation of polynomials, exp/log, trig, powers,  f-1(), interval averages, prob/stats, bounded region areas and a handful of related concepts. All good stuff, and nicely couched in practical applications.

But just look at what appears to have fallen over the cliff.

Let’s start with differentiation. Only the differentiation from first principles of linear and quadratic functions is covered, so students faced with unfamiliar formulae will be completely unarmed. When it comes to integrals, only polynomials and exponentials are included. Limits seem to be ignored. Using derivatives to find tangents, gone. Forget ever seeing turning points, inflections or asymptotes. The Taylor Series has terminated! The course refinement has eliminated the Newton-Raphson method. Students will no longer experience integration by parts or substitution. The syllabus has converged on the idea that the Ratio Test is unnecessary.

But if, like me, you’re a computer scientist, then prepare yourself for more bad news. They have removed vectors. (How can any mathematician survive without vectors?) I’ll say it again: they removed vectors! And before you get a chance to recover from that, here’s another: they’ve also removed matrices!! No more funky equation solving, or cool rotations of n-dimensional solids. Shame! And they are indifferent to difference equations. Coordinate geometry has lost ellipses…

The list of casualties goes on, but it’s just too depressing to list them.

Mathematics has beauty in both its depth and breadth. Project Maths has removed much of the breadth. It does not appear to have increased the depth of what remains, but at least it is doing that remainder in a much more accessible manner. What Project Maths really needed was more time, so that the breadth could be retained.

I can see that in a few years, at third level, there will be a lot more Remedial Maths. In fact, there may be so much RM that what would normally be covered in the first year of a typical science/engineering course will have to be pushed into year 2.

It doesn’t take a mathematician to figure out where this will all lead. (Or maybe it does.)

Categorised as: LUE

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