The ‘new’ mathematics

Let me start with a disclaimer – I’m not an expert in mathematics, mathematics curriculum or the jobs that require mathematics. I am however, an educator, a teacher educator, a parent, and, I like to consider myself someone who might have a relevant opinion on mathematics education, so here it is.

I was a good student throughout my schooling career without ever having to put in too much effort. Although my focus when I got to university was in the social sciences, I was a pretty good mathematics student throughout high school and still had to take a couple of math classes in university. While I’m still quite numerate, I don’t consider myself a good mathematician. I put it down to the adage: use it or lose it and I don’t use it on a regular basis. So, much of the upper-level calculus I learned has been all but forgotten (derivatives and integrals anyone?) and I have to say, it doesn’t seem to have done me any harm. To suggest that many jobs/professions/vocations require upper-level mathematics is simply not true. That said, I’m not sure analysing Shakespeare in mandatory year 12 English or studying Leni Riefenstahl’s role in propagandizing the arts during the Third Reich in year 12 modern history is going to get us very far in most of our later careers either.

This brings me back to the same argument I seem to have to make in every one of these posts – when we are debating aspects of education and schooling it is imperative that we are on the same page in regards to what we are debating.  What are we trying to achieve and whose purpose are we serving in school?

As part of the new curriculum overhaul (more on this next week), the 2019 announcement by the NSW government that Maths will be compulsory for all students up to year 12 was a welcome announcement, in my opinion. I think they outlined it well, with the Premier (Australian version of a governor) stating, “My vision is for every child in NSW to have the necessary maths skills to succeed in life, whether that’s managing home budgets or preparing them for the jobs of the future in science, technology and engineering.”  Clear, concise and, again in my opinion, on point. What this suggests is that there will be various math pathways for students of varying abilities, especially in the upper years (11 & 12), where mathematics will now be compulsory for all students. However, and this is a big however, the curriculum overhaul, which moves the entire K-12 curriculum into what I’ll call more functional and practical mathematics, may not prepare high achieving students for the type of math in those advanced streams in the later years. The new curriculum has received criticism from mathematicians and mathematics academics, who say that the new curriculum is ‘faddish’ and that eliminating and/or delaying fundamental skills will see Australian students continue to fall in comparison to international peers on international assessments. While I don’t particularly care about these assessments our government does and seems to announce a new review into teaching education every time the results come out and Australia slides farther down the rankings.

So, what does this tell us? It tells us that we need to look very carefully at what we do as educators and how we do it. Mathematics and, more importantly, numeracy, is an imperative life-skill. However, while being numerate is incredibly important, understanding complex mathematics may not be. How do we create a schooling system, and more importantly a mathematics curriculum, that can cater to the needs of preparing students for essential STEM careers, while also teaching students the fundamentals of budgeting, compound interest and amortization tables in loans as invaluable life skills?

The first thing to do is to listen to the experts and unfortunately, that seems to be lacking in this instance. Maybe, and I realise this is a radical idea, we need to ensure that trained mathematics teachers are actually teaching mathematics classes in schools.  Yes, you read that correctly. According to an analysis of TIMMS data almost 1 in 4 Australian year 8 students are taught by teachers whose major qualification was in a field other than mathematics. If you have a look at the graph from The Conversation you can see how well students are faring in mathematics by the qualification of the teacher.

What can we conclude from this?  I think the data speaks for itself – the teachers with the best results are those that major in both mathematics and education and the results get worse the farther teachers’ education moves away from mathematics. We need to focus on ensuring the right teachers are in front of the classes that need them most.  It is nonsensical to think that mathematicians can teach and that teachers of other disciplines can automatically teach mathematics. Teaching, especially at the high school level, is nuanced – one needs both discipline knowledge and knowledge, experience and expertise in the art and science of pedagogy. If there is a teacher shortage in mathematics and science, as we continue to hear that there is, incentivise experts in those areas to study to teach or incentivise excellent teachers to retrain in mathematics. With the right incentives, I’m sure this can happen.

However, coming back to the mathematics curriculum, it seems there is a meshing of the  fundamental ideas of mathematics and numeracy. What the curriculum seems to be proposing is numeracy, which is a general capability that is taught across all curriculum areas and includes mathematical knowledge. Numeracy or being numerate is basically the practical application of mathematical knowledge in real-worlds contexts. Mathematics, on the other hand, is an abstract science of numbers, quantity and space.

The basics of mathematics, as taught in the Australian Curriculum, has four strands: Working Mathematically, Number and Algebra, Measurement and Geometry and Statistics and Probability.  We shouldn’t confuse the teaching of a science of numbers with the practical application of that science in real-world contexts. In other words, understanding how compound interest works and why investing in your Superannuation (401K) today will benefit you even more in retirement is not the same as understanding P (1 + r/n)^(nt). That said, one does need to understand the premise of equations and the order of operations in order to be able to predict how much $1000 put into retirement savings today will equal in 40 years’ time.

The basics of mathematics is not being more numerate. The basics of mathematics is still mathematics, the same as the principles of learning English are not just being literate, but understanding principles of grammar that underlie reading literacy.  Maybe that’s not the best analogy, but, to double down on the point I was trying to make, understanding that I was trying to form a good analogy to better make my point is another linguistic expression within the English discipline.

The point I’m trying to make is that the basics of mathematics are imperative for all the functional and theoretical mathematics that come later. A ‘back to basics’ move that loses focus on the specific language and foundations of the science of numbers, quantity and space will not only not prepare our students for the STEM careers of the future, it will also limit their capacity to be numerate in the functional and practical aspects of applying the basic concepts of mathematics to everyday situations such as mortgage amortization and compound interest. One may fundamentally be taught and understand the concepts of compound interest and amortization (mathematical literacy and/or numeracy), but being able to solve P (1 + r/n)^(nt) or ƥ = rP / n * [1-(1+r/n)^-nt] ƥ = 0.1 * 100,000 / 12 * [1-(1+0.1/12)^-12*20] is another story.