Australasian Science: Australia's authority on science since 1938

## Maths Teaching Faces a Crisis

By Michael O’Connor

**With student numbers swelling, new graduate teachers alone cannot make up for the impending retirement of many mathematically qualified teachers.**

If your child’s team needed a new coach, would you choose an enthusiastic volunteer who has never played the game, or someone who had played and been coached themselves by professionals?

In recent months, the Australian Mathematical Sciences Institute (AMSI) has published two papers on the current status of mathematics teachers in Australia (https://bit.ly/2FF83jX; https://bit.ly/2EOPMh3). We identified a steady decline in qualified mathematics teachers at high school over the past three decades. The reasons for this are many and varied, but in this article I want to focus more on why qualifications matter.

To be qualified as an in-field mathematics teacher in this sense is defined in Australia as having studied mathematics or mathematics education units to at least the second year of an undergraduate degree. The expectation should be even higher for teachers of Years 11 and 12.

Having taught high school mathematics for many years, having a wider knowledge of the subject than just what is contained in the curriculum or textbook has allowed me to connect what is going on in the classroom with the world outside. It’s in the best interests of the students to have teachers who have the tools and understand enough extra mathematics to be able to make sense of wing aerodynamics, the spread of disease or data encryption, because these are part and parcel of our modern world.

Mathematics is a difficult subject precisely because it deals with things that cannot been seen and not easily related to perceived experience. This does not make them any less important to understand. Often this is seen as a difference between thinking in either absolute or relational terms.

As an example of the difference between the two, I recently heard a media commentator trying to explain away climate change using a bag of rice. He likened Australia’s carbon dioxide contribution to being equivalent to a single grain of rice. In absolute terms how could something so small make a difference?

However, the effect is not one of volume but of attributes that cannot be seen. For example, a carbon dioxide molecule is about one-and-a-half times more massive than either nitrogen or oxygen as it is made up of three atoms rather than two. If two identical bags of rice were placed on a scale balance they would be equal. Changing just one grain of rice for one the same size but heavier would tip the scale out of balance. And the problem of climate change is essentially one of tipping the balance.

Another characteristic of the unseen nature of mathematics is that it requires the mind to be trained to imagine and explore what it cannot see. I remember a story I heard decades ago about a factory where a piece of machinery stopped working. None of the operators could determine what the problem was, so they called the manufacturer for help. The manufacturer sent out one of their engineers, who first listened to the workers to find out as much information as possible. Then he picked up a hammer and gave the machine a tap in a particular spot. The machine started working again.

Before before leaving he wrote out an invoice for services to the total of $1000. The foreman immediately started protesting: $1000 just for a tap with a hammer? Surely not!

Without a word the engineer took back the invoice and made a correction. Tapping with a hammer: $0.50. Knowing where to tap: $999.50.

Teachers often have similar situations in their classrooms. However, in addition to providing the answer, teachers need to be able to communicate what they know and can picture in their minds. Teachers are like trail guides, both navigating a path and highlighting history and scenery of the landscape through which the group is travelling.

Mathematics classes in high school are often heavily dependent upon textbooks as a source of practice materials. Without a teacher who possesses background knowledge and experience this can become just training in routines, much like “learning” one’s tables. The learning of tables will aid in quick recall but does not connect those facts to what happens to the force needed to lift a car when you double the length of a lever, or why, when you want to double the area of a photograph, you multiply by a factor of square root two. What is lacking in many secondary school mathematics staffrooms in Australia is a critical mass of teachers educated in the ideas that make the routines applicable to real life.

Last year an Australian report published in Research in Science Education (https://bit.ly/2JSYQ8U) quoted a qualified biology teacher who was also required to teach senior mathematics:

Not knowing the content and not being able to answer the kids’ questions if they throw you a curve ball. I’m having a real problem with connecting concepts because I’m learning the concepts separately. A ‘good’ teacher would connect it all, tell the kids how this relates to that, but I can’t see it myself, so I can’t tell the kids. That’s another source of my frustration.

There is a lot of good work being done by out-of-field teachers, but they lack the method experience to recognise the connective tissue between ideas and often have no colleagues from whom they can learn.

In 2016 there were 1683 mathematics graduates teaching in schools, or about 6% of the 29,000 teaching workforce. Of those, the single largest age group was between 50 and 59 (Fig. 1).

These teachers will have entered retirement within a decade, and present trends show they will not be replaced by teachers with similar qualifications. Compounding the problem are estimates that around 30% of the remaining teachers in mathematics classes classify as out-of-field.

To solve the problem, it is necessary to tackle it in two ways:

- encourage more students to study mathematics at university and then become teachers; and
- retrain the existing teaching workforce to increase their knowledge, skills and understanding in mathematics through formal pathways.

The scope of the problem requires decades of persistence and the effort of a multitude of stakeholders: government, tertiary, teacher bodies, education departments and jurisdictions, and teachers themselves. A coordinated approach similar to the one outlined in AMSI’s first occasional paper (https://bit.ly/2FF83jX) may restore the balance over the next 10 years, but a longer time period will be needed to change the cultural mindset to one of valuing teachers and making it an aspirational first-choice career. The cost will be considerable, but the cost of not addressing the issue will be more.

I want to return to the question I posed at the start of this column. I have been an enthusiastic volunteer football coach. More precisely, I was enthusiastically volunteered by my 8-year-old son. In the 3 years I worked with them I saw him and his teammates come along well. In all honesty, however, I was always aware that a more skilled and qualified coach would have given them much more than I had to offer.

**Michael O’Connor is Schools Outreach Manager for AMSI.**