‘I started my PhD because I wanted to learn something about myself. I’d been teaching secondary maths for about 15 years and I was trying alternative assessments, like group work and peer reviews, to mark students on skills like inquiry and problem solving.

I was finding it hard to figure out the best ways to assess these skills, so I decided to research how and why other teachers marked students the way they did in the hope that I could improve my own practices too.

Teachers have to balance what they need to do, what they want to do, and what they’re able to do when it comes to teaching and marking.

When I looked into it, I found that there were few case studies about how this happened in real life. That was one of the biggest challenges because no one wanted to be studied.

I could delve into their background, their teaching and marking practices, and the individual decisions that they made over two school terms. I eventually ended up with four teachers so I was able to really study them well.

At first, I planned to follow 10 teachers, but it took me three months to just find one. I gathered the data in four ways: interviews, observations, questionnaires and artefacts, which included printed material like class tests and feedback.

I did almost 14 hours of interviews, sat in on 27 hours of classes, collected 49 artefacts and conducted six questionnaires with each teacher. I collected so much data that even just managing it felt quite overwhelming at first.

“Higher-order” maths means an in-depth understanding of how and why certain things in maths work the way they do. So, instead of just rote learning formulas, higher-order maths prompts students to think about how and why they come to their conclusion.

In studying four very different teachers, I found four different patterns. If I studied 50 teachers, I’d probably find 50 patterns.

‘At first I planned to follow ten teachers, but it took me three months to even find one.’

I can’t generalise my findings, but all four teachers did have one thing in common: they all wanted to improve teaching and testing higher-order maths skills.

A question that engages higher-order thinking might involve different mathematical steps and you would then ask the student to explain why they came to their answer.

It often involves reasoning and one question can have several acceptable answers. For example: “How do you know that the surface area of shape X is bigger than shape Y?”

What my study showed is that all four teachers approached higher-order thinking very differently and not always correctly. Of course, this led to them teaching and testing for it in different ways. They even defined what it was differently.

There was a tendency to think of higher-order questions simply as “harder” questions, when in fact they’re not the same thing. Higher-order thinking is just more sophisticated.

The curriculum says that these skills need to be covered but previous research also suggests that Victorian teachers are concerned about not assessing them properly.

‘By the end of the study all four teachers started to reflect on how and why they teach.’

I’m doing report cards for my Years Seven-to-10 students at the moment and one thing I’m not happy with is that we have to give the students a single mark across the term. This number doesn’t tell parents what area the student is struggling in.

I found that one of the teachers in my study was actually combining marks for effort and maths skills in the same single score. We have to make sure that the mark is giving us information about the student’s capability, because otherwise what is the use of assessing?

By the end of the study, all four teachers started to reflect on how and why they teach. Me, too. I’m more aware of how I balance what I want to do with what I can do in the classroom now.

I’m hoping these case studies serve to help other teachers think about their own practices and can also identify where more tailored professional support is needed. There’s no one right way of teaching and marking. It’s important we acknowledge that it’s a balancing act so we can work to understand it and improve it over time.’

Rohani Mohamad’s PhD is titled: “How and Why Secondary Mathematics Teachers Assessed the Way They Did.”

*My PhD is an irregular series in which The Citizen speaks with recent Melbourne University Phd graduates.