I always knew I wanted to be a teacher - even as a little girl. But if you had told me that one day I'd be a teacher and a mathematics education researcher, I probably would have laughed at you.
Mathematics and I did not always have the best or easiest relationship at school.
Like many people, I had absorbed plenty of "ideas" about what mathematics was and who was "good at mathematics".
I had also built up a picture of what kind of people taught mathematics and what teaching mathematics involved.
Looking back, I sometimes wonder how much those experiences led me towards the question I would eventually spend a few years researching: what is "success" in mathematics education?
We use the word "success" all the time, particularly in education. "Success" is an aspiration, an objective, and often a justification for the decisions we make. "Success" appears throughout policies, initiatives, documents, and slogans.
Yet, for a word we use and rely on so heavily, it is rarely - if ever - explained.
So, what is "success" in mathematics education? What does a "successful" mathematics classroom look like, sound like, and feel like? And how do we determine whether students are experiencing "success" in learning mathematics?
These curiosities sat at the heart of my PhD research and a national study involving primary and secondary teachers across Australia.
I learned a lot along the way - including enough, perhaps, to bust a few myths.
Rebecca Burtenshaw as an unassuming school student
MYTH: A "successful" mathematics student is the one with good grades and scores
One of the clearest distinctions to arise from my research is that success is not synonymous with achievement and performance.
Primary and secondary teachers consistently distinguished success from marks, grades and scores, instead describing success as something much richer, more enduring, and connected to the development of the learner more broadly.
Although we are often accustomed to using achievement measures as a proxy for success, many aspects of success were instead seen as the foundations from which achievement and performance could grow.
MYTH: Being "good" at mathematics means being fast, getting the right answers, and remembering formulas
Quick recall and accuracy certainly have their place in mathematics, but they are only part of the picture.
Rather than focusing only on what students could do, teachers emphasised how students engaged in mathematics.
They described students' willingness to have a go (super important!), take risks, persevere, explore, come to see themselves as capable "doers" of mathematics and gradually develop a positive relationship with mathematics both at school and in life beyond.
Process and effort mattered more than notions of innate ability.
In mathematics education research, these kinds of qualities are often described as part of a productive disposition - something long recognised as essential to mathematical proficiency.
MYTH: Mathematics is all about what you can do in your head or from a textbook
When teachers described what successful mathematics classrooms looked, sounded and felt like, they rarely described quiet rooms, isolated textbook or worksheet drills, or students simply reproducing procedures.
Instead, they described highly active and social spaces: students talking, questioning, exploring, collaborating, trying different strategies and learning with and from one another.
In other words, mathematics was not something that happened only inside a student's head.
It was something students actively did together, with ideas, materials, questions, mistakes and discussion all playing a part.
Once we broaden what success in learning mathematics looks like, it becomes difficult not to think differently about the role of the teacher too.
Teachers do far more than deliver content. They shape the classroom culture, what gets noticed and celebrated, and the kinds of mathematical experiences students are invited into.
So, while we're busting myths…
MYTH: Teachers of mathematics just stand up the front of the classroom talking at students
I simply do not have enough word count to explore how wrong this myth is.
Teaching involves listening, questioning, noticing, making visible connections, responding to misconceptions, deciding when to step in (and when not to), and developing exciting investigations that challenge the idea that only certain kinds of people are "maths people" (another myth!), and that we are surrounded by mathematics.
It involves creating a classroom environment where students feel safe enough to say, "I don't know yet," "I tried this," "I disagree," or "Can I show you another way?"
And yes, primary school teachers are absolutely teachers of mathematics.
Primary school teachers teach mathematics every single day and help build the mathematical foundations children will draw upon not only through school, but as future workers, professionals, and members of their communities.
MYTH: Being a teacher is the "back-up plan" for other careers in STEM
*Eye roll* Teaching is not the lesser option.
Teachers are part of the reason future scientists, engineers, mathematicians and technologists come to imagine those futures in the first place.
There is also something special about sharing something you value with others and helping them see possibilities they might not yet see for themselves.
Teachers can challenge narrow cultural ideas about mathematics and STEM, including who is seen as belonging in STEM.
And honestly, changing generations of myths about mathematics and who "gets to do" mathematics sounds like a pretty complex, worldly problem to me!
MYTH: You've got to be "good" at mathematics to teach mathematics
Some of the best teachers of mathematics I have met did not grow up seeing themselves as "maths people".
Some had complicated experiences with mathematics themselves - experiences that can become powerful resources when working with students.
For example, they might remember what confusion felt like, understand why one explanation might not be enough, or recognise the courage it can take to risk being wrong and persist anyway!
Now, that is not to say a solid foundation in mathematics should be disregarded.
It is essential. But mathematical knowledge and skills can be developed and strengthened over time - through effort, persistence and a willingness to keep trying, even when things do not make sense straight away.
I have the privilege of working alongside future teachers every week.
We grow our skills, develop new strategies and try unfamiliar approaches. We question our assumptions and challenge our perceptions of classrooms. We get surprised, get frustrated and laugh - a lot! Most importantly, we keep learning.
My students might be a little older these days, but the privilege of teaching remains the same: helping people discover what they are capable of, who they might become, and which ideas or myths might otherwise constrain their opportunities for 'success'.
Rebecca Burtenshaw's PhD is investigating how schools, teachers and education systems define "success" in mathematics.
