As a school student, mathematics was definitely not Sandi McCutcheon’s strong point—her memories of the subject at high school are mostly of being sent to sit in the corridor during lessons.
Recently, however, Sandi graduated from Victoria University of Wellington with a PhD in education, specialising in mathematics teaching—and no-one is more surprised than Sandi herself.
Sandi’s background is in primary teaching, including a period as a sole-charge principal at a small country school. After moving to a bigger school, she was put in charge of professional development for the other teachers. That experience led to a job at Victoria’s Faculty of Education where she spent four years advising on a nationwide development tool for teachers called the Numeracy Project.
“From the Numeracy Project I learnt more maths than I had in my entire lifetime,” she says. “That was because I realised I could actually do it my way—I didn’t have to do it the way the teachers had told me.”
The experience inspired Sandi’s PhD. “Because I hadn’t been a successful maths learner, I became very passionate that the kids in my class would have strategies to be successful. So my PhD is looking at how teachers position themselves with the students so that know-how can be shared.”
Sandi carried out her research at two Wellington primary schools—one low and one high decile. She videoed and observed lessons in 12 different classrooms, concentrating on the lowest and highest achieving groupings within those classes.
“I measured engagement, not just in terms of talking,” she explains. “I looked at whether the students were focusing on the lesson, or whether they were preoccupied with something else. I was also able to measure their participation by how the teacher responded to them.”
Sandi says the thinking behind her study was to encourage teachers to discuss all the students’ responses, whether they were right or wrong. “When a teacher explores students’ ideas, even if they’re incorrect, the pupils get a better understanding of an issue than if the teacher just said they were right or wrong.”
The teachers Sandi worked with on the project have been fascinated by her findings.
“They’re adopting ideas from what I’ve been able to show them. It’s very hard as a teacher to notice what you do—it’s usually very much ‘in the moment’—whereas this provides an opportunity for reflection.”
From her research Sandi has created a set of guidelines on strategies to engage, and get the best out of, students, which she hopes teachers will use to analyse the way they work.
“There are ideas coming through from this which give some good suggestions about how to effectively teach mathematics and how to have the students doing more of the mathematics than the teachers.”