Imagine a young girl sitting at her desk, having just been given a maths task that seems a bit more challenging than usual. The task looks intriguing, but she’s not sure how to tackle it. Around her, a hum of focused activity fills the classroom. The walls are adorned with reminders that mistakes are a natural part of learning, and that maths isn’t about memorising but about making sense. Despite being unsure where to start, the problem piques her curiosity. She takes a deep breath and whispers softly to herself “This is tough, but so am I”. She looks up and sees her teacher, smiling encouragi ..read more

What does mathematics look like to outsiders? It’s often presented as a polished, existing entity to be memorised, rather than as a messy and creative exploration of one’s own ideas. Reuben Hersh used a metaphor of mathematics having a ‘front’ and a ‘back’. The ‘front’ represents the formal, precise, and abstract mathematics encountered in textbooks and lectures, akin to the formal dining room in a fancy restaurant. In contrast, the ‘back’ is informal, intuitive, and tentative, similar to the chaotic scenes in a restaurant’s kitchen where chefs experiment, taste and tweak. Hans Freudenthal use ..read more

As part of a suite of actions to address the teacher shortage in Australia, the Federal Government recently released its latest reform agenda for initial teacher education (ITE) titled ‘Strong Beginnings: Report of the Teacher Education Expert Panel’. Among other actions, the report identifies and mandates four areas of core content that must be included in every accredited ITE program. I read, with great interest, the section on ‘numeracy’ and tweeted my initial reaction. (Spoiler, I didn’t like it much.) While ‘the Panel acknowledges that the core content is not intended to cover everything ..read more

In 2015, Coca-Cola ran a television ad in the Middle East reminding that labelling people builds prejudices and often divides rather than unites us. You can watch that ad here. There are two labels in mathematics education that particularly rankle me: labelling learners as ‘low/high’ and labelling teachers as ‘out-of-field’. Both labels are heavy with insinuation. The first label often implies that ‘low’ children are not capable students. The second label often implies that ‘out-of-field’ teachers are not competent teachers. Out-of-field teaching Out-of-field teaching is commonly understood to ..read more

When was the last time you got caught up in the quest for the ‘perfect’ task? Scouring the internet for a rich activity to make all students think, about mathematical ideas, and in meaningful ways. Even for an experienced teacher, with a curated set of reliable sources1 and the skill to judge whether a task aligns with their learning intention, this can be a huge time-sink. The challenge is even greater for novice teachers. Where to look? Which websites are trustworthy? Is the task a good fit for the topic? For the students? It’s understandable that we can find ourselves short of time and defa ..read more

In an earlier blog post I examined how the term ‘problem solving’ means different things to different people, and how this can lead to unhelpful cross-talk in discussions about teaching mathematics.  So what about the term ‘rich task’? The use of these tasks is often encouraged as good pedagogical practice. But are we talking about the same thing? Before reading further, I encourage you to pause to articulate what you mean by rich task as it will be helpful to have some kind of image in mind before continuing on. To explore what ‘rich task’ means, I turned to some of my favourite thinkers ..read more

In the last blog post I described the origins of pedagogical content knowledge—‘that special amalgam of content and pedagogy that is uniquely the province of teachers’—by Shulman and colleagues. PCK, as it is commonly known, is an important acknowledgment of the professional skills of teachers in combining knowledge of subject-matter and of teaching. But what does it look like in practice?  In another classic paper, ‘Content Knowledge for Teaching: What Makes It Special?’, Deborah Loewenberg Ball, Mark Thames and Geoffrey Phelps reviewed the literature published in the 20 years after PCK ..read more

There’s a saying that “everyone thinks they are an expert in education because they went to school”. As policymakers propose a suite of actions to address the teacher shortage by attracting, training, and retaining people in the profession, it seems more important than ever that people gain a deeper understanding of the complex work of teachers. In this blog post, I identify some of the key points from a classic paper examining the knowledge and skills required for high-quality teaching.  Subject-matter (or content) knowledge is clearly a necessary ingredient. In a seminal paper ‘Those Wh ..read more

I was on the radio this morning, talking about the power of mathematical stories. Ockham’s Razor is a ~10 minute program, broadcast each Sunday on ABC Radio National—and webcast around the world—to provide “a soapbox for all things scientific: stories, insights, arguments or tributes”. I was one of eight speakers recorded at a live event in November 2022, and my story was broadcast on Sunday 4 December. The talk is quite different to my recent blog post, despite being on the same theme. You can listen to the episode here, and download the script of the talk here. Naturally, I couldn’t give due ..read more

Mathematics is full of stories. Stories that delight and intrigue, like Fermat’s note promising a proof too large to fit in the margins of the page, and (apocryphal) stories of insight, like a naked Archimedes leaping from his bath shouting ‘Eureka!’.  Stories bring mathematics to life. They also help us to make meaning of mathematical ideas. In his book ‘Mathematics for Human Flourishing’, Francis Su writes: “For millennia, humankind has used stories to convey history or essential truths. A story creates a narrative from disparate events and connects listeners to itself and to one anothe ..read more