About Primary Maths Craft

The craft of teaching primary mathematics

Primary Maths Craft is a professional space for thinking deeply about the teaching of primary mathematics.

It is built on the belief that effective maths teaching is not defined by activity, coverage or resources alone. It is shaped by the precise decisions teachers make about how mathematical ideas are structured, represented, questioned, connected and brought into focus for pupils.

Through the Primary Maths Craft framework, the site explores the craft beneath the surface of a lesson: the architecture that connects ideas, the representations that reveal structure, and the careful direction of attention that helps pupils understand what matters.

About the author

Phil Hackett

Primary mathematics specialist, teacher and founder of Primary Maths Craft.

I’m Phil Hackett, a primary mathematics specialist with over 12 years’ experience teaching across every primary year group.

My work has grown from years spent in primary classrooms, teaching mathematics to pupils at every stage of the journey. Alongside this classroom experience, I have worked closely with NCETM and Maths Hub approaches, engaged deeply with research-informed practice, and completed the NPQLPM as part of my work in leading and improving primary mathematics.

Over time, this has developed into a sustained and deliberate focus on the craft of teaching the subject. I think deeply about the decisions teachers make within lessons: how ideas are structured, how representations are chosen, how attention is directed, how language is used, and how teachers respond to what pupils are showing.

This thinking has culminated in the Primary Maths Craft framework: the Architect, the Artist and the Conductor. The framework gives language to the high-level pedagogy behind effective mastery teaching. It helps communicate the craft beneath the surface of a lesson: the structure that connects ideas, the representations that reveal mathematics, and the careful direction of attention that helps pupils understand what matters.

I am not a mathematician in the academic sense. My expertise is in the teaching of mathematics. My work is concerned with how primary pupils encounter mathematical ideas, where misconceptions begin to form, and how careful instruction can help pupils build secure, connected understanding.

Primary Maths Craft is where I write about that work. It is a space for exploring the craft of teaching primary mathematics and the decisions that help pupils see structure, make connections and understand the mathematics more deeply.

Explore the blog

What Primary Maths Craft Focuses On

Primary Maths Craft focuses on the instructional decisions that sit beneath effective primary maths teaching. It is concerned with how teachers design learning, reveal mathematical structure, direct pupils’ attention, use language precisely and respond to what pupils are showing.

The site is rooted in mastery teaching, but it is not about repeating familiar mastery language. It is about making the craft behind that teaching more visible: the choices, questions, representations and responses that help pupils build secure and connected understanding.

The focus is practical, but not superficial. Primary Maths Craft explores how high-level pedagogy translates into the everyday work of teaching: planning examples, choosing representations, interpreting misconceptions, building fluency, designing diagnostic assessment and deciding what needs to happen next.

The Primary Maths Craft Framework

The work on this site is organised around the Primary Maths Craft framework: the Architect, the Artist and the Conductor. These are not separate strategies or lesson ingredients. They are interconnected aspects of expert classroom practice, helping to describe the craft beneath effective mastery teaching.

The Architect

Structure

The Architect considers how mathematical ideas are built, sequenced and connected. This includes the structure of a lesson, the progression across a unit, and the way learning connects across topics and year groups.

The Artist

Representation

The Artist considers how mathematics is made visible. Representations, examples and tasks are chosen carefully so that pupils can see the structure of the mathematics, not just complete the activity.

The Conductor

Attention

The Conductor directs pupils’ attention towards the mathematics that matters. Through explanation, questioning, emphasis and response, the teacher helps pupils notice, connect and understand.

The framework gives language to the decisions that shape a maths lesson: how ideas are structured, how mathematics is revealed, and how pupils are guided towards what matters.

What You Will Find Here

Primary Maths Craft brings together reflective writing, practical resources and diagnostic tools, all shaped by the same central concern: how teachers help pupils understand mathematics more deeply.

Framework thinking

Posts exploring representation, structure, mathematical attention, teacher language, example design and the craft behind effective mastery teaching.

Classroom application

Practical thinking about the decisions teachers make in lessons: what to show, what to ask, where to direct attention and how to respond.

Fluency and diagnosis

Work on arithmetic practice, diagnostic assessment and how teachers can move from marks and scores towards more meaningful mathematical insight.

Year-group responsibility

Future writing exploring the mathematical responsibility of each primary year group and how learning connects across the wider primary journey.

The aim is not to offer quick tips for the sake of tips. The aim is to make visible the thinking behind effective mathematics teaching, so that classroom decisions become more deliberate, more connected and more mathematically purposeful.