Inquiry Maths

Inquiry Maths is a model of learning that encourages students to regulate their own activity while exploring a prompt (an equation, statement or diagram). Inquiries involve the class in questioning, conjecturing, generalising and proving and, when required, in listening to an explanation. In Inquiry Maths, students learn to take responsibility for directing the lesson with the teacher acting as the arbiter of legitimate mathematical knowledge and activity.

Inquiry Maths establishes a culture of curiosity, collaboration and openness in the classroom. Students meet new concepts and procedures when they are necessary, meaningful and connected – necessary to make progress on a line of inquiry, meaningful in the context of the inquiry and connected to other concepts and procedures in the field of inquiry.

Introducing Inquiry Maths

New on the site for January 2022

The new prompt this month invites students to verify and extend an inequality, before using different representations to explore further.

Chris McGrane reports on an inquiry he carried out with his S1 class. Students were being mathematicians during their conduct of the inquiry.

We report on a structured inquiry into the equations of a circle prompt. Year 12 students agreed on the steps to test different cases.

Most viewed inquiries in December 2021

Mathematical inquiry processes: Interpret; identify patterns; conjecture, generalise and prove. Conceptual field of inquiry: Algebraic terms and expressions.

Mathematical inquiry processes: Generate examples; conjecture; test particular cases. Conceptual field of inquiry: Pythagoras' Theorem; trigonometry.

Mathematical inquiry processes: Identify properties; generate examples; find all cases. Conceptual field of inquiry: Multiplication; algebraic expressions.

What students say about Inquiry Maths

Illustrations: Year 11 students evaluate an Inquiry Maths lesson on mini-whiteboards and a year 7 student gives written feedback.

“Doing Inquiry Maths was the best maths lesson I ever had because it taught me how to think." year 7

"My independent learning ability has improved. It made me think outside the box!" year 11

"Having a say in what we do makes me work harder." year 10

"I ask lots more questions in maths after doing inquiry lessons. Last week I made up my own inquiry on enlargements." year 8

"I used to just explore a problem, but now I have to stop and decide what to do." Year 10

What teachers say about Inquiry Maths

"The Inquiry Maths process gave the students the experience of being real mathematicians, something which is far too rarely the case in schools. They loved it and I felt that I learned much more about their strengths than I had in the preceding lessons." Luke Pearce

"It was an absolute joy to teach in this way." Emmy Bennett

"The students’ responses were inspiring, amazing, and truly beyond any of my expectations." Michelle Cole

"I didn’t expect the level of commitment and mathematical language from the class. It was one of the best lessons I have had with them!" Shawki Dayekh

"Some brilliant work from the students. One of those lessons that makes you love being a teacher." Chris McGrane

"An inquiry approach is ideal for a mixed attainment class because it supports and challenges all students and allows them to direct their own learning." Helen Hindle

More comments from teachers

Habits of Mind poster

Hamdi Ahmed, a teacher in north London (UK), designed this poster for her classroom. The inner ring displays specifically mathematical habits of mind, while the outer ring shows more general habits of mind that are developed through inquiry. Hamdi focuses on one of the habits in each of her Inquiry Maths lessons. She says that one of the most important is the management of impulsivity. When students notice something in a prompt, they often want to dive in and explore without first thinking of the best way to inquire.

Inquiry Maths habits of mind poster.pdf

Dr Andrew Blair, a secondary school teacher in London (UK), created the website in 2012 to promote inquiry learning in mathematics classrooms. Independent of all companies and organisations, the site is being developed in collaboration with teachers from around the world. Their experiences and reflections enrich its pages.


We welcome feedback about the Inquiry Maths model and using the prompts in classroom practice. Contact Inquiry Maths


The first five prompts on the Inquiry Maths website were developed with the assistance of a Teacher Fellowship from the Gatsby Charitable Foundation in 2004-05.