# Research and articles

# Articles

Mathematics Teaching 281, 2022

In Building an inclusive community of mathematical inquiry, Hollie Walton and Andrew Blair argue that inquiry classrooms are equitable classrooms.

Hollie and Andrew discussed the article with MT editor Tony Cotton for a podcast. They also ran a workshop at the Mixed Attainment Maths conference in London (UK) in July 2022.

The relationship between inquiry and instruction Andrew Blair (Mathematics Teaching 277, 2021)

Inquisitive about inquiry? Loaded with cognitive load Mike Ollerton, Jude Stratton and Anne Watson (Mathematics Teaching 270, 2020)

Planning and unplanning mathematical inquiry Andrew Blair (Mathematics Teaching 271, 2020)

Capturing mathematical curiosity with notice and wonder Aaron M. Rumack and DeAnn Huinker (Mathematics Teaching in the Middle School, 2019)

Models for teaching mathematics revisited Andrew Blair and Helen Hindle (Mathematics Teaching 268, 2019)

Inquiry Maths: an idea whose time has come Andrew Blair (Mathematics Teaching 240, 2014)

Inquiry in mathematics education Michèle Artigue and Peter Baptist (2012)

Getting started with student inquiry (2011)

Effective questioning and responding in the mathematics classroom John Mason (2010)

Inquiry teaching Andrew Blair (Mathematics Teaching 211, 2008)

When the problem is not the question and the solution is not the answer Magdalene Lampert (1990)

# Featured research article

Makar, K. (2024). Primary teachers' early and retrospective instructional vision of mathematical inquiry. Journal of Educational Change, 25, 173 - 196.

Professor Makar explores how teachers' perceptions of inquiry evolves as they gain experience of teaching mathematics through inquiry over five years.

# Research

## Reading list

This is our reading list of books, chapters, PhD theses and articles from research journals about inquiry in mathematics classrooms. Topics covered include the nature of mathematical inquiry, classroom practice, outcomes of inquiry learning, and training teachers in inquiry methods.

Contact Inquiry Maths with suggestions to include on the reading list.

Last updated in March 2024.

## Research questions

Postgraduate students and trainee teachers who are interested in carrying out research into the Inquiry Maths model and mathematical inquiry more broadly might consider research questions related to the following topics:

types of students' inductive and deductive reasoning (exploring, conjecturing, reasoning and proving) in mathematical inquiry;

establishing a culture (or community) of inquiry;

the negotiated regulation and direction of inquiry;

the development of students' questioning and noticing of properties;

mathematical discussion;

learning, connecting and representing concepts;

the development of lines of inquiry;

the teacher's role in orchestrating, structuring and guiding inquiry;

incidences of student agency, initiative and independence; and

the psychological and philosophical bases of mathematical inquiry.

Research-based structured inquiry

When Richard Glennie, a teacher of mathematics at Levenmouth Academy (Fife, Scotland), started using Inquiry Maths prompts he devised a structured approach to classroom inquiry. Richard divided each inquiry into four stages: notice, wonder, explore, and found.

He designed an organiser so that students could keep a record of their inquiries as they passed from one stage to the next. Richard also used the organiser to plan inquiries, replacing the final stage with 'learn' (see 'Planning Inquiry Maths lessons' here). To support his model, Richard linked each stage to research.

# Essays and theses

University of Edinburgh, 2023

Emily Borrill, a newly qualified teacher, compares philosophical inquiry (PwC) with Inquiry Maths.

Emily submitted the essay as part of her postgraduate qualification in mathematics education (PGDE).

University of Cambridge, 2017

In her MPhil thesis, Jane Moss explains how she and her colleagues used a lesson study approach to implement Inquiry-Based Tasks. Aiming to develop reasoning in A-level classes, the teachers "evolved from a group of practitioners into a collaborative democratic partnership, where rich dialogic and supportive discussions emerged."

# Universities

## Inquiry Maths workshops

There have been Inquiry Maths workshops at the following universities:

Birmingham (UK)

Brighton (UK)

Cambridge (UK)

Dundee (Scotland)

London Metropolitan (UK)

Manchester Metropolitan (UK)

Maryland (US)

Part of a workshop on approaches to learning mathematics.Nottingham (UK)

Sheffield Hallam (UK)

St. Mary's (UK)

UCL Institute of Education, London (UK)

Sussex (UK)

Warwick (UK)

## Trainee teachers' reflections on Inquiry Maths

### London Metropolitan University

Trainee teachers at London Metropolitan University have been using Inquiry Maths in their practice since 2016. Some have created their own prompts, while others have devised new concepts with which to plan and analyse inquiry lessons. Below are links to a selection of the trainee's projects:

Developing independent and self-aware learners

### University of Brighton

Trainee teachers on a course at the University of Brighton (UK) in 2014-15 review an article about Inquiry Maths.

Masters in Education interview

Chelsea Young, an MYP teacher at the Canadian International School in Singapore, contacted the Inquiry Maths website with four questions for her Masters in Education course. Dr Andrew Blair replied.