# Research and articles

# Articles

**The relationship between inquiry and instruction**

(*Mathematics Teaching *277, 2021) Andrew Blair discusses the relationship between inquiry and instruction in two models of educational psychology.

**Planning and unplanning mathematical inquiry**** **

(*Mathematics Teaching *271, 2020) Andrew Blair considers the detailed planning in preparation for inquiry and an openness to ‘unplanning’ in the moment of inquiry.

**Inquisitive about inquiry? Loaded with cognitive load?**

(*Mathematics Teaching* 270, 2020) Mike Ollerton, Jude Stratton and Anne Watson on the limitations of cognitive load theory and the forms of thinking promoted by inquiry.

**Models for teaching mathematics revisited**

(*Mathematics Teaching* 268, 2019) Andrew Blair and Helen Hindle contrast the 'path-smoothing' small steps approach to 'challenging' inquiry and student-led learning.

**Inquiry Maths: an idea whose time has come**

(*Mathematics Teaching* 240, 2014) Andrew Blair looks at the nature of inquiry and shows how it is compatible with the inductive and deductive nature of mathematics.

**Inquiry in Mathematics Education**

(2012) Artigue and Baptist lay out the theoretical model of the EU-funded Fibonacci Project in this booklet.

**Getting Started with Student Inquiry**

(2011) A summary of the roles of student and educator in the inquiry classroom.

**Effective Questioning and Responding in the Mathematics Classroom**

(2010) John Mason on developing a conjecturing atmosphere.

(*Mathematics Teaching* 211, 2008) Andrew Blair discusses how the Inquiry Maths model harmonises concepts with the method of learning.

(1990) Magdalene Lampert's seminal paper.

### 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 for teachers in inquiry methods. In April 2021 we updated the reading list with suggestions from **Hollie Walton**. Hollie is a teacher of mathematics and is studying students' experiences and perceptions of Inquiry Maths for a Masters degree at the University of Cambridge (UK).

**Hollie Walton**. Hollie is a teacher of mathematics and is studying students' experiences and perceptions of Inquiry Maths for a Masters degree at the University of Cambridge (UK).

# Research

## 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.

## 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.

## Inquiry Maths workshops

There have been Inquiry Maths workshops at the following universities:

Birmingham (UK)

Brighton (UK)

Cambridge (UK)

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)