# 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.

# New on the site for November 2022

We have updated the **product of factors inquiry **with resources for a structured inquiry** **and describe how to incorporate a student's question into the structure.

**Raj Vara**, a teacher in London (UK), explains how his department increased levels of student engagement by using the combined transformations inquiry.

We are grateful to **Dr Jennifer Chang Wathall** for allowing us to post her video introduction to inquiry-based learning in mathematics on the website.

# Most viewed inquiries in October 2022

**Mathematical inquiry processes:** Identify patterns; conjecture, generalise and prove; extend to other cases. **Conceptual field of inquiry:** Multiplication and addition; algebraic terms and expressions.

**Mathematical inquiry processes: **Identify properties; generate examples and counter-examples. **Conceptual field of inquiry: **Multiplication of numbers with two or more digits; algebraic expressions.

**Mathematical inquiry processes: **Notice properties; generate examples; conjecture, generalise, prove. **Conceptual field of inquiry: **Sum of integers; collect like terms; Yang Hui's (Pascal's) Triangle.

The **Mathematics Hub** funded by the Australian Government Department of Education, Skills and Employment recommends 50 inquiries from this site.

# What students say about Inquiry Maths

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

"My maths this week using a prompt has improved significantly because I have noticed and seen things I didn't even know was possible." **Year**** 6**

“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**

"It was a new technique, a maths prompt. For some reason questions just flew out of me." **Y****ear 6**

"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**

" The inquiry was so interesting that it was the first time I talked about my maths lessons at home." **Year 7**

# What teachers say about Inquiry Maths

"I love the focus in Inquiry Maths on developing mathematical behaviours in students whilst keeping the integrity of the subject." **Claire Lee**

"I was blown away by the by the depth of student responses." **Devon Burger**

"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**

# 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.

**www.inquirymaths.org **

**www.inquirymaths.org**

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.

**Feedback**

**Feedback**

We welcome feedback from teachers who use Inquiry Maths prompts in the classroom. **Contact Inquiry Maths**

**Acknowledgement**

**Acknowledgement**

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.