10 things students learn in Inquiry Maths classrooms
Why should teachers adopt an inquiry model of teaching? It can be daunting to take the risk of opening up the lesson to students’ questions and even more so if you invite students to direct the lesson. Yet, if you ask students, they will tell you that they learn maths better in inquiry classrooms. Here are some of the statements they have made during Inquiry Maths lessons over the 2012-13 academic year.
1. Students learn mathematical concepts and, at the same time, they learn how to learn.
"Doing inquiry maths was the best maths lesson I've ever had because it taught me how to think."
"You can learn in different ways - talk to the person sitting next to you, work on your own to understand everything or just do a small part of the inquiry. Before, we didn't think about that because the teacher just told us."
2. Students learn that mathematical concepts are inter-related.
"Lots of different ideas come up in the same lesson. It’s not like having a lesson objective that everybody has to learn."
"It’s better in inquiries – sometimes there are so many ideas, I only realise what I've learnt at the end."
3. Students learn how to apply concepts and skills to new contexts.
"I think I am better at solving problems now. I look for alternative ways of doing things, especially trying to use algebra."
"I've learnt new techniques to use in the future."
"My independent learning ability has improved. It made me think outside the box."
4. Students learn how to regulate and monitor their learning.
"I used to just explore a problem, but now I have to stop and decide what to do."
"Using the cards has really helped me to understand how many different ways I can solve problems."
5. Students learn how to ask questions and pose problems, and decide which questions and problems are mathematically valid.
"I ask lots more questions in maths after doing inquiry lessons. Last week I made up my own inquiry on enlargements."
"I've learnt how to find answers to my own questions."
6. Students learn to explore, make conjectures and prove for a general case.
"I benefited from an inquiry lesson as I could show how I proved my answer was correct using algebra."
"Sometimes we make up examples, but my favourite bit is when we talk about how to prove an idea with algebra. Then it has to be right."
7. Students learn to use the authority they have responsibly.
"I like inquiries because I'm partly in charge."
"I think the class behaves better when we’re all working together on an inquiry."
8. Students learn how to be independent inquirers who can maintain high levels of motivation.
"What’s different is that I feel I have a say in what we do. That makes me work harder."
"When I ask a question, I want to answer it more."
9. Students learn to identify when they need to know new concepts and to seek out sources of that new knowledge. 
"We can ask the teacher to explain if the inquiry gets stuck." 
"There’s a lot more people helping each other in inquiry lessons. It’s a good way to learn."
10. Students learn that learning can be unpredictable, novel and exciting.
"Inquiry maths has really given me an insight into investigating problems with an array of answers for all different levels."
"Inquiry is more fun because I'm learning loads, but it doesn't feel like it."

Andrew Blair
July 2013