Asking better questions in math leads to better math talk.
We all know that we need to get students thinking. But how do we do this? In order to get better thinking out of our students, we ultimately need to ask better questions. This builds up students creative and critical thinking abilities.
Open vs. Closed Questions
Closed questions or problems test whether the student has a factual understanding. There needs to be more creativity and generally only one correct answer.
Open-ended questions or problems involve more thought. They require students to be creative and often think of more than one solution. Some have a limitless number of correct answers, while others have a finite number, but it is definitely more than one.
Questions and problems can even extend into investigations and projects, which further challenges students to think creatively and critically.
But can you just do it with questions?
Yes, you can. By thinking about the questions, you are asking students; you can adjust your questions to prompt more creative or critical thinking.
This ensures questions are not just yes or no questions. They should invite students to share their knowledge and understanding. These sorts of questions might also show misunderstandings and help correct them.
The conversations that occur due to asking these questions are mathematical discourse. Students can reflect on their understanding. They also can listen to, take on, adjust, and critique the ideas of others. They can make conjectures and be comfortable and supported in these potentially not being correct. Finally, they can link their ideas to the ideas of others and other topics or subjects.
Through such discourse, they refine their understanding by either confirming it, adjusting it or completely changing it. They also take ownership of their mathematical learning and understanding. This would not necessarily occur in a more – teacher-centred environment without such discourse.
Students learn through modelling and practice to use mathematical language to share and discuss their ideas.
Teachers also gain the benefit of getting a deeper insight into their students’ thinking and understanding, which allows for better assessment and curriculum adjustments. They begin to understand what students know and the methods they use. They also get an insight into how well students understand the ideas. It also enables teachers to correct any misunderstandings that they might not have been able to identify before.
Benefits of Better Questions
There are many benefits of using better questions in class for students. Students:
- are working together as a class or in small groups
- become more confident in themselves and their mathematical ability
- learn to reason and justify
- reflect and evaluate their mathematical processes and understandings
- learn to connect between concepts and disciplines
- focus more on mathematical skills, not just a rote understanding of processes
Creating a Supportive Math Environment
For discourse to occur, you must ensure that the learning environment welcomes such discussion.
In such an environment, students:
- question each other using mathematical language (see creating a culture of questioning)
- learn from mistakes by discussing them with the teacher, acknowledging that they, too, make errors
- reach conclusions based on their understanding and don’t rely on the teacher to tell them the conclusion
- use a variety of approaches to share their understanding
The Understanding That Mathematics is a Language
As teachers, we need to acknowledge and understand that mathematics is a language and should be taught as such. To be considered a language, it must have the vocabulary, grammar, syntax and people who use and understand it. Mathematics meets these criteria. It is also a universal language. Mathematical discourse enables students to develop this language. Critical and creative thinking questions can help with this.
Classification of Questions
Questions can be classified in many ways. It is up to you to find a system that makes sense to you.
You could use starter questions, questions that stimulate mathematical thinking, assessment questions and final discussion questions. You could arrange by what you are checking for – accuracy, understanding, and clarity.
Or you could organise your questions by levels of mathematical thinking using Bloom’s taxonomy. Sunders (1964) split the comprehension level into two categories and created a Seven level taxonomy that might be helpful in mathematics. This added translation and interpretation Instead of just comprehension.
Implementing Math Talk Easily
So now you know it is the right thing to do, how do you actually do it?
- Ask more open-ended questions
- Push students to collaborate, explain or clarify their thinking – I am a big fan of ” so”, “what makes you say that”, and “keep going”
- WAIT TIME! When they think they have finished answering, the student’s time to respond to your questions. They need time to think. It’s hard but count and wait.
- Encourage reflection on what they have learnt and their practices
- Follow the conversation- What I mean is let it get off the road a little to see where it is going as long as it stays semi-relevant. You don’t want to stifle any connections being made that could lead to understanding
- Open up questioning of each other – model this, and your students will be doing it in no time.
Annie Fetter does a great video about asking students “what they notice” and “can you say more about it” – Amazing presentation.
But What Questions Do I Ask?
Well, to help you out, we have created a question bank for you. It is in pdf format and is a list of questions that you can ask during your lesson.
We have included multiple formats to make it easy to use.
- 1 page with all questions by category
- Question strips to laminate, hole punch in the square, and pull out for lesson use – coloured and black and white
Ideas for using this file:
- while planning, add specific questions you want to ask
- write 2 or 3 focus questions on the board to use during lessons
- pull out a few of the Strips to remind yourself
- have the whole page in front of you
- pull out a question during a discussion at random
- have a student choose a random question