No easy answers

Teachers tend to teach (initially anyway) in the manner in which we were taught. Direct instruction has traditionally typified mathematics teaching, although there has been a push towards constructivist approaches to teaching and learning over the last twenty years. However, when beginning my teaching career in 2011, exactly how to promote communication, justification, and mathematical reasoning, was a bit of a mystery to me.

Understanding how to respond to student questions was a great ‘unknown’ for me when I started teaching.

Much of our teacher training involved curriculum, understanding the New South Wales Institute of Teacher Requirements, educational psychology, and contemporary issues in education. Like many graduate teachers the day-to-day ins-and-outs of classroom management were still somewhat of a mystery to me.

An area I particularly lacked knowledge and skills was that of questioning. I firmly believe that questions are one of the biggest tools a teacher possesses. Careful questioning scaffolds students’ thinking: enabling them to see connections between concepts and link new learning to prior knowledge.

As a beginning teacher I was somewhat scared of questions. I wasn’t quite sure how to ask them, nor how to respond to them. Posing questions is an enormous topic that I’ll devote another blog post to, in order to keep the focus for this article on responding to questions.

A huge trap I fell into when I started teaching was wanting to give an ‘easy’ answer to questions. My kids felt safe with the straight, easy answer and so did I. Providing a straight response was quick for me, and let me move onto some other activity or student, and avoided getting involved in more ‘tricky’ situations.

The sort of question that maths teachers hear all the time

“Miss is this right?”

“How do I do this Miss?”

“What am I meant to be doing Miss?”

and so forth.

Initially, lacking confidence in my teaching ability and having limited pedagogical knowledge I would typically respond to these questions with


“Like this”

“Page 59, questions 2, 4 and 6.”

Then I implemented the policy of answering a question with a question.

I wanted to challenge my students to become more independent learners. I wanted them to be able to develop metacognitive strategies: by answering a question with a questioning I was scaffolding thinking that they would one day internalise. By taking this approach I was no longer treating them as ‘giant buckets to be filled with information:’ I instead considered them to be capable of intelligent, engaging discourse.

My responses are now more likely to be

“Do you think that’s a reasonable answer? Why?”

“Why would you think your answer is wrong?”

“Given what we’ve covered today in class, where do you think you might start that problem?”

“What information do we have that we can use to solve this?”

“Where might you find out, other than asking me, what you are meant to be doing today”

These responses force learning to be student-centred: it puts the onus back on the student. It signals to the student that they have the knowledge, and the capacity to work through the issue themselves. It creates an environment where students are empowered and are afforded a higher degree of autonomy.

It shifts the role of the teacher from being the bearer of all knowledge, to a facilitator of the learning process.

It signposts to students that I’m not just interested in their answer, I’m interested in the process and I’m interested in their reasoning. As I have said many times in class: ‘if you can’t convince me you’re right, as far as I’m concerned you’re wrong.’

Obviously, answering a question with a question is not going to be applicable in every circumstance within the classroom. Sensitivity is required, especially when beginning to implement, to know how far to push students: some students will find this approach extremely frustrating (and even a little scary).

However, the benefits to my teaching practice have been overwhelmingly positive. I’m a far more interactive, student-centered teacher, and I’m working with (instead of ‘directly instructing’) my students to be more independent, empowered, and engaged.


About madelinebevs

Mathematics and religion teacher and researcher. Runner. Home-renovation enthusiast. PhD Candidate. I'm excited by education. Having taught high-school mathematics for several years I am currently studying a Master of Education (Honours) in mathematics education, with the aim to ‘upgrade’ to a PhD later this year. My research is addressing how the constructivist epistemology (more specifically explicit instruction in metacognitive and self-reflective strategies) influences students’ affective domain. Mathematics education and research excites me greatly. I’m thrilled that I have the opportunity to write and work in this area. This blog will be (mostly) a collection of opinion pieces published several times a week on contemporary issues in mathematics education, with an Australian focus. More often than not topics will be generated from recent news headlines.
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2 Responses to No easy answers

  1. cpaterso says:

    I’m enjoying this post and I wholeheartedly agree. Fat questions, open-ended questions, Socratic questioning may well be the holy grail in the classroom. Once teachers recognise the need to move away from guess-what’s-in-my-head I think we are approaching nirvana. Thanks for sharing your thinking.

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