A snail is climbing out of a well. Every day it climbs up 3 metres, each night it slips back 2 metres. If the well is 10 metres deep, and it begins at the bottom, after how many days will the snail be free?

Teaching critical thinking skills is a complex process, but the mathematics classroom is fertile ground for helping students to improve in this area. An excellent example occurs when a child is asked to explain his/her thinking to the rest of the group regarding a mathematics situation or problem. When a student is asked to work a problem at the board, the teachers are not asking him/her to tell the class the answer to the problem in question, or tell us how he/she did the particular problem. Instead, we reiterate to the students that we want them to “show us how they thought about” the particular mathematics problem. It is their thinking we are interested in, as careful analysis leads both to clearer and deeper conceptual understanding of the mathematics and to stronger general critical thinking skills.

The student who is working the problem and the rest of the class group are all improving their thinking skills during these moments. First, the students who are not at the board are working to grow in their ability to listen attentively and persistently, to follow another person’s thinking, to analyse the clarity of thought of the student at the board, and to ask supportive questions that help the student think more clearly. This is hard intellectual work, and especially difficult when the teachers, as we do, really push the students to actively do this work. Constant feedback, reminders, questions, and praise keep everyone carrying the heavy weight of this intellectual work.

You’ll often hear us saying things such as:

• Think hard. It’s the work of mathematicians.

• I need to hear from someone new – someone who hasn’t commented on our colleague’s thinking.

• Just take a risk and put something out there for us to think about.

• When someone is at the board explaining, it isn’t a time for you to stop listening. Mathematicians are very keen observers – you don’t want to miss a thing.

• Let’s hear from everyone else. Do you all agree or disagree with your colleague’s statements about this problem?

Also, consider the child who is at the board articulating his/her thinking. The child is asked to very precisely walk step by step through his/her work so that everyone can hear him/her using mathematical vocabulary. He/she is pushed to not assume anything, and to explain each leap in his/her thinking, and he/she is held to high standards when explaining. We don’t guess what’s in his/her mind and assume we know what he/she meant to say, we ask him/her to do the bulk of the cognitive work and actually figure out the way to articulate each step of his/her thinking all by him/herself. Any steps that don’t make sense — either seem to be unclear or do not have a mathematical property governing them — are brought to the class community for discussion. The students agree, disagree, ask questions, and grapple with their peer’s work.

It is in these moments — when one of our students steps to the board to analyse a problem — that you see what it really looks like to grow critical thinking skills, expand students’ ability to think in a disciplined manner, and empower children to understand the beauty and richness of mathematics.

Donovan Doyley is a lecturer of mathematics at Sam Sharpe Teachers’ College and former principal of a technical high school. Send comments to the Observer or donovandoyley15@gmail.com