On teaching without giving away the answer

“The mind is not a vessel that needs filling, but a fire that needs igniting.” ― Plutarch

“If you want to build a ship, don’t drum up the folks to gather wood, divide the work, and give orders. Instead, teach them to yearn for the vast and endless sea.” ― Antoine de Saint-Exupéry

One of my motivations for founding VISST was to cultivate curiosity and a sense of wonder in students. When holding office hours as a professor at UBC, I would be excited to nerd out about AI and data science but would more often be approached by students asking what will be on the test or disputing a small deduction of marks. I wished for more curiosity. And yet anyone who has interacted with children knows that they are born with a drive to wonder and inquire.

Cultivating curiosity is a laudable goal, but how does one achieve it in practice? My approach is foremost to assemble a team of life-long learners who model what intellectual curiosity looks like to our students. Practically, this impacts the types of questions we ask in job interviews and how we evaluate potential hires. We look for teachers who are passionate about what they teach — perhaps reading, consuming podcasts, tinkering, dabbling, consulting or otherwise practicing and life-long learning outside of their teaching duties. 

Beyond hiring decisions, we can promote curiosity in the way that we teach. The most common advice I give to new teachers, or students mentoring other students, is to not be too helpful. This may sound tongue-in-cheek but it is serious advice! A common misconception is that, when a student is working on an assignment or problem, the goal is for them to finish the task. Hence, helping them finish. But finishing is not the goal at all; rather, the goal is learning. As previously discussed on this blog, growth requires struggle. I view curiosity and productive struggle as in a sort of feedback loop: curiosity provides the motivational fuel for struggle, while struggle and overcoming challenges can pique curiosity for what comes next. 

In practice, every teacher will have their own approaches given their subject areas and personalities, be it inquiry-based learning, project-based learning, demonstrations, experiments, games, special guests, field trips, or something entirely different. In my math class, I often try to answer questions with questions. If a student asks how to do something, I ask them how they think it might be done. If they ask whether an answer is correct, I ask how we might assess correctness, even through a simple sanity check. Through this apparent unhelpfulness, I hope to instill the habit of questioning, as well as self-reliance and justified self-confidence.

A master of teaching without giving away the answer is celebrated Australian math teacher and YouTuber Eddie Woo. For example, in this excellent clip on the Pythagorean theorem, it’s not until almost 9 minutes into the video that he actually states the relationship a² + b² = c². This is left as the punchline. Eddie Woo knows not to give away the answer too early because doing so would short-circuit the process of wondering, “How are the sides of a right-angle triangle related?” This moment of wondering is too precious to skip. 

(Teaching without giving away the answer is one thing but, occasionally, I also engage in the more extreme practice of teaching without knowing the answer. This may come about, for example, during a math appreciation session when the thread of inquiry tugs us in an unexpected direction. I generally don’t recommend teaching without knowing the answer of course, but from time to time it can help to model forging into the unknown and create authentic moments of vulnerability as a teacher.) 

One of the many difficulties of teaching is providing just the right amount of help so that students are able to make progress, but must practice their sense of curiosity and challenge themselves along the way. It is my sincere hope that, as educators, we can help ignite the fires of curiosity, and take good care to keep them aflame. 

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If you are seeking a way to build mathematical curiosity before high school, consider checking out VISST’s Math Club for Grade 5-7 students.