Every time I teach something, I want to teach it again straight away. Why? Because on the second time around, the teachable moments are far more obvious and, perhaps, more frequent.

As a compulsive dad-joke teller (often seen as a pre-requisite for maths teachers), I will do anything to maintain the attention of the young minds in front of me. Often it’s waiting an awkwardly long period of time after saying something pun-ny to see a student roll their eyes and hear them mumble, “yes, we got it..”. Other times it’s relating The Big Splat to restoring Earth to ‘factory settings’ like an iPhone to solve environmental and political issues. Such is my commitment to making maths a relevant necessity for my students.

My aim as a teacher is to have students appreciate the place that maths has in our lives. My ‘aim’ tends to change pretty frequently and is often just a paraphrased version of, “I want students to enjoy their learning”. In order to do so, a few critical things have to happen.

## There has to be a hook

An equivalent of Dan Meyer‘s Act 1 aims to draw students in and entice their curiosity in an engaging way. Does it have to be an awesomely captivating video clip or intriguing image? No. When I was a student, I had some incredibly interesting teachers (none of whom taught maths, unfortunately) who were able to spark my interest just through the way they pitched the content and made it relevant to us. We felt like we had to learn more about something because it was so damn interesting. In fact, an engaging video or picture that has great potential to captivate and have students ready to learn could fall through the floor without an enthusiastic teacher to “make it happen”. Whether it’s your ability to come up with a weird metaphor that explains a particular mathematical relationship or concept, or just simply your passion for learning and helping others, do whatever you can to **develop the need for maths** in your lessons.

Matt Vaudry and John Stevens (authors of *The Classroom Chef*) talk about how important the presentation of the problem in increasing the cognitive demand of the learners. In their book, they describe the plating of the meal as one of the critical elements of the lesson (along with the reveal) and emphasise how the presentation of a lesson can massively impact student engagement. I found this image on Google that, for me, illustrated one of John and Matt’s chapter titles perfectly, *The Plating – Presentation is Everything*:

Same ingredients, one burger clearly prepared with more effort and thought for the customer. Which one would you prefer? If this was a choice between a lesson that was well-prepared or rushed, which one do you think your students would prefer?

## Don’t give away the plot twist at the beginning

The Lord of the Rings trilogy isn’t about the trip from Mordor to The Shire after Frodo destroyed the ring of power. Yet, so many lessons are framed in that way. I see the *teaching* of the maths (a method or way of thinking – formula, rule etc) as the one of the key moments of the lesson. In order to make this moment more memorable, relevant, and meaningful for the students, I need to let them experience everything that leads to it. Jon Orr (a self-proclaimed math geek) describes this experience as the “Hero’s Journey” – connecting the tension built up through an adventure movie to the tension in a maths lesson. I see starting a lesson by teaching a particular procedure with step-by-step instructions the equivalent of telling a reader how the book ends in the blurb. If the learners have no context or need for the maths, they are learning it by memorisation for the moment where they might need it in the near future (most likely a test).

I had a teacher observing my lesson the other day and she asked me a question just before it started in front of the class. I was incredibly reluctant to answer the question, “what are you teaching today?” I whispered to her that the students would be learning about compound interest, in the hope that no student would overhear what I had said. Why didn’t I want the students to know? Learning about compound interest requires students to differentiate between compound and simple interest, a key mistake I was hoping students would make in their initial calculations. I knew that, for the students, this could have been a sacred “a-ha moment” – a goal in for maths teacher.

## Students should be able to estimate the answer

I want the learning experience to feel as real as it would if you weren’t a student in a school. What I mean is that, as adults, we encounter problems that we assume we can solve with our current “skill set”. From working through a problem there often comes a point when we realise that we either need a different approach or need to think differently about the problem entirely. It is at this moment we look to learn something new because we have a need for it, a purpose. Our students need to be provided with the opportunity to do the same. I was asked to talk to a small group of teachers about how they could promote inquiry in their maths lessons and provide some tips for them. I found myself emphasising the importance of creating the need to learn. Here’s a tip that I’ve suggested time and time again:

Let your students find an answer that isn’t accurate in an inefficient way before teaching the correct method

In your class, this might involve students finding an answer that is correct, or near enough, through trial and error. The need for learning maths here is being able to come up with a more correct, efficient, and satisfying answer. This teachable moment is far more powerful if the students experience what it is like without the ‘right way’ of working through the problem. Dan describes this process as creating the headache and prescribing the aspirin.

These are the key aspects that I think are important, what are your thoughts? Have any to add or take away? Comment below!

Great post! One of the things I love about using an inquiry based approach is that my students are pulling math out of the world and then putting it back. They are learning to make sense of the world in a way that builds on their conceptual understanding and leads to fluency. Another critical piece I would add is spending sufficient time anticipating student responses before launching a task, especially if it’s the first time I’ve done it with kids. Then I can more carefully plan my questions that will hopefully help advance the learning of the class. If we don’t do this, we run the risk of the “oh crap” moment… When students do something unexpected and we either shit it down or give away too much. Thanks for writing! Keep it coming!

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Oh my gosh. My comment should say shut, not shit. Lol

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Haha man I love typos!

I agree. I often try to keep the language I use with my students in context when working through a real-world problem. This helps them notice how reasonable their answer is and keeps the focus on solving the problem and using maths as the way to find it 🙂 I do love it when I know in advance “where the story is going”, it allows us to build it up at the right times – all part of the fun of teaching!

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