Long-time readers will know I am a massive, unapologetic proponent of explicit instruction. I love nothing more than a well-crafted, teacher-led I Do to explain a procedure to students.
However, where explicit instruction fanboys like myself often fail—and where proponents of inquiry-led instruction excel—is conveying the purpose of the procedures we are teaching our students.
Diagnosis
- Do your students ever ask: What is the point in learning this?
- How do you convey the purpose of what they are learning to your students?
Evidence
It is all well and good designing explanations, checks for understanding, and activities based on principles from cognitive science, variation theory and the like. But if our students do not care, we will fight a losing battle.
And often, students do not care.
Why should we learn how to solve a quadratic equation or add two fractions together? What is the point?
Solution steps
A word of caution
Before we get too bogged down in trying to convey purpose to our students, I want to and consider why a student might ask: “What is the point in learning this?”.
Sure, they may generally be curious, and conveying the purpose in the way we will discuss below should help get them on board.
However, I believe this question is more often than not a way of disguising confusion or a lack of confidence. I very rarely hear students who are experiencing success with a topic ask what the point of learning it is. Their success motivates them.
However, as we have all experienced, when things get tough, we tend to question why we are doing whatever we are finding difficult.
So, the takeaway from all of this is simple to state but tough to implement—teach students well, make them feel successful, and the chances are they will stop questioning why they are being asked to learn this new idea.
Where does Purpose fit into a lesson?
In a previous section, I shared three possible lesson structures:
Lesson Structure #1
Lesson Structure #2
Lesson Structure #3
I convey the purpose of the new idea we are learning between the Do Now and Atomisation. This is deliberate. The Do Now is a spaced retrieval opportunity whose content is disconnected from the rest of the lesson. Atomisation is where we forensically prepare to learn the idea that is at the heart of the new lesson. Conveying the purpose of that new idea to students sets them up to be interested and motivated to dedicate the attention necessary to thrive in the Atomisation and all that follows:
Today we will be learning this… Here is why you should care about it… Right, let’s learn it.
It is a short phase of the lesson – 2 minutes at most – but it could make all the difference.
1. Connect prior, present and future knowledge
What foundations is this new idea built upon, and what doors will it open in the future? If we can show students that their past efforts have put them in the perfect position to learn the new idea and that if they put in the effort required to master it, they will be able to access many other exciting ideas, we might get their buy-in.
I like to do this with a simple flow diagram. Here is one I use when I am about to teach students how to find the area of a circle:
This approach conveys the purpose of the current lesson and has the advantage of conveying the purpose of the prerequisite knowledge check that will follow, as everything in green is prior knowledge that needs assessing.
2. Share hinterland knowledge
Core knowledge is the facts, methods, and techniques that students must understand and retain to succeed with our subject.
Hinterland knowledge is the rich array of content, stories, and examples that give meaning to the core.
Maths teachers have a rich history to draw upon. Every technique our students need to learn was born from a need in a time gone by, and that cast of characters involved in their creation is worth sharing.
Let’s imagine I am preparing to teach students about the mean. Here is a story I could tell:
You may have heard of someone called Pythagoras. Now, in Year 9 we will learn that Pythagoras and his friends got more than a little obsessed with right-angled triangles. But they also did a lot of other things, one of which was inventing what we will be looking at today – the mean.
But here is the twist. What Pyrthgoars called the mean, is not what we called the mean…
And so on
Daniel Willingham describes stories as being psychologically privileged as humans have evolved to enjoy and retain the narrative structure.
3. Use real-life contexts
If the concept students are about to learn is used in the real world, then it is worth sharing with them.
The lethal mutation of this is shoe-horning procedures into real-life contexts, like pretending footballers plot out the equation of quadratic curves when lining up a free kick, or my all-time favourite example of algebra in the “real world”:
Students see right through this, and it can reduce motivation.
But if you can share a genuine real-life context with students they can relate to, it can help convey the purpose of the idea we are about to teach. The use of prime numbers in cybersecurity or averages to compare players in sports are two examples that tend to work well.
4. Introduce a headache
The headache-aspirin approach was pioneered by maths educator, Dan Meyer. The idea is that we try to show our students that, without this new idea, their life at this very moment would be a bit painful. In other words, before we provide the aspirin (the new idea), we need students to experience a headache.
Here are a few examples of headaches I use:
- Asking students to calculate 693 + 693 + 693 + 693 + 693 + 693 + 693 + 693 before teaching long multiplication
- Asking students to copy down the mass of the earth as 5970000000000000000000000 kilograms before teaching standard form
- Winning at “rigged” games before teaching probability
An important point here is that the struggle is short. 2 minutes at most. In my eyes, this makes it distinct from those lessons where students wrestle with a problem they don’t yet have the tools to solve for many minutes, with the teacher slowly facilitating their path to the solution. No, I am talking about a couple of minutes of pain, followed by a clear, concise I Do.
Summary
No topic lends itself to every one of these ways of conveying purpose, but I have yet to encounter a topic where one of them is not applicable.
Can AI help?
When used with the right prompt, AI is pretty good at helping is with this challenge. You see the prompt I use and AI’s outputs for three different ideas here.
