In order for us humans to learn, we need to think.
That part’s obvious. But here’s the kicker: have you ever considered what kind of thinking is actually happening in your classroom?
Is it expansive and open-ended? Or narrow and precise?
Let’s take a look at both ends of the spectrum—and why the sweet spot is having both.
The Familiar Question
Here’s a maths problem you’ve likely seen before:
A gardener plants 24 flowers into 6 equal rows. How many flowers are in each row?
Classic, right? Students calculate that 24 ÷ 6 = 4. One correct answer. Done.
This is an example of convergent thinking—linear, focused, and heading toward a single, right solution. This kind of thinking matters. It builds fluency and accuracy.
But what if we shifted the frame just slightly?
A Small Tweak. A Big Change.
Try this instead:
You are a gardener. You have 24 flowers to plant in equal rows. How many different garden designs can you create?
Same numbers. Very different task.
In this version, students become the gardener. They have choices. They experiment. They justify. We’ve now invited divergent thinking—where students generate possibilities, test ideas, and think laterally.
You might hear:
“Wait—6 rows of 4 is the same as 4 rows of 6, right?”
“I’m going to do 3 rows of 8 but with a twist…”
“What if we made a triangle?”
Some students will still land on “6 rows of 4”—but they’ll do it with more understanding, more creativity, and way more enthusiasm.
What Kind of Thinking Are We Prompting?
Convergent tasks like the original question are essential. We need precision. We need confidence with numbers. But when we only ask for one answer, we miss the opportunity to develop flexible, curious thinkers.
That’s why the best tasks blend both types of thinking.
They start wide—open, playful, exploratory—and then funnel toward focus, accuracy, and insight.
Let me show you a few.
Tasks That Start Wide, Then Go Deep
These are three of my go-to favourites—each one starts with a spark of creativity and ends in rich reasoning:
Behind the Yellow Door
This Sembl original invites students to explore relationships in a playful, visual way. They’re presented with a row of colourful doors, some revealing parts of a hidden equation. As they begin, they’re asked a simple but powerful question: “How many possible equations can you think of?” With limited information at first, students brainstorm and test ideas. Then, as more doors are opened, they revise their thinking, identify patterns, and refine their equations. It’s an engaging blend of creative reasoning and structured problem-solving—inviting students to think broadly before narrowing in on mathematical precision.
Boxes
Boxes is one of our most quietly strategic Sembl Play games. Students are given a target number and build an equation using a series of digits—revealed one at a time. With each new digit, they must decide where to place it, knowing they can’t move it later. This simple constraint creates real tension. Students constantly shift between big-picture planning and precise calculation, thinking ahead while adapting to new information. The result is a rich blend of divergent and convergent thinking, where every choice matters and no two games play out the same.
Number Hive
Anyone can jump into a game of Number Hive—but the best players don’t just play; they plan. They assess the board, explore their options, and weigh up the factors they need to win—and the ones they can’t afford to leave behind. That constant shifting between zooming out to see possibilities and zooming in to make precise moves is exactly what makes games like Number Hive so motivating—and so powerful—for building real mathematical thinking.
Final Thoughts
When we shift our focus from just getting the answer to exploring the thinking behind it, something powerful happens.
Students don’t just engage more—they start seeing maths as a playground for ideas, not a checklist of procedures.
And no, it’s not about ditching right answers or ignoring rigour. It’s about using divergent thinking to get to those right answers in deeper, more meaningful ways.
So here’s your move:
Next time you plan a lesson, take one problem and ask:
“How could I open this up?”
“What choices could I give?”
“What if I let them think bigger, before zooming in?”
You might just find your students think harder, talk more, and start enjoying the ride.
Let’s not just teach maths.
Let’s teach students to think.
Thanks to James at Sembl for this guest Blog! You can learn more about James and Sembl 👇
Sembl: A curation of incredible maths tasks for deep thinking (https://sembl.app)
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