A little bit of problem-solving in every lesson: 10 tips to make it happen

Ideas to embedd proble-solving consistently in your curriculum

Mar 19, 2024

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Welcome to a series of posts where I will share 10 ideas to supercharge some of my favourite student practice activities. We will cover:

Venn Diagrams
SSDD Problems
Intelligent Practice
A little bit of problem-solving in each lesson (this post)

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A little bit of problem-solving in every lesson

I wrote recently about the work I have been doing with a maths department to ensure that problem-solving is embedded in their curriculum so that all students get regular opportunities to try unfamiliar problems. I recommend you read that post first as it describes:

What I mean by problem-solving
Why embedding problem-solving is a challenge for many departments
Approaches that don’t work
The approach we developed
What happened when teachers tried it

Then come back to this post where I will share 10 practical tips to help you do the same.

Problem-solving: 10 top tips

Find good sources of problems. As maths teachers, we are so lucky with the quantity of high-quality, free resources available. But, of course, there is a downside: the time it takes to sift through them all to find what we are after. So, for the type of problem-solving I am talking about here - short, sharp problems that can be done in around 10 minutes - I limit myself to three main sources:

Eedi: We have four problems for every maths topic on one giant spreadsheet.

Open Middle: Fill in the gap challenges amidst various constraints

NRICH short problems: questions adapted from the UK maths challenge

Do the problems yourself as a mathematician. Don’t be tempted to just give the problem a cursory glance. It is only when we sit down and do a problem that we notice fun twists and turns, can predict where our students might struggle, or get inspired to think of variations and extensions. If doing this in a departmental meeting, I would recommend 5 minutes working on a problem on your own, and then 5 minutes sharing where you have got to with a colleague.
Then put your teacher hat on. It is important not to get too engrossed in the problem. I have arrived at many lessons excited to share a problem with my students, only to find that my students struggled, finished early, or simply did not enjoy it. The mistake I made was not pausing to think about how to help my students get the most out of the problem. So, after you have wrestled with a problem, I find these are two good questions to consider:
1. How would you support a student who is struggling?
2. How would you challenge a student who has finished?
Set an alarm when there are 10 minutes of the lesson left. Time files in lessons, and if we are not careful, we will not leave ourselves sufficient time to get the most out of the problem. Setting an alarm on my phone helps remind me to get cracking with the problem.
Plan how you will pitch the idea to students. Students find unfamiliar problems challenging, and thus may be reluctant to engage with them for fear of failure. So, how we introduce the problem is important. The pitch will be different from class to class, but here are some things to consider:
1. Keep the stakes low
2. Emphasise the importance of effort
3. Share your belief that they can do it
No talking or writing for 30 seconds. I am sold on this approach after trying it a few times. No speaking stops the inevitable I don’t get it. No writing stops students from diving straight in, forcing them to pause and think. Students are likely to be reluctant at first, so sharing the rationale is important. But eventually, you will find they appreciate the headspace.
Give students a mini-whiteboard. Mini-whiteboards are the ideal vehicle to tackle unfamiliar problems. Students have less fear about writing their ideas down as they can be rubbed away if needed. And as I wrote about here, the simple act of putting two mini-whiteboards together provides the catalyst for focussed, positive student collaboration.
Use the 4-2 approach. You want students to work independently on a problem, but also to reap the benefits of collaboration. I find the 4-2 approach works well here, with students spending 4 minutes working on their own to see how far they can get, and then having 2 minutes to collaborate with their partner to compare progress and approaches.
Ask questions to find the best pairs to call upon. After the 2-minute paired discussion is a good time to start collecting ideas about how to solve the problem. Here are three good prompts to help choose which pairs to hear from:
1. Put your hand up if you disagree with the answer of your partner
2. Put your hand up if you changed your mind during your discussion
3. Put your hand up if your partner said something that you found interesting
Showcase students’ work. It is always a good idea to share students’ work with the rest of the class, especially when tackling unfamiliar problems. Students can benefit from thinking hard about the approach of others. There are loads of different ways to share students’ work, including under a visualiser, recreating it on the board, or simply holding it up. My favourite is to use the infinite canvas on Jake Gordon’s Maths Universe website. It is completely free, and it is amazing!