Teaching Mathematics through high-interest problems

Nicos Georgiou, Reader in Mathematics in the School of Mathematical and Physical Sciences and winner of a University of Sussex Education Award 2023, shares his approach to teaching tough mathematics to nervous students.  

What I did 

I use current and everyday problems and in-class group work to engage students on my year 2 core module, ‘Introduction to Probability’. I make my content engaging by applying rigorous mathematics to practical problems such as understanding why one should never gamble, comprehending how likely it is that an election is fraudulent, checking the production of a factory, and even producing magic tricks for parties.  

I create space within teaching sessions to work through problems in groups by asking my students to do a lot of independent work. To support this, I’ve created a booklet for the module with chapters mapped to the lecture topics. The booklet includes clearly signposted questions for students to work on, from basic to the more challenging and interesting ‘cool problems’ (example recreated below), some of which we explore in class.  Topics range from probability problems rooted in movie plots or TikTok trends, anime films (e.g. Kakegurui based on a manga series about gamblers and how to beat those who cheat), serious cases of statistical misinterpretation, probability modelling linked to global challenges such as climate change, and questions used in job interviews by popular graduate employers.  

If it’s important students know a solution, I’ll provide it in class but, especially if a version appears in their ‘homework’, I’ll leave them to figure it out and tell them to come to me if they get stuck. The homework sheets also contain questions from basic (the material they need to understand to pass) to the more interesting, which encourages students to stretch themselves.  

Cool problem 3. The frog riddle that broke YouTube 
 Frogs in a lake are equally likely to be male or female and you cannot visually tell the difference. What is the probability that there is a female in the pair if: The pair contains a male frog You heard a frog croaking and it had the distinctive sound of a male. Assume that frogs croak with equal probability independent of their gender.   Consider visiting https://www.youtube.com/watch?v=go3xtDdsNQM for a resolution. We will solve this faster and rigorously after we establish some facts on conditional probability.  

Why I did it 

Probability is an intimidating topic, even for mathematics students.  It demands my students grapple with randomness which, for pattern-seeking humans, is counterintuitive. Using real-world problems makes the topic more engaging by asking students to contextualise and humanise maths.  

Also, my classes are typically 2 hours long, often timetabled towards the end of a seven-hour day of mathematics lectures. Getting students to problem-solve in groups, maybe a few times each session, keeps them active and engaged. Working in groups also makes it easier for students to check their understanding with peers and provides valuable experience of group work and collaborative problem-solving.  I also make sure I wander around the room while they work, which helps maintain focus and makes it easier for individuals or groups to ask me questions.  


Creating the booklet to go along with the module took a lot of time but, arguably, it also demonstrates to my students that I am committed to their success. Also, I expect my students to undertake a lot of independent study. Therefore, I set expectations early and also make clear what they should expect of me. This includes how to address me in an email (I won’t answer emails which don’t address me by name) and how to follow up with me if I don’t reply within one working day (i.e., come to my office hour).  

In the classroom, it’s sometimes necessary to provide guidance on how to work collaboratively. Also, we do sometimes get stuck on a question so don’t get through all the content. Students know that they can still work through it independently and approach me for support.  

Impact and student feedback 

Colleagues have consulted me on my approach and applied it in their own teaching. One colleague reported that, in their module evaluations, what students liked the most was exactly what I had suggested.  

That said, my approach might need tweaking to suit people’s own personality and style of teaching. I consider teaching as a performance and, although my expectations around their engagement and application remain very high, I am quite informal with my students and am happy to be interrupted. This doesn’t work for everyone so, for others, it might mean planning in more space for students to ask questions. Also, my approach isn’t necessarily preferred by all students. After all, not even Dumbledore* had universal approval. 

Top tips   

  1. Understand why you are excited about teaching the material – if you aren’t excited then maybe the material shouldn’t be taught in the classroom. 
  1. Always be alert to what the students see in their everyday lives – motivate them by bringing it into the classroom. 
  1. Don’t worry if something doesn’t go right the first (or second or third) time around – it happens to the best of us. Be honest about it with yourself and your students – an email to ask them what they think went wrong will help you prepare or design differently for next time (and is much better for everyone than your students just grumbling to one another via social media).  

*Fictional. Headmaster of Hogwarts School of Witchcraft and Wizardry. Famous alumni: Harry Potter.  

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