17/10/2025
Aalto University hosts an annual maths camp for upper secondary school students of ages 16-18, and I was kindly granted two 1 hour sessions in the camp this year. Given this unique and exciting opportunity, I wanted to give my best shot at designing a fun activity for the students. Since accomplishing anything requires a solid plan, I first asked myself what goals I want to achieve in the sessions before settling on a specific topic.
For me, the most exciting part of mathematics at that age was discovering something new by myself. Therefore, my first priority in the activity was not to lecture the students but instead have them explore maths themselves either by trying out things with pen and paper or by searching the internet for resources.
Also, I wanted to do my best to give them a wide range of directions to choose from; Maybe some like doing more concrete things while others are fascinated by abstraction, and some like visualisations while others prefer rigid, logical structures.
As for the topics, I wanted to stay away from the kind of maths that you only find in recreational books; The ones that provoke a sense of wonder which fades away as soon as you close the book. I wanted to present them with real maths that might even be useful to them.
After defining the constraints for the activity, it was time to figure out a suitable theme. At first I thought of taking the complex numbers as the theme for the activity. I would give a brief overview of the complex numbers in the first session and then present the students with a range of things one can do with them. They would then choose a specific topic which to study over the rest of the activity. However Aleksis, who gave me excellent advice in planning the activity, made me realise that complex numbers are too advanced for an activity of this type. So, I went back to the drawing board and tried to think of a better theme.
The theme I settled with was functions. Everyone knows what a function is (at least on some level), and they pop up literally everywhere. With the theme of the activity finalised, I started compiling a collection of topics related to functions that the students could work on. I also made a website that lists the topics I compiled and short explanations here. I decided to split the collection into "geometric" and "algebraic" topics based on whether the topic is more visual or more abstract. Also, I tried to include lists at the end of each topic suggesting activities the student could do related to the topic. This website is really the meat of the whole activity and curating the topics was the hardest part of the prep work.
Finally, I made detailed plans for the two sessions:
We followed the plan quite closely, but we decided it would be better to give them more time to do their research instead of having groups present to each other. 15 minutes before the end of the last session, we gathered all the groups in the same class room and asked for volunteers who wanted to say something about what they learnt or discovered. A few students came up and gave short, improvised presentations on what they found.
The first thing that became quite evident soon after the groups had started working is that the topics and activities could have been way easier still. Even though we had one adult accompanying each group to assist them, many students still got completely stuck on the topics they chose.
Putting that aside for now, I think the activity worked well for the students who did understand the assignment. The enthusiastic students got to choose topics that they found relevant and interesting, and some student brought up this freedom to choose in a feedback questionnaire, where they were asked what was good about the camp. Another student said that they liked being able to discuss maths freely with other students and us volunteers and staff, which is something I was also hoping this activity would enable.
For me the most rewarding part of this activity was being able to witness first hand the excitement and the feeling of accomplishment in the students, when they learnt or discovered new mathematics. To top it off, the enthusiastic students got the chance to present the mathematics they learnt in front of the class, which I believe was a very meaningful experience for them.
The first thing I would change about this activity is the level of difficulty. I had proposed activities such as "Explore graphs of implicit equations using Desmos" and "Find an interesting integer sequence online" on the website, and these were supposed to be the easiest activities that the students could do if everything else was too difficult. To my surprise, almost all students shied away from such exploratory activities and preferred reading about some new maths they hadn't seen before.
Therefore, I would change the activity by adding easy topics which would be accompanied with a structured set of problems in the same style they are accustomed to seeing in school. Then, the students who do not know much mathematics beyond what they learn in school could still learn something new and interesting, while the material would be presented in a way that is already familiar to them.
On the other hand, I would like to encourage the more advanced students to do open-ended exploration, because I believe it is one of the most valuable skills for a student who is serious about maths. Aleksis had a good comment regarding these exploratory activities: He said it would help to specify the goals of these activities better for the students, so as to make it easier for them to get a grip on them. I think this is exactly right, and I will try to think of ways to guide the students to open exploration as much as I can while not spoon-feeding them with ideas they could discover themselves. In addition, I came to the conclusion that compared to exploring maths, it is not as useful for students to just learn something more advanced by reading and not actually getting hands dirty, so I would just cut down on the more technical topics altogether.
As a final note, here are some practical points that could be improved. Firstly, we ended up running a bit low on time, so it would have been better for me to be more time efficient with the starting presentation. I spent quite a long time making sure everyone knows what functions are and understands the arrow notation, followed by listing notations for many different sets. After the presentation I asked the students how well they understood my points by show of hands and most students understood everything completely. In hindsight, I think it would have been better to just cover the arrow notation as quick as possible while making sure everyone got it and reserve the set notations for a "cheatsheet" section on the website which the students could refer to if they come across set notation they haven't seen before.
After cutting down the length of the presentation, there would be more time to explain to students what is the point of this exercise and which topics are recommended for more advanced students. Also, during the workshop, the students didn't ask questions from us adults as much as I had hoped for, so it would be good to really emphasise that the students should do that and try to have discussion with the volunteers and staff.
Conducting my experimental maths camp activity revealed that the level of difficulty was set too high, but luckily it is very easy to fix that. The positive outcomes of the experiment we saw with the more advanced students leads me to believe that the activity could be refined to a successful one after lowering the difficulty and implementing the other fixes mentioned above.