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Tom Coenen is a secondary math teacher and a math teacher educator from the University of Twente in Enschede, the Netherlands – the same university where he obtained his PhD in mathematics. As a math teacher educator, he is one of the members of the consortium LessonStudyNL which is a cooperation between a number of Dutch universities and academies that promote and research Lesson Study – a professional development approach.
1. What’s your earliest memory of doing mathematics?
As a kid in school I loved doing math. I remember enjoying playing with numbers and completing exercises as early as elementary school. One of my very early memories is the day we got a substitute teacher. She explained how to calculate the answer to a problem. After she was done, I raised my hand to correct her. She told me I was wrong and that she was right. I went home for lunch break (common to do over here) being mad. During lunch I complained to my mom that I was right, and the teacher was wrong, and I refused to go back to school. She convinced me to go anyway. When I arrived at school the substitute teacher told me she checked the answer to the problem and found out I was right after all and apologised. Guess I was a know-it-all at an early age…
2. How has mathematics education changed in the time you have been involved in it?
Education in general has evolved quite a bit since the years that I was following classes. As far as I remember, almost every class involved sitting down, listening to the explanation the teacher gave and completing exercises. This was in secondary education, but also in college. Nowadays I see many different approaches being adopted in institutions, such as group work, different types of interaction, experiments and of course a lot more use of the digital tools available. Also, at university I see a shift to more project work as opposed to classes. When it comes to the subject, math curriculum has changed over the years, again partly due to the rise of digital options. The use of graphical calculators and computers has been incorporated into education.
3. Tell me about a time in your career when something totally flabbergasted you.
Two situations come to mind. The start of my passion for math was when I realised that you could take a real-life problem, convert it to a mathematical model, start calculating and reach a solution that would tell you the best approach to take in order to tackle the problem. Many years later, having graduated from university and with a PhD, I found myself teaching not only at university but also in a secondary school. When teaching there, I realised how much teachers seemed to depend on the books they were using, following them almost to the letter. Collaborating with teachers in the area, I was included in a Lesson Study (LS) team and we discussed many different topics that were being taught in class. At that time, our students were having difficulty understanding these subjects and we tried to figure out why. With eight teachers, some new, some very experienced, we devised a different approach that we thought would work well. Boy, were we wrong! The class I got to teach was the test group and at the end all my students looked at me with the expression of What was that all about? Apparently, the eight teachers from different schools had a completely wrong idea about how our students would react to our approach. Luckily, we had the chance to try again and we devised a new approach that was successful. This made me realise that no matter how many years of experience an educator might have, there is still room for gaining insights into students and learning. Since then, I have grown to believe in Lesson Study.
4. Do you practise mathematics differently in company?
This depends on the company. I am a teacher therefore when I do math with students, I need to work in a way that allows them to clearly see what is going on, what steps I am taking and why. When working on a problem on my own, I skip the steps that are clear for me. Even though I teach my students that it is crucial for them to write down each step, I guess I am not always practising what I preach when it comes to solving problems.
When doing my PhD, I often struggled with the challenges to make some progress. One of the hardest parts was sitting behind my computer, trying to find a solution or a next step. The best solution almost always was to go to a colleague and tell them about the problem I was facing. Even if they did not have any answers or advice that would get me to a next step, I would often gain more insight in the problem I was facing. Furthermore, sparring about a problem is so much more fun than trying by yourself. It became very clear to me that science should always be done in groups. Surely, some people will disagree, but my mind was made up: put me in any team to work on a problem together, it’s fun!
5. Do you think a brilliant maths teacher is born or made?
No one is born being brilliant at anything. It takes dedication and practice in my opinion. When it comes to teaching, however, I do think there are people that may not take to the job as easily as others. No matter how hard they practise, they might not get the “feel” that others get when doing the job. A common saying is also that not a single day is the same for a teacher and that is true. So even the most experienced teacher can find him- or herself in a situation where they don’t know how to react at first; for example, when a student uses an approach the teacher doesn’t immediately grasp. Not that I believe that a brilliant math teacher has the right solution/answer/reaction to any situation. To me a brilliant math teacher is the teacher that connects to their students on their level, reaching an understanding of math in ways that the students enjoy. If the many years of Lesson Study in math education have taught me anything, it is that every single new lesson can add new insights and even the most brilliant math teacher will not be able to predict up front what is going to happen.
6. What’s the most fun a mathematician can have?
Oh, this is a hard one! There are so many great things to mention here. As a teacher there is the obvious joy of seeing a student go from almost despair to complete understanding. Their joy becomes your joy. It doesn’t matter (to me) if it is a small kid getting to add numbers, a student being able to solve a differential equation or a PhD student taking a final step to finish a paper.
For me personally, the most fun I remember is solving exercises and getting insight into new things. For example, after learning about limits, there was this exercise asking how much water would fit in a funnel that would go on indefinitely (for example using f(x)=e^(-x) and revolving this around the x-axis from the y-axis on). Any kid in class “knew” the answer had to be that there would be an infinite amount of water – how could this ever be different in an infinite funnel? The correct answer (being π/2) stunned me at first, yet I loved that the “obvious” answer wasn’t correct.
Many other answers to the question can be given though. Simply solving fun puzzles can give so much joy. Helping people, schools, companies or society through research is so rewarding. All the models used in this Corona-crisis time are very relevant examples. I love math for its practical application, so I find fun in it every single day.
7. Do you have a favourite maths joke?
Funnily enough, I learned the most basic “math” joke ever when I was about 23 years old. It’s the classic “why is six afraid of seven?” … “because seven ate nine”. Only works in English though as far as I know. Remains brilliant in my opinion.
Nowadays the best jokes involving math are used in pictures or memes. I love it when students come up with new ones. A few examples are students with a sweater saying "I don't know how many problems I have because math is one of them", or a picture of the normal distribution followed by a picture of a ghost with the caption "paranormal distribution", or a picture where i says "get rational" to pi, who responds with "get real". Always puts a smile on my face!
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