The value of encouraging mathematical talents
I am Catharina Gathmann. I am studying economics in Hamburg after having passed my final school examinations last year. At the same time, I work in the "PriMa" programme, headed by the president of the MCG, Marianne Nolte. This programme, which takes place at the University of Hamburg, was introduced in 1999 and supports mathematically gifted students from upper primary to secondary grade (third to tenth grade in Germany). I have participated in the programme since I was in third grade and stayed there until ninth grade. Subsequently, I remained in the programme and have been a tutor since 2017.
I have experienced that being interested in mathematics is often associated with being a nerd or a geek at school. That is why I was a bit overwhelmed when I was accepted into the programme after the selection process in third grade. Apart from going to university as a primary school student in between all those grown-ups (!), I met people who did not come up to me to ask me what the task was about and how I solved it. Instead, we asked each other questions about the problem and discussed our ideas. I suddenly found myself in a community with people who had the same interests in mathematics and were my age - and with each successive grade, I can say that this sort of intersection became smaller and smaller at school. But there, it was just us. Some knew each other from school or other hobbies. So, what was a bunch of strangers in the beginning became an acquainted group.
We met every month on a Friday afternoon or evening and for 90 minutes every one of us agreed: maths is not black and white, not just yes-no: maths is a lot more and it is fun to think about all these different problems than just getting through them. And there is not just one way of doing it: For example, in one question, you can use the left-hand numbers in the pyramid, the right-hand ones or the ones in the middle to get the result - or you can simply multiply. There is no denying that some methods were more time-consuming than others, but everyone in the group equally appreciated each way and each particular "trick".
In the eighth grade, I started tutoring mathematics at my school. In the process, I noticed that those students saw mathematics as the subject in which you can only be right or wrong. Additionally, they seemed to think that the one and only way to solve the problem is the one presented in the book, usually without much further explanations and examples despite the abstract illustration. They did not see that sometimes you can become faster with simple tricks in mental arithmetic or that it's easier to calculate by memorising a few fractions. That was when I realised that this kind of imagination deepened when I went to PriMa while they pursued their own interests. In the programme, we just discuss patterns, generalisations and methods, so I had mistakenly assumed that everyone else would probably understand it that way somehow too. However, one of my friends, for example, had problems with adding and subtracting fractions (part of the German sixth grade curriculum). It was only in tenth grade when she told me about the "butterfly" trick of multiplying the denominators and numerators crosswise! She was astonished when I told her that I had always done it that way. And me? I didn't understand why she hadn't just always used that.
Because of this, and in contrast to being a tutor in PriMa, I realised what understanding I had gained by participating in the programme: Mathematics is not just about calculating with learned formulas. It is rather about exploring and developing patterns, strategies and methods to make solving a problem easier - you modify that question and start all over again. And as a tutor in the programme today, I even have the chance to follow individuals' thought processes and discussions and observe their approaches to the tasks - ways that I sometimes did not explore back then. And it additionally allows me to pass on the motivation that inspired me back then. So, it is up to us as tutors to offer them tasks that confirm their interest in mathematics and encourage them to develop their mathematical problems, resulting in these lively discussions on Friday afternoons between ice and sunshine as well as between biscuits and Christmas songs.
I believe this programme is an excellent opportunity for mathematically gifted students to exchange ideas with like-minded people and work together on mathematical problems related to current topics in school. They find their own approaches and learn how to solve and pose them. In discussions with others, they improve their ability to clearly express and convey their reflections and results. Additionally, they use, for example, game theories that have been discussed in their everyday lives when they play these games at home. Along the way, observations can be made from a research perspective about how these students approach problem posing and solving.
Finally, these groups are an asset for anyone interested in mathematics. Because they make sure that you can be proud of your mathematical talent and interest. So, I wish we could have more of these groups. Because they go beyond the one-sided view of what the mathematical universe is and make it more versatile by leaving room for creativity. Because they make you feel that being interested in mathematics is definitely not exclusively for "nerds "or "geeks ". It is for everyone. And because it is cool to be good at it.
You are wise for your young age. Many people never get the joy of experiencing what some refer to as "real mathematics." The word "real" in this context doesn't always refer to real life applications but, instead, to gaining power over mathematics rather than being subservient to seemingly unfounded rules of procedure. In mathematics, the journey (and the fellowship with those who take the journey with you) is more critical than the destination. Creativity thrives when using a map with only a starting point and a possible destination and very few connecting routes. It is through the effort expended in making those connections that one grows mathematically. Keep growing, as we all should.ReplyDelete
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