«Catching up in maths is difficult»

Peter Geering, professor emeritus of maths didactics, taught trainee teachers how to support children in maths. He says that success promotes enjoyment of maths and that children need one thing above all: more time.

Mr Geering, you were a teacher of mathematics and mathematics didactics. What experiences were particularly formative for you?

At the teacher training seminar, I experienced many pupils who struggled with maths - a difficulty that some children already experience in primary school. They can no longer follow maths lessons, lose interest and self-confidence and can develop an aversion to the subject. This prompted me to change my approach. I wanted to give my pupils positive experiences in maths instead of preparing them to study maths and science.

What are possible triggers for pupils' aversion to maths?

From the first grade onwards, many children have too little time. The pace of learning is prescribed by the teaching materials. By the end of the year, the teacher must be finished with the planned material, as the next stage continues straight away. However, some children need longer to complete certain learning steps. They do not have the time to process them sufficiently. As a result, these children stop developing in this subject. They just do what the teacher says without really understanding what they are doing. This causes anxiety. The anxiety is intensified by exam situations. The children know that they can't do everything that is asked of them. The pressure increases because those who are bad at maths have more difficult access to secondary schools: Maths is a convenient selection subject.

Peter Geering was a professor of maths, physics and subject didactics. He worked for 30 years at the Rorschach Teachers' College and then at the Zurich University of Teacher Education until his retirement. Together with special needs teacher Werner Fessler, he developed the supplementary teaching aid "Atlas Mathematik", which is designed to facilitate development-orientated teaching. www.atlasmathe.net
Peter Geering was a professor of maths, physics and subject didactics. He worked for 30 years at the Rorschach Teachers' College and then at the Zurich University of Teacher Education until his retirement. Together with special needs teacher Werner Fessler, he developed the supplementary teaching aid "Atlas Mathematik", which is designed to facilitate development-orientated teaching . www.atlasmathe.net

Do children who can't keep up give up?

They develop survival strategies. For example, they justify their failure with their predisposition: «I'm just not gifted» or «My mum was bad at maths too». This attitude is of course counterproductive. They try not to get into trouble, cheat their way through lessons using tricks and detours. They do the minimum possible and learn everything by heart. This turns maths into an incomprehensible game of rules. The problem is that those who learn the incomprehensible by heart have no foundation for more difficult content in maths.

How can teachers promote children's understanding?

I see the primary task of the teacher as being to show the child that they can do something and not to harp on about mistakes. Some schools also teach maths procedures that are opaque and difficult to explain. The abbreviated procedures date back to a time when the aim was to write down as little as possible. The crazy thing is that you don't adapt the procedure to the children, you adapt the child to the procedure.

Do you have an example of such a calculation method?

For example, written multiplication: with one more line, the teacher can see if something is wrong. It is also important for the child to see where they have miscalculated. If they write a text, they need their own words and can use them to write a large number of correct sentences. In maths, however, there is only one correct solution. That's why we have to make mistakes visible.

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This article is part of the online dossier "Maths anxiety". Read here
why so many children struggle with maths - and how parents and teachers can support them.

Do you think today's teaching materials promote understanding?

They promote understanding by tying in with everyday life. But it's not always the child's everyday life. We once gave first-graders a book with twenty-five blank pages. They were allowed to write or draw something on each page that matched the number of pages. It was a world of its own that came to light. We should involve the children and their everyday lives more in the lessons. But that is time-consuming. A lot of things fail because of the extra effort. What's more, it takes a strong back to deviate from the annual teaching plan as a teacher. There are demands from parents, colleagues and head teachers.

Is it true that you yourself were once appointed director?

Yes, I introduced the idea that pupils could take a resit exam in their free time if they had failed a test. Suddenly they were interested in what they had done wrong. We looked at their difficulties together. They improved and I was able to hand over responsibility. The headmaster said I couldn't do it like that. His argument: nobody does it like that. He couldn't justify it pedagogically. So I did it anyway.

Together with your colleague Werner Fessler, you developed the «Atlas of Mathematics». Does this teaching aid follow a similar ideology?

In «Atlas Maths», lessons are structured in cycles. Each school year starts from the beginning. Those who understand maths well quickly work their way through to new and more difficult tasks, while those who still have gaps repeat the same material until they understand it. The teacher can see what level the individual pupils are at. The advantage of this teaching aid is that even a child with learning difficulties can work at a level that suits them and achieve something. If the child were to drop out after the first class, they would take nothing with them apart from the feeling: I can't do it.

When do you recommend clarifying dyscalculia?

I am hesitant to answer. I can't imagine that there are only problems with arithmetic. What a child needs above all is time. If it comes to a remedial teacher, the teacher works on additional material so that the child can catch up with the mainstream class at some point. But the child who is too slow is pushed until he or she gets close to the train he or she is chasing. In my experience, it is difficult to get back on track. This problem could be solved with cyclical teaching. But that contradicts the teaching material. A reform is not in sight.

Which reform have you found to be the best so far?

That set theory has been abolished. It is clear and plausible, but too abstract. Children have to go through a development from the beginning until they understand the abstraction themselves. But as I said, they need more time for this.

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