Is there something math can't explain

«Mathematics cannot simply be explained»

we parents: Ms. Schmassmann, you run a math laboratory in Zurich. What do you have to imagine by that?

Margret Schmassmann: In my math laboratory, I advise teachers who have questions about math lessons and parents who are worried about their children. I also accompany children and adults in their often difficult mathematics development and give courses, give lectures and help develop textbooks.

Are people with math problems clients or should we speak of patients?

Clients, because math problems are not a disease. The WHO lists arithmetic weaknesses in its International Catalog of Diseases ICD under mental deficits and behavioral disorders. But this definition is controversial, among other things because it only recognizes dyscalculia if the performance in other school subjects is significantly better and because it completely ignores the influence of teaching. Math difficulties are also not innate. Neuroscientists are concerned with the question of whether the dyscalculia can be found in certain brain regions or whether a responsible gene can be found. But this hardly helps the pedagogical implementation.

So there is no such thing as dyscalculia?

Yes, but it is not a disease. It can be described by phenomena such as performance deficit of up to four years, noticeable slowness or solidified error patterns, lack of understanding of numbers and arithmetic operations as well as finger arithmetic. But children with restricted requirements can also find access to mathematics if they are taught accordingly.

Little consolation for children with math difficulties, because school is all about following the school material.

This is exactly where I see a big problem. Dyscalculia is now defined as a failure in math class. This means that the problems are closely linked to the classroom. In everyday life, children encounter mathematics on many occasions, but it is translated into written characters and formulas in school. This step can be unsettling and therefore the quality of the teaching, especially in the lower grades, is of great importance for the development of mathematical thinking.

What is math thinking exactly?

It means connecting, networking, establishing relationships, solving problems, finding simplifications and generalizations. For example: the number 7 alone is not very interesting. What is important about it is that and how it relates to other numbers. 7 is 1 less than 8 and 1 greater than 6, is a prime number and can be broken down into different numbers. Children at school should be able to discover and use such connections. Mathematical thinking has nothing to do with specifications and trampled arithmetic methods, but with trying out. Regulations prevent thinking and creativity. How would you calculate 7 plus 8?

I fill in to 10 and then work out what is left of 8 and add that to 10.

So the classic filling. Not a bad way, but not the only one. But at school, the children are often told: This is how you do it with the tens! It then works as follows: The first step is called “7 and how much is 10?”. To do this, a child must already have the decompositions of 10 in mind. As a result it gets 3. In the second step it has to think about how much of 8 is left and have the decompositions of 8 ready for this. It now gets 5. Now five different numbers are floating around in its head: 3, 5, 7, 8 and 10. How is a child with memory or concentration disorders supposed to get this in line?

What could be easier?

First of all, the child should be able to try out for themselves how to proceed. Maybe it has an idea. But if it reaches a dead end, it can be supported in using its existing knowledge. For example, doubling "7 + 7 = 14" helps. 7 + 8 is 1 more, i.e. 15. Once a child has recorded the doublings, it can establish relationships with all the bills around it. Mathematics is an activity, is creative and has to be discovered by yourself. They cannot be explained, especially not by giving recipes. Children with learning difficulties often misuse them and those without difficulty do not need them.

But given solutions still work. After all, generations of students have learned math according to scheme X.

Yes, unfortunately. But many people have had a terrible math history. It is shocking to hear what I hear from adults who are downright traumatized, who trembled and cried before class, who got sick before exams and who remember these negative experiences long after leaving school. Many still managed to get through to the Matura, sometimes without really understanding the multiplication. Although they solved hundreds of worksheets with coloring calculations and colored in figures to check. If there was a parrot, the results were correct. In this way, of course, they could not learn to assess and check results themselves.

And is the school responsible for that?

Yes, if teaching aids are used that understand mathematics in the sense of «demonstrating - imitating - inquiring». In the meantime, however, we are in the process of rethinking math didactics and changing both the textbooks and the training of teachers. Today, lessons are more creative with many teachers and are not based on the motto “This is how it works!”, But rather encourage self-discovery.

But it cannot be argued away that math is an important selection subject, for example in the transfer test for high school.

Math is misused for selection because it is apparently objective, because one falsely assumes that only the result counts. It's not about diligently practicing standard tasks, but about finding your own ways. With a good tolerance for mistakes!

How can parents support their child when math doesn't work?

You should encourage them to first come up with a solution and then ask, "How did you do it?" Instead of showing how you did it yourself. In any case, you should stay away from questionable exercise material. Blocks for "happy practice", in which bills are hidden in Easter eggs or poinsettias - that doesn't help. There is well-structured material that clearly presents the central topics such as counting, the decimal system, arithmetic operations, factual arithmetic and sizes and offers them without frills.