##### Buried under phenomena

The "Application reference" The teaching of mathematics in this way prevents exactly what it was supposed to achieve: Enthusiasm for mathematics as a cultural science

Slowly but surely, the public awareness of conflict on the subject of "education" is increasing (overburdened schoolchildren and politicians on a denial tour). Mathematics, which belongs to the cultural core of the Enlightenment, takes a key position in this process. Whoever wants to reduce it to its application-related practicability, however "well-intentioned" his intentions may be, destroys our culture.

A vehement, general debate on the subject of math didactics last took place more than thirty years ago, when the ie was the use of set theory. Die Gegner befurchteten vor allem, fur den Alltag notwendige praktische Fertigkeiten wie schriftliches Addieren und Dividieren wurden einem kindischen Herumschieben bunter Figuren geopfert, die Kinder wurden nichts furs Leben lernen. The different points of view were represented with immense vehemence and probably had less to do with pedagogical questions than with diverging ideas of society.

Nevertheless, mathematics was sometimes discussed in passing. Thus, even one or the other non-mathematician learned that already since the beginning(!) of the 20. the set theory of the ingenious Georg Cantor had become in reality the common framework of almost all mathematical fields in the early twentieth century and was not just the lappish teaching method of anti-authoritarian do-gooders. Unfortunately, this selective enlightenment had no effect on public awareness.

### The mathematical time machine, or: The love of brutal pedagogy

Until the "PISA shock," the subject of mathematics almost completely disappeared from the public consciousness, as did the "mathematical" natural science, physics. Only the bad results of the German schools in the international comparison changed this. Above all, the lack of ability of German schoolchildren to develop creative solutions to problems was conspicuous. A look into the schoolbooks gave an explanation. The mere opening of a textbook was enough to demotivate any intelligent, bright student. Tightly and densely packed, there were pages and pages of mindless arithmetic problems. These were also used abundantly, because not infrequently the children at home simply had to exercise vast amounts of, for example, written divisions.

Since the vehement debate about set theory, a silent reactionary roll-back had taken place. Welcome to 1900! After the set theory war, opposition from parents to the return to teaching methods that had been "preserved" for decades was neither to be expected nor did it occur to any significant extent. Parents obviously want their offspring to be taught life skills that are close to the real thing. Brachialpadagogik comes simply better, than a differentiated procedure, with which also things are learned, which are not directly useful.

In the meantime, the old math books have been replaced by new ones. They follow the approach of making mathematics more accessible through application. The range of tasks is now more diverse and much more varied than before. Which, by the way, does not please every teacher, because now tasks must be deliberately chosen by them. The same approach can be found in the natural sciences, especially in physics and chemistry. The idea is not least to arouse and maintain interest in poor or initially uninterested schoolchildren. There is no question that the new approach is clearly preferable to the old one. However, the intensity with which the application reference is targeted also has dangerous consequences.

### "Save the Phanomene!"

In 1975, the teacher and didactician Martin Wagenschein published his appeal "Save the phenomena", which is well known among experts!". In it he demanded that in the natural sciences not only abstract knowledge should be imparted, but also that pupils should learn through active investigation *make them more accessible to themselves* to enable them to understand phenomena, to learn scientific methodologies. His aim was not to teach practical applications, but rather, like the first scientists, to have the students start from phenomena that they themselves could observe and, in the course of investigations, develop theoretical concepts and possible explanations for them. As an example, he cited a group of students who are studying how shadows are created. The hypotheses and theories to be developed by the students are always abstracting. However, in contrast to simply putting forward theories, Wagenschein demanded that children be *the abstraction process itself* should learn. He was uncompromising on this point and said that what was not phenomenologically accessible to schoolchildren should not be taught in school.

It is an offense to young people to try to teach them something they cannot possibly understand, or, to make it understandable, to misrepresent it.

Martin Wagenschein

Nuclear physics was a particular thorn in his side: "I don’t think it’s good to talk a lot about nuclear physics and electrons in secondary school. Any vivid spatial idea of these entities is quite simply wrong."

Wagenschein’s approach can easily be transferred from physics to mathematics. Mathematical methods can also be learned by starting from questions that are directly accessible to the students.

Superficially, Wagenschein thus becomes the early protagonist of a practical didactics of mathematics and physics "at hand. In his time, however, his appeals were largely ineffective, at least as far as German school practice is concerned. However, anyone who thinks that the current post-PISA focus on practical applications is a late rehabilitation of Wagenschein is very much mistaken.

### No time to learn

Wagenschein was not concerned with practical utility, with application, but with learning scientific methods on the basis of individually experienced phenomena. For this, he willingly sacrificed pure factual knowledge for the learning of methodologies. This is the exact opposite of what takes place in German schools. „Lernen zu lernen“ ist heute kein wirklich gelebtes Motto, sondern blob eine gerne wiederholte Floskel. This is clearly shown by "G8", the shortening of nine to eight years of high school until the Abitur. A de-trumpeting of the subject matter did not take place in the process. Since in most of the federal states the 10. The fact that the school year has been cancelled means that the increased amount of material affects all students, even those who do not want to take the Abitur after middle school. (Model "9+3" instead of "10+2")

The prere on the students is thus increased more and more – learning assessments, examinations after the 10th grade, etc. Class, standardized central baccalaureate, head marks, and above all: no more substantial options. Even the deselection of the worldview subject religion, which is completely superfluous for a central subject canon, was negatively sanctioned by the introduction of pseudo-moral compulsory substitute subjects, which often come along eloquently under the label "ethics. Behind this is the opinion of some teachers, parents and education politicians alike, that in the past students had chosen religion out of laziness in order to have more free hours. Whoever holds this opinion, which is not exactly imbued with confidence in the decision-making abilities of the young generation, will naturally only be satisfied when the learning time of children and young people is completely regulated and quantitatively measurable. This does not create a basis for lifelong, independent learning.

### Mathematics, the unknown abstract being

There’s no doubt that the approach of teaching mathematics and the natural sciences in a way that motivates students to go to school is more entertaining than a series of dry facts that have been calculated and memorized ("New task culture" makes the subject of mathematics more lively). However, if this approach is not used, as Wagenschein had suggested, to explain mathematical-scientific *Methods* to learn, there is an acute danger of the profanation of mathematics and physics. The impression is created that mathematics – to stay with this subject as an example – is "simple" because calculated everyday experiences are sufficient to understand it. However, this is simply not the case.

Mathematics is abstract. Even calculating with natural numbers requires a high degree of abstraction. This is often overlooked, because the abstraction from "1 apple plus 1 apple equals 2 apples" to "1+1=2" is supposedly easy for most people. However, people who find mathematics difficult – either because they are real dyscalculists or because they simply look more closely – have major problems with it, because, strictly speaking, two apples are never as identical as two mathematical ones (are there actually *two* mathematical ones?).

Therefore, repeated references to concrete applications can make learning mathematics difficult *concepts* because the application references made again and again have to be abstracted again and again. A very tedious, repeatedly frustrating process. The Max Planck Institute for Human Development also came to the same conclusions ("Can we be a bit more abstract?").

### The end of enlightenment – the burial of mathematics

If phanomata are misused for the entertaining connection of mathematical contents to applications, there is a danger that paradoxically those people are left behind who should be helped by the application – namely those who have difficulties in accessing mathematics. Far more serious, because more general, is a second danger: The focus of mathematics and the natural sciences on their applicability devalues both fields as cultural studies.

Mathematics and natural sciences appear only as secondary auxiliary sciences for solving everyday problems that are not really profound. They are highly *useful*; but no longer really *important*, when it comes to the central things in life. This not only suits studied, Islamist terrorists who purposefully pilot modern passenger jets into skyscrapers, such as Mohammed Atta and his teams on 9/11. It also fits into the categories of thinking of Western moralizers like the teleprasent and journalistically active "psychotherapist, physician, theologian and connoisseur of philosophy" Manfred Lutz, who in his popular pamphlet "God – A Short History of the Coarse "1 even let himself be driven to the ludicrous assertion that the theory of evolution had no meaning for the "science-believing atheists of the 19th century". The scientists of the twentieth century" carried the "seed of catastrophe of their view of the world", because according to the theory of evolution "not everything developed inevitably according to the laws of nature". He uses Popper’s theory of science – scientific claims can only be empirically falsified, not verified – to exclude the natural sciences from any discussion of "absolute truths". This Popper’s statement bending vulgar argumentation is meanwhile well established and very popular among science critics. It works like a Pavlovian dog: somebody says "evolution theory" or "quantum theory" and immediately it resounds back with Popper: "All blob theory and not provable". Lutz does not recognize the fact that scientific findings always break through the limits of their methodological procedures and thus cannot be locked in.

There is no philosophical boundary that physics, dedicated to the quantum smallest and the astronomical coarse, could not cross. And there is no ethics that could resist evolution. If not mathematics, which discipline should appeal to the ultimate reason of man?? Whoever wants to limit mathematics and natural sciences to purely practical things, for whatever well-intentioned reasons, erodes the foundation of enlightenment.