math – update

blogging & searching for true math …

Haben Schüler immer weniger Lust auf Mathe??…

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Nein! – Diese deutsche Schüler  – wie fast alle anderen Schüler –  haben die Mathematik noch nicht einmal kennengelernt!

In mathematik.de: New-mathematically-results-from-pisa-2012  Source: Deutsche Schüler haben immer weniger Lust auf Mathe – Von Christiane Habermalz we can nearly for the first time read some (in)convenient truths. The only but could be that we are still calling “math” to what we are doing at schools. And that might be the real problem, since “school-math” is not math!

Actually, we have no idea if our kids would do well or badly at mathematics! We haven´t even tried to find out. The only good reason for that is that there are not enough teachers that would be able to teach true mathematics, since teachers themselves belong to the system, and thus they as well haven´t had the proper chance to learn real math.

Die jüngste PISA-Studie stellt dem deutschen Mathematikunterricht ein schlechtes Zeugnis aus. Obwohl die Schüler immer mehr Zeit im Mathematikunterricht verbringen – im OECD-Schnitt 13 Minuten [pro Woche] mehr als noch 2003 – gab weit über die Hälfte – 57% – der sozial benachteiligten Jugendlichen an, noch nie von einer quadratischen Funktion gehört zu haben. Bei den Kindern aus bessergestellten Familien war es nur ein Drittel.
Laut OECD ist die Art des Unterrichts dafür verantwortlich, dass Kinder aus sozial schwachen Familien besonders häufig schlecht in Mathe seien. Gerade in Deutschland würde in Haupt- und Realschulen zu viel mit simplen Routineaufgaben und angewandten Textaufgaben gearbeitet. Andreas Schleicher, OECD-Direktor des Direktorats Bildung, fasst das Problem zusammen: Da wird also mehr in einfachen mathematischen Kontexten und Textaufgaben gearbeitet, in angewandten Zusammenhängen. Und insofern werden Schüler aus ungünstigen sozialem Umfeld doppelt benachteiligt. Zum einen haben sie das Gepäck des sozialen Umfelds, zum anderen leiden sie unter ungünstigem mathematischen Unterricht.”

If in a country like Germany with an amazing math tradition – and still very well positioned worldwide – some problems are clear… Then, why is it sooo difficult to recognize  – not only because the topics and motivations we are trying to communicate at school are about 300 years away from now –  that we have to change the whole idea of mathematics  – in our Head & ❤ –  and in our schools??…

Null Bock auf Mathe wird immer häufiger. 4% weniger deutsche Schüler als noch zehn Jahre zuvor gaben an, Spaß an Mathe zu haben. Woran liegt das? Ist der Unterricht so schlecht, zu wenig inspirierend? Zu schwer?

Yes?! No!?

Isn´t it obvious that in this new information age we have entered, we must learn/teach how to think??… This is, how to think mathematically!!…

Mathematical freedom and ideas are fascinating! We not only can  – and must –  explain the logic behind arithmetic and algebraic rules, but we may also show amazing math stuff, like finding the sum of all the powers of 1/4 just by using the drawing of a triangle, or proving the existence of infinite many prime numbers in only 5 lines, or we may see in sunflowers and pineapples one of the most astonishing succession of numbers ever!!… -. These and many other real mathematical ideas may be explained and studied at school, with examples from the most simple to the more complex. But always recalling that math becomes more and more complicated rapidly, and thus we don´t need to make it unnecessarily complex. Actually, not every answer may be found at school… But every question may be asked.

Guter Matheunterricht müsse aber eben auch ein konzeptuelles Verständnis von Mathematik vermitteln. Die Schüler müssten lernen, zu denken wie ein Mathematiker, sich frei in den Strukturen zu bewegen, fordert Schleicher. Darauf würde an Haupt- und Realschulen zu schnell verzichtet. Machen es die Schulen in Deutschland ihren Schülern zu leicht?

Skills in arithmetics are obviously needed, but disgusting routine calculations are not. Furthermore, a wonderful and special feature of math is that if you understand what you are doing, say dividing numbers of 2 digits, then you know how to do it with numbers of 3 or more digits… Understanding replaces repeated calculations!… Understanding replaces brute force 😉 …

Mathematik soll Schüler inspirieren, sagt der Mathematiker Günter M. Ziegler

❤ Yeah!!… Since that´s Mathematics!!…

Excepting for the survivors of the system who go into STEM careers  – where the system justifies itself, and where students too must discover math many times by themselves, if at all –  the rest of people say the truth: They have completely forgotten the so-called “school-math”! That means almost 12 years of senseless time at math classes!… 😦 How can we live with that!?!

Mathematics  – this amazing discovery & creation –  has always evolved, while trying to find answers to the practical problems of each epoch, and since more than 2500 years, also to problems of its own. Something that todays schools seem to have absolutely forgotten.

Furthermore, math has exponentially grown in the last few decades. Many new “branches” of mathematics  – around 70 –  are now part of what we should recognize as “math”. We have gained new, deeper and fascinating insights of our field. Something we must learn to communicate. For example, as physicists do!

On the other hand, elementary mathematics  – the math we should be teaching at school (not to be confounded with trivial!) and which every educated person should aspire to know, at least to be aware of one of the greatest achievements of mankind, if not for hundred other reasons –  will always remain the most beautiful and comprehensible part of math. How lucky 😉 we are!!…

Der Mathematik-Professor G.M. Ziegler schrieb heute im “Berliner Tagesspiegel  ein flammendes Plädoyer für einen inspirierenderen Mathematikunterricht. Mathe müsse den Schülern auch als Kulturleistung nahe gebracht werden, als eine Wissenschaft voller großer Rätsel, schwieriger Probleme, großer Entdeckungen und wunderbarer Strukturen. Natürlich auch als Teil des Alltags, der in Wetterberichten, in Bahnfahrplänen, im Chipdesign steckt. Aber auch als Wissenschaft der Logik und des Argumentierens, von Beweis und Widerspruch. Dafür aber braucht es vor allem gute Lehrer. Die aber fehlen.

Anything to add??… Maybe just an idea: Math should also be taught in context!!…

If you get to know the motivations of a mathematical concept, say of Logarithms  – the need of quickly multiplying two big numbers, and which Logs achieved by transforming multiplications into simple sums -, then you will surely understand and remember that Log (a x b) = Log(a) + Log(b) for ever!

Moreover, telling the story behind the formula, gives back to the subject the passion that is inherent to the mathematical creation and it serves as motivation and provides strength for the tough times. Since mathematics is tough and mathematicians have always struggled through it! That´s the truth! This fact should be seen, not as a disaster, but as part of its fascination. And mistakes must finally lose any negative connotation and be just regarded as what they are, an inevitable part of the art of doing math!

Wouldn´t it be interesting to  – kind of –  split math classes into a more historic-cultural part and a more technical-abstract one??…Wouldn´t all of we  – teachers included 😉 –  be more successful, educated and even happier 🙂 ??…

“Sehr schädlich ist es jedenfalls, wenn Eltern ihren Kindern sagen: Mathe konnte ich auch nicht!”
Das sagt die frühere Mathematiklehrerin Stephanie Schiemann. Sie arbeitet im Netzwerkbüro Schule-Hochschule der deutschen Mathematiker-Vereinigung. Schiemann hat besonders die Rolle der Eltern im Blick:
“Das ist jedenfalls kein gutes Vorbild, man sollte Kindern dann mehr Mut machen. Sonst kriegen sie Angst vor dem Fach”.

“Es würde schon helfen, wenn weniger Unterricht ausfallen würde, denn guter Unterricht brauche Zeit”, sagt Schiemann. Und:
“Wir bräuchten auch einfach neuen Nachwuchs, also junge Leute, die Lust haben auf den Lehrerberuf. Da könnte man Kampagnen machen, um vor allem auch bessere Abiturienten dazu zu kriegen. Es ist ja jetzt leider so, dass eher die schwächeren Abiturienten Lehrer werden, was auch nicht so eine tolle Entwicklung ist.”

A “teaching career”  – especially in mathematics –  must seek to obtain the worldwide recognition and status it needs and deserves. This may be achieved with the right political and cultural mind shift. Professional mathematicians should be a decisive part of this process.

The subject called “school-math” needs an immense transformation… To recognize this is the first step…

 

“In Mathematics the art of proposing a question must be held of higher value than solving it.”

 

“Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.”
Paul Lockhart, A Mathematician’s Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form
Paul Lockhart

 

“How is it that there are so many minds that are incapable of understanding mathematics? … the skeleton of our understanding, … and actually they are the majority. … We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.”

Henri Poincaré


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Author: Math - Update

Updating Math In Our Mind & Heart!!...

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