math – update

blogging & searching for true math …

Do today´s pupils feel less and less like learning math??…

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NO! – Those German pupils  – as well as almost all other pupils –  still haven´t actually met real math!

The following article in New-mathematically-results-from-pisa-2012* is clear. Nearly for the first time we can 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.

The latest PISA report says German pupils learn less math at school. Although they spend more time on math classes   – on average 13 more minutes per week as in 2003 –  well over half of socially disadvantaged youngsters (57%) and 1/3 of children from families with a higher income, admitted they have never heard of a quadratic function.

Also, the way of teaching would be disadvantageous for the pupils from socially vulnerable families. In Germany, in the lower secondary schools, teachers work too much on simple mathematical contexts, routine and applied problems.

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

No motivation for math is more and more frequently! 4% less German pupils than ten years ego, say they have fun with math. Why is that??… Are math classes so bad, so uninspiring??… Too hard??…

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 at school. 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.

“A good math class should also convey a conceptual understanding of math. The pupils should learn, to think as a mathematician, to move freely in the math structures”, calls upon Andreas Schleicher (Organisation for Economic Co-operation and Development) OECD-Director of the Education Directorate.

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 😉 …

Mathematics must be inspiring for pupils, says the mathematician 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!!…

Professor Ziegler writes in the Berliner Tagesspiegel a passionate plea for inspiring math classes. Math should also be presented to pupils as a cultural achievement, as a science full of puzzles, hard problems, great discoveries and wonderful structures… Of course also as a part of our everyday life, since math is hidden in weather forecasts, in traffic plans, or chips designs. But also as a science of  logic and reason, a science of proofs and contradictions. For this, one needs first and foremost gut teachers. And they are missing.

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  – not only as an inevitable part of the art of doing math –  but furthermore, as the only way 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, better educated and even happier 🙂 ??…

Stephanie Schiemann, former math teacher and actually working in the networking office between schools and colleges  – Netzwerkbüro Schule-Hochschule –  of the German Mathematical Society, says: “We just need new offsprings, young people, with motivation for a teaching career. One could initiate a campagne on this issue, to get better high-school graduates interested. Right now, unfortunately, are most likely the weaker graduates the ones who become teachers, which is not a good perspective.

Schiemann cares especially about the role of parents: “Extremely harmful is also, when parents say to their kids “I also coudn´t do math!“. That is absolutely not a good model, one should give courage to the kids. If not they become scared of the subject”.

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

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


* Source: Deutsche Schüler haben immer weniger Lust auf Mathe – Von Christiane Habermalz.  – 


Paul Lockhart

“Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations”
“[Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on.”
Paul Lockhart, A Mathematician’s Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

Author: Math - Update

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

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