GIESSEN — It will make you crazy — the pyramid simply does not want to fit into the glass cube. Melih turns it again, this time just a little, and then sticks it in the open side of the cube again. No luck. He tries more forcefully, pressing down on the pyramid. But the fifth grader’s strength is not enough to break a law of mathematics.
Just as Melih is about to give up, it works. He’d turned the pyramid exactly right, so that its edge aligned with the cube’s diagonal, and it slipped right in. Instead of frustration, he now sports a satisfied grin. “It was pretty hard to twist it right,” the boy says.
The theme of Melih’s class visit to the interactive Math Museum in the central German city of Giessen is “shapes.” It’s a place to “experience math without pressure or fear.” That’s the way it’s described by Albrecht Beutelspacher, a mathematics professor at the University of Giessen and the museum’s founder.
The Aha! approach
There are no equations to solve here, just little experiments. “You can’t solve them with patience or luck. There is a little trick,” Beutelspacher explains. “And when you figure it out, there is an aha moment.” Those moments hold the potential to bring the visitor closer to math, and the museum has indeed won several prizes for its methods since opening in 2002. It attracts about 150,000 visitors per year — around 400 per day.
“Pressure” and “fear” are two words that many schoolchildren associate with math.
And according to Stuttgart math professor Christian Hesse, it is also the most loathed subject in school.
German parents spend around 1.5 billion euros per year for tutoring, estimates the After School Help Schools professional group. “More than half of that is for math,” says Cornelia Sussieck, the group’s chairwoman. That proportion has been steady for years, so there must be something wrong with the way math is taught in German schools. But are people aware of the problem, and do they have the will to change it?
Critics say that traditional math classes concentrate excessively on exercises and equations. Kids often don’t understand what the point is. They don’t have the freedom to experience math on their own, with teachers to help them understand the concepts.
“There is math hidden in every church tower and traffic sign,” Beutelspacher says.
A thing of joy?
At the entrance of the math museum, there’s a red carpet with the words “Math Makes You Happy” written on it. As one ninth grade girl sees that, she touches her head in disbelief. It would be like writing, “Vacuuming makes you happy.”
Zita Sprengard is the girl’s math teacher and knows that her subject has a problem that even beautiful concepts and museums can’t solve: Math is part of school, and school takes time away from the rest of life. At least that’s how many young people think, and it’s the framework that teachers have to work with, especially when it comes to math. “We are trying different, better ways to teach things,” Sprengard says.
Last year, she taught her students how to calculate volume. “We gave the students the task of designing and building packaging for one liter of fruit juice, as if they were in a design studio. And they had to show how they had done the calculations. There were some cool things that came out of it, and at the end we had an exhibition at the school.”
This year, she is working on the theme of variables, and she started the year with a trip to the Math Museum to try to find a good approach. There’s a game that might help: It’s a graph that students control by standing on numbers on the floor. The goal is to copy another graph that is constantly changing. The students jump back and forth from the numbers on the ground, with the aim of understanding independent and dependent variables in an equation.
Two hours later the visit is over, and back in school the teachers will see and test if anything has stuck. Sprengard has resolved to make the most of the Math Museum experience during her lessons.
Amazement isn’t enough
Kristina Reiss, a math teacher trainer at the Technical University in Munich, appreciates the Math Museum in Giessen, but says a single visit per year isn’t enough to sustain student interest in the subject. “Amazement won’t make anyone smarter,” she says.
Beutelspacher says that math teachers have a particularly tricky task. “Math is the subject in which there is the clearest difference between right and wrong. That’s good, but it’s also merciless,” notes the museum founder. “There is a danger that the teacher will become the Lord of Right and Wrong. Power creates fear.”
The discussion about how to rid math of its bad reputation has been going on for a long time. Beutelspacher and Reiss both stress that things are much better now than they were 20 years ago. Reiss says that in the early grades math instruction is going quite well. “The problems begin in puberty. The math gets more abstract then, and at the same time the kids are going through a difficult personal phase,” she says.
Critics say that the subject should move closer to kids’ lives, that more time should be spent on math and that higher-level math should be left out of schools. That’s a sticky question, though. In theory, every high school graduate should be able to study any subject at university, but leaders of engineering schools are already complaining that new students lack a solid math foundation. And engineering is not the only subject that requires higher math.
Reiss says that there have already been things thrown out of the curriculum. “We have to prepare students for the time after graduation and also be mindful of the practical applications,” she says. “We have to find the balance.”
Russia has decided to cut off relations with the Western military alliance. But Moscow says it was NATO who really wanted the break based on its own internal rationale.
MOSCOW — The Russian Foreign Ministry's announcement that the country's permanent representation to NATO would be shut down for an indefinite period is a major development. But from Moscow's viewpoint, there was little alternative.
These measures were taken in response to the decision of NATO on Oct. 6 to cut the number of personnel allowed in the Russian mission to the Western alliance by half. NATO Secretary-General Jens Stoltenberg said the removal of accreditations was from eight employees of the Russian mission to NATO who were identified as undeclared employees of Russian intelligence." We have seen an increase in Russian malicious activity for some time now," Stoltenberg said.
The Russian Foreign Ministry called NATO's expulsion of Russian personnel a "ridiculous stunt," and Stoltenberg's words "the truest hypocrisy."
In announcing the complete shutdown in diplomacy between Moscow and NATO, the Russian Foreign Ministry added: "The 'Russian threat' is being hyped in strengthen the alliance's internal unity and create the appearance of its 'relevance' in modern geopolitical conditions."
The number of Russian diplomatic missions in Brussels has been reduced twice unilaterally by NATO in 2015 and 2018 - after the alliance's decision of April 1, 2014 to suspend all practical civilian and military cooperation between Russia and NATO in the wake of Russia's annexation of Crimea. Diplomats' access to the alliance headquarters and communications with its international secretariat was restricted, military contacts have frozen.
Yet the new closure of all diplomatic contacts is a perilous new low. Kommersant sources said that the changes will affect the military liaison mission of the North Atlantic alliance in Moscow, aimed at promoting the expansion of the dialogue between Russia and NATO. However, in recent years there has been no de facto cooperation. And now, as Foreign Minister Sergey Lavrov has announced, the activities of the military liaison mission will be suspended. The accreditation of its personnel will be canceled on November 1.
NATO told RIA Novosti news service on Monday that it regretted Moscow's move. Meanwhile, among Western countries, Germany was the first to respond. "It would complicate the already difficult situation in which we are now and prolong the "ice age," German Foreign Minister Heiko Maas told reporters.
"Lavrov said on Monday, commenting on the present and future of relations between Moscow and the North Atlantic Alliance, "If this is the case, then we see no great need to continue pretending that any changes will be possible in the foreseeable future because NATO has already announced that such changes are impossible.
The suspension of activities of the Russian Permanent Mission to NATO, as well as the military liaison and information mission in Russia, means that Moscow and Brussels have decided to "draw a final line under the partnership relations of previous decades," explained Andrei Kortunov, director-general of the Russian Council on Foreign Affairs, "These relations began to form in the 1990s, opening channels for cooperation between the sides … but they have continued to steadily deteriorate over recent years."
Kortunov believes the current rupture was promoted by Brussels. "A new strategy for NATO is being prepared, which will be adopted at the next summit of the alliance, and the previous partnership with Russia does not fit into its concept anymore."
The existence and expansion of NATO after the end of the Cold War was the main reason for the destruction of the whole complex of relations between Russia and the West. Today, Russia is paying particular attention to marking red lines related to the further steps of Ukraine's integration into NATO. Vladimir Putin's spokesman Dmitry Peskov previously stated this, warning that in response to the alliance's activity in the Ukrainian direction, Moscow would take "active steps" to ensure its security.
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