Learning Math (Germany vs. the US)

I’ve been reflecting about the differences between math instruction/learning in the U.S. and Germany, partly sparked by discussion of the latest PISA results (international testing) and an editorial in the New York Times (“Who Says Math Has To Be Boring?” published Dec 7 and posted by several friends on Facebook).  Here are a few comments on our experiences with German math in 3rd and 6th grades.

…On the one hand, Marlena has more practice in math this year than she’s ever had.  I don’t want to say drilling, because I feel like that connotes repetition of the same facts with little variation, and these exercises are more creative than that.  She has a workbook in which she has to complete two pages per week, and they have daily practice at the beginning of each math class (which meets three days per week).  Each page in the workbook has a few sections.  The first is usually straight writing out of math facts, but with a few parts:
example:  8 x 9 = ____ || ___ / 9 = ___ || 8 x 90 = ____ [the last column is usually an extension]
example:  81 / 9 = _____ || 82 / 9 = _____ || 83 / 9 = ____ [teaching them about remainders]

The second part often has patterns, such as:

9 + 5 = _____ || 9 + 15 = ____ || 9 + 115 = ____
29 – 15 = _____ || 79 – 15 = ____ || 78 – 14 = ____

Or they have to show how to solve more difficult problems by mentally breaking them down:

60 x 15 = 60 x 10 + 60 x 5 =

The third part is usually some kind of puzzle that involves math, mixing together adding, subtracting, multiplying and dividing.  The workbooks have colorful graphics (without being overwhelming or distracting) and they mix up the problems enough that they don’t get boring.  It’s been excellent reinforcement of her computational skills.  And as an added bonus, when you complete each page, you get to put a sticker on a big picture at the end of the book; when you’ve completed the workbook, you have filled in all the blank space in the picture.  [She has a similar book for German grammar/spelling/vocabulary.]

…On the other hand, Henry is completely bored in math.  They move very slowly through topics.  Because the entire class has all of its instruction together as a unit, there is no way to differentiate for students who may be better or worse in a particular subject.  Henry has definitely benefited from the acceleration provided by our Brighton school district.  Your only option here would be to send your child to the Carl-Zeiss Gymnasium (5-12th grade school) that focuses particularly on math and science.  That’s unfortunately more complicated to get into when we’re only here for a year.

…A fun activity that Henry is participating in this month is “Math in Advent.”  It’s a nationwide competition sponsored by the Deutschen Mathematiker-Vereinigung (German Mathematicians Association).  You can sign up as an individual and/or as part of your class at school (with approval by your math teacher), and each day from December 1-24 there is a question posted online.  The top winners in different age groups have the chance to win prizes and go to Berlin for an awards ceremony.  The questions are all word problems that involve elves or snowmen.  One involved calculating how many trees would be saved if children wrote their wish lists to Santa on recycled paper; another looked at snowballs stacked in squares or triangles; another involved attendees at Christmas Markets.  I like the fact that there is this external activity which involves some creative problem solving.  There may be things like this in the U.S. if I knew where to look, but this was sent home from his teacher so we didn’t have to search it out.

I just noticed that there’s also a Physics in Advent set of 24 experiments.  We’ll have to check those out also.  If you can’t tell, Advent is big here!



Yeah, can you believe it?  We actually went into a sauna as a class.  Clothes.  Well, the girls and the boys didn’t go in together.  But still.  At the beginning I was a little uncomfortable, what with being naked in front of our teacher.  At least she was wearing a bikini.  We went into the sauna area in our school and got undressed.  After that, we took a warm shower.  I wasn’t quite yet comfortable.  Then, we went into the sauna for 15 minutes.  I practically died.  You may think 15 minutes is not a long time, but in a small room with a lot of people and a lot of humidity at 158 degrees, it can get pretty hot even for 15 minutes.  To help pass the time, we told funny stories or riddles to each other.  There was an hourglass to keep track of the time.  In the last few minutes, I kept looking at it, hoping it would just quickly run out.  It had marks for every minute you had left.  When it finally ran out, we left the sauna room and took cold showers.  I felt like ice was being put all over me.  After that, we went into a big room where we relaxed.  About two minutes later, we went outside on the balcony, again clothes. But I wore my bathrobe.  We played tag naked.  I was still a little uncomfortable.  People could see us from outside.  Luckily there wasn’t anyone outside.  After that, we went inside to the big cooling-off room, had some nice fizzy pear juice with fruit, a special sauna drink, and Frau Wetzel, my teacher, read to us.  After a little bit of cooling down, we went back into the sauna.  I died even more this time.  But this time we didn’t take a shower right after.  Instead, we went right out onto the balcony and ran around.  I was a little more comfortable by then, so I didn’t bother to put anything on.  I just went naked.  We played tag again, again without anyone seeing us, and then went back inside, took cold showers, and Frau Wetzel read to us again.  I felt really nice. We listened to some music and just relaxed and drank.  Finally, we had to get ready to go home, because these were the last two periods of school.  I thought to myself, “I hope we do this again!”  (Notice:  no pictures for this post!)

Jena’s Long Night of Science (Lange Nacht der Wissenschaft)

On Friday night, we participated in the 5th annual “Long Night of Science” in Jena.  The evening took place from 6pm-midnight and was an overwhelming collection of things to do across town.  University departments and labs and affiliated institutes opened their doors and sponsored various demos.  This included the University hospital and several medical clinics.  I liked that it wasn’t just natural sciences; everything from the Departments of Ancient History to Geography to Languages sponsored events.  Companies also participated, and there were abundant goodies to collect along the way.  Our ticket to the event also got us unlimited free transit on the buses and trams.  The most frequently-running bus up to the Beutenberg Campus, home to most of the research institutes (including Andrew’s), was called the “Denkbus” (Thinking Bus).  Some of the things we saw and experienced:

– In Andrew’s building, the Institute for Photonic Technology, we saw part of a Science Slam (the top student received an iPad) and got free “mad scientist” drinks at the Gin and Photonics bar (pictured below).


At the Institute next door, the kids were able to get pens with their names and the date laser-engraved on them, in addition to several other cool-looking pens and pencils that were free for the taking.  Conveniently, Henry had just learned the name of his secret Santa partner from school that afternoon and Andrew was generous enough to pose as Elias, enabling Henry to include a personalized pen as part of the gift.

At the Fachhochschule (technical college), Henry learned a new math game, Marlena made cool bubbles with geometric shapes, they both got a print-out of where their birthdate first falls in pi (around the 67-millionth digit for Marlena and 132-millionth digit for Henry), went into an acoustic lab, and saw other various posters and demos.

The highlight downtown was going up to the 14th floor of a company building (Jenoptik) where they were shining lasers in various patterns onto the ground nearby.  It was cold, windy, and drizzly, which was semi-miserable but made for a great visual effect, as you could see the beams of the laser as they passed through the droplets in the air.  Andrew took a bunch of pictures but unfortunately none came out very well.

All in all, it was an enjoyable evening and we managed to stay out until 9.  It was made even more fun by meeting up with Marlena’s English teacher and her family, and their giving us a ride home through the ever-increasing rain.  There were still lots of things we would have liked to see but didn’t have time for, but that’s the challenge with having such a large-scale event.  Seeing the number of people who turned out to experience it, though, was inspiring.  Jena was named a “City of Science” in recent years, and this was a good opportunity to see why.

Holidays in Jena

– We’re having a low-key Chanukah celebration, enjoying the chance for simple traditions in this new setting.  The initial menorah was one that belonged to Grandma Barbara, bought in the early 60s when she was at University of Rochester.  A second one was added to this collection as a free gift from the Berlin Chabad; Andrew happened past their candle-lighting when he was in Berlin for a conference last week. I was able to find the Gelt at our local market; they’re enjoying the various Euro dominations.


Tonight we had a home-made latke meal.  Well, really it was a potato “nik” or one mega-latke, recipe courtesy of Mark Bittman in the New York Times.


– Earlier today we went to the Weihnachtsmarkt (Christmas Market) in the center of town. One of these days I’ll get pictures of all the cute wooden stalls from which they sell lots of food, drink, sweets, candles, toys, and other assorted gifts.  Dessert for the kids was chocolate-covered fruit (that’s a half-pear of Marlena’s masquerading as a mouse, and Henry’s is a banana not claiming to be anything else).  Beyond the sweets, the kids enjoyed some of the rides set up in the parking lot just outside the old market square.