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!