GERMAN MATH + ENGINEERING 🇩🇪 Are Our American Kids Getting a Better Math Education Here?
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- čas přidán 18. 06. 2024
- Kevin was excited to GEEK out in this video about German engineering and math! It has been really interesting to see just how different math is taught here in Germany compared to the USA. They are truly teaching engineering concepts and vocabulary from the first and second grades, something that is not done in the US until college! We are confident our four kids are getting an amazing math education here in Germany.
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//CHAPTERS//
0:00 - I take you on a winter hike right out of our backyard!
1:04 - A little bit about our family of 6
2:19 - Check out our series on what German school has been like for our American kids
2:41 - German Math - it's more conceptual and open-ended than in America
4:07 - German Math is tied to more practical, everyday scenarios
7:10 - There's a stronger focus on Arithmetic in America
8:10 - Engineering terms and concepts are taught from very early in school (Würfelgebäude)
I saw this interview, a couple years ago, with two German teenage~adolescent girls that had been on student exchange in the USA for 6 months, after some time being back home again. Q: "What do you miss most about the USA?" A: "High school!" Q: "Why?" A: "Because it was so easy!"
a few of my classmates went to the US for an exchange year and they found the level also to be very low (and they were average students in Germany). one even wrote the best english essay of her grade in Florida!!
@@felimuller909 one of my classmates in 11th grade went to the USA for a semester, and he was sent straight to college. He was an intelligent guy, so he managed quite well and returned with just a slight advance in math (calculus) and really good spoken english. But yeah, he missed out in chemistry and geography, because 11th grade just brings you on par in ALL TEH SUBJECTS.
Seriously, 1st semester of 11th or E-phase is just like the first weeks of freshman semester in any subject that had a prior school version.
It's interesting to hear about your experiences with mathematic. I remember that there has been a foreign student from russia in my class about 30 years ago. He couldn't speak German but he once ended up at the blackboard after a math lesson discussing the way to solve a mathematical problem with the teacher just by using mathematical terms written in chalk. This was his only possibility to "speak" with a teacher and to show his talent for doing logic. It was cool.
So cool! Math is a more universal language.
Migrants from Russia & Kasachstan had a reputation of being good at math. For them, it apparently was a common thing to solve math problems together with the family from a young age.
Our physics professor entered the lecture hall with only a pack of chalk for the blackboard. The problem was presented verbally and the mathematical solution developed on the blackboard. I don't know any different. The American way of teaching does not seem to me to be aimed at recognizing problems and thus being able to solve them. You cannot work as an engineer if you have only learned to solve calculations correctly, but not to understand the problem.
@@faultier1158 Look at the list of chess grandmasters. A lot of them are from the "east".
@@faultier1158 You're right. We got 2 girl from Kasachstan in our class one year. I think at 6th. All math lessons they where extremely bored and at the end of every year the best of all.
As a math teacher at a gymnasium I really appreciate your insights. Mathematics is so much more than calculating things (which can be done by a computer faster and more accurate - if you program it correctly) - stiil, you need to know what the computer should execute and if this makes sense.
It is abour seeing patterns and thinking logically - something that you need as an interdisciplinary everyday skill. And of course you first have to learn the basics as a tool kit so that you can later mathematically solve the real (and not just designed for classroom) questions in the upper school.
Many complain in Germany that you learn too much at school that you don't need.
If it was only about learning what I really need in everyday life, then schooling could be shortened to around 4-5 years. Strictly speaking, you only have to be able to read and write, as well as master the basic arithmetic operations (although every pocket calculator or computer can do this more reliably than humans. But I have to know whether the calculation that I let the computer do makes sense at all) .
But now we live in a world that is a little more complicated, in which know-how and technical progress are becoming more and more important.
The three types of school in Germany are each geared towards different educational goals. Mittelschule and Realschule are designed to enable vocational training. Therefore, subjects are taught here in a much more practical way. The aim of the Gymnasium is the general higher education entrance qualification, so it should enable one to study every potentially possible subject. From German studies to philosophy to the natural sciences. Of course, everyone has their own interests, strengths and inclinations - but I can only find them out when I have had the opportunity to get a taste of as many areas as possible. And for this I also need perseverance, as it usually takes a little while to work my way into something, to understand it and then to discover whether I enjoy this topic and whether I am interested. Think, for example, that I am trying to juggle. The probability is very high that I won't be able to do it the first time. Then probably not fun either. But should I stop immediately because of that? Wouldn't that mean missing out on the opportunity to discover my own skills and interests?
Many always complain that school didn't prepare them for life (and that's true, because education is so much more than just coping with everyday life). As an example, it is often cited that one would never have learned how to prepare a tax return. Then I always ask myself: How do these people imagine it actually? Who decides what things should be taught in school? In addition to tax returns, buying a house and other often mentioned aspects: why not also how to cook, clean, wash clothes, iron, tie your shoes, ride a bike, ...
The list could be extended endlessly. In other words, you would be in school for almost your entire life. So where should the limit be set as to what should be taught in school and what is personal responsibility? School cannot do that. And by the way, that is not what you want.
To use math as an example, which is very often seen as "unnecessary": of course, you will probably not need the Pythagorean theorem in your later job. But that's not the point either. Above all, subjects like math are there to train logical thinking, to be able to draw logical conclusions and to be able to acquire things for oneself. The same applies to poetry analyzes in German. Sure, I will specifically need this in very few situations after school, but analytical skills are also trained here. By memorizing poems, a wide variety of learning strategies can be practiced at the meta level (mnemonic techniques, loci method, ...), and soft skills such as the ability to concentrate, discipline and perseverance are trained.
And that's not limited to math or German. In everyday life one constantly draws logical conclusions in all possible situations in life. At school you learn a number of soft skills that you need in order to acquire knowledge yourself - e.g. also to find out how to file a tax return or what to consider when buying a house. Regardless of this, it would hardly make sense to deal with the topic of tax returns in the 9th class, as this topic only becomes really relevant for the students much later (and by then a number of things have probably already changed again). In my opinion, the subject of tenancy law, which is of course very important for everyday life, has no place in school. It feels like it changes every few months due to various court rulings and is also very complex. In school this topic could only be dealt with very superficially and the content would be out of date for a long time after a year. It cannot be the task of the school to take up the topic annually in order to constantly convey all updates. Then you would be very busy with your time and could hardly devote yourself to other topics.
And last but not least, math (and the reasoning behind it) occurs in almost every profession in some way.
The shopkeeper has to calculate sales and purchase prices as well as invoices.
The psychologist must collect data from random samples and evaluate them statistically in order to derive meaningful conclusions.
The gardener has to calculate areas in order to know how much can be planted. He must be able to handle volumes, for example to calculate the need for soil or filler material.
The craftsman and the architect need spatial imagination and have to consider various aspects such as the nature of the subsurface, energetic properties of the materials used, sensible laying of cables and connections, ... To do this, they have to be able to think logically.
Now many argue that this content could simply be moved into vocational training.
Problem 1: the training courses would be significantly longer in terms of time.
Problem 2: very few pupils already know from the 6th grade which profession they want to take up one day. Career aspirations change. Therefore one should be as broad as possible with the school education.
Regardless of this, the different types of schools have different requirements: Middle and Real Schools should prepare for vocational training, and grammar schools should also allow access to higher education. To do this, different skills and more abstract knowledge and thinking are required.
It is simply a matter of a broad general education in order to be able to develop one's own interests, for example. If I've never heard of biology, I might never discover my interest in cell structures and what goes on in the body.
And it is also not a "must" to study with a high school diploma - the high school diploma only offers more options, but it is absolutely legitimate to do an apprenticeship after graduating from high school. Unfortunately, this is often no longer accepted in today's society.
And yes, the educational opportunities in Germany unfortunately still depend too much on the parents' home. But school cannot take over all the tasks of the parental home, such as complete upbringing, education and the imparting of knowledge that is necessary for life. Parents, too, have a responsibility that, unfortunately, in some cases they are less and less able to live up to. School CAN'T catch everything.
In school, the foundations should be laid in order to be able to acquire things for oneself. And ultimately, education is reciprocal, i.e. an offer that the respective student must also accept. And yes, nowadays you can googling almost all information - but I still have to classify it myself and draw and reflect on my own conclusions.
Soory for this book of a comment :-)
Top notch comment!
Danke für diesen tollen Kommentar.
Also you don't know as a pupil what you will later need at a university level.
I was happy after my English abitur exam, no more English. Fun fact - the whole literature (e.g. journal papers) in the university classes was written in English.
Great comment. Just to add a bit more: Sure you can google just about everything, but that doesn't mean that what you find is actually always useful or even correct, so acquiring those logical, analytical and critical thinking skills at the primary and secondary school stages is a great help later on. I do think that "internet literacy" should be taught.
Wow. I've never seen such a long comment on CZcams since I've been using it. And it makes so much sense. Thanks for sharing your opinion 👍
What I really like about this video is, that compared to others, who just say the American education system was bad, you were able to really explain in which ways they are different.
We are glad you enjoyed it! Thank you.
That was just their polite American sugarcoating not to mention it like this! ;-)
Because Americans (and British people!) never say something is bad, they just go around it with other words 🤣 Europeans on the other hand will tell you how it is, which is the reason we are often considered rude by Americans
@@silmuffin86 especially the Germans :-) Usually they don't need a euphemism or a "nice expression", they just say it how it is or how they see it. 😂 . . . and this is for Americans kind of rude.
I'm a German who went to US high school for a year. Granted, I had very good math grades in Gymnasium, but as a 10th grader I took AP Calculous in high shool, surrounded by seniors.
And I tried to take chemistry and physics. The only class they offered was Chem/Phys and it was so basic that both sides agreed it would be a waste of time for me. Never caught up again back in Germany in these two subjects.
Yeah, I did my 12th grade there... American public school is terrible and I believe it's on purpose
That’s why, at least at my school, if you chose to do a year in the US, you would repeat that year in Germany. You just lost too much in some subjects
@@bellathemusicaddict And that was also true in the 80s when i thought of doing 12th grade in the US but ended up not doing it. When my classmates came back after a year, their english was significantly better then ours, they had improved in sports a lot but with one excemption they all had to repeat 12th grade for lack of education in any other subject.
@@bellathemusicaddict Same here. Only if you were one of the top students who might possibly skip a grade anyway, you'd be allowed to join your old class.
in my school if you went abroad for an entire year they usually gave you an exam to see if you could rejoin your class or needed to repeat, no matter where you went. Which was one of the reasons why I only went for 5 months. But I went to Canada and had a similar experience, though Canada is said to have a better public school system than the US. Still, I was a rather average math student in Germany and I still passed the Senior year advanced math class even though I was a Sophomore.
As a German engineer, I found this video particularly interesting. It would be great to learn more about Kevin's work experience in the US and now in Germany.
It's amazing that you find the time, alongside all your experiences and work, to put out a great video every week.
It would also be interesting to learn how engineering studies in Germany differ from the US.
@@petraw9792 we American though them the engineering
@@mikemer79 Huh? 🤔
I second that, I would love to hear about Kevin's work experience! (also a German engineer here :D)
@@arvedludwig3584 I feel you. :D I don't know what Semesterferien are supposed to be. You write your exams or several term papers or both during the vorlesungsfreien Zeit. Even worse when you have family, lectures and/or exam preparations are always during the school breaks.
I wasn't even aware of this difference until I lived in the USA. I was surprised how rudimentary math skills were in the USA (in general in everyday life) . Starting with the simple ability to quickly calculate the change for a purchase to more complex calculations or just plain, simple additions of decimal values. I helped a friend renovating his house for 6 months and he was surprised about my metric "Zollstock" (ironically Zoll means inch) and how quick I measured and added or subtracted values. Something nobody would be surprised about in Germany. Who in the world would want to add 5""1/32 + 18"1/8 + 14"1/2 when you can simply measure everything in millimeters (mm) and be able to calculate the sum of the values in a heartbeat? Not even Americans (the average person that is) if they actually knew how much easier it can be done ... I am pretty sure of that.
I heard that there is a lot more waste of building materials when using the imperial system because people just get used to rounding up a lot to be safe.
@@germansnowman I could see that been a thing
The decimal calculation they do all day.. they should measure and calculate in USD $ ;-)
Kids in the US spend huge amts of time on fractions, which are really hard from a child development statement, because they involve part to whole relationships. The US started going metric and then just stopped, I think back in the 60s or 70s. People worry we couldnt' adapt, of course we could because you just learn to think in metric. Translating from one to another is ridiculous. I really wish we would go metric (and I'm in my 70s, pretty sure I could adapt).
At 15 years old I went to Argentina for one year. I studied in a private school which was deemed to be at a high level in Buenos Aires. The first day in the teacher gave me Math problems to solve just to see at which level I was at. Well let’s say I wouldn’t have to be sitting in classes till maybe one and a half year later. In Physics it was even worse and they didn’t teach Chemistry at all. Forget about doing experiments either. There was non of that! Other subjects were closer in standard, but it was still way to easy to pass the classes…
Now I am a Maths and Physics teacher in a German Gymnasium and I have to say, our school system actually could be soooo much better, but than I think back to Argentina or think about standardized tests in USA or even the high pressure in most Asian schools and I‘m glad our students have a comparatively good education here. I'm happy and proud top teach here. Still, I'm up for a few changes;)
This is very interesting and makes me curious about what it is like in Turkey. They say Turkis kids from Turkey are quite good at maths
Man könnte anfangen mit Ganztagsschulen, dann hätten die Kinder auch mehr Freiheiten und vielleicht auch Spaß etwas neues zu lernen.
You are *SO* American, it's adorable! It is heartwarming and uplifting to see how you found a home in Germany, especially with your bubbly personalities explaining all the peculiar detail we Germans take for granted.
Hey ihr beiden! Nur ein kurzer Kommentar: Danke! Leute wie ihr passen hier super gut rein! Schön, dass ihr gekommen seid um zu bleiben!
I love your videos. From what I know the children in The Netherlands have similar mathematics education.
I'm 69 and live in The Netherlands. I went to the Elektro Techische School in Amsterdam and I sure had to learn German technical language because most of the engeneering in those days, 20 years after WW2, was from Germany. I got an internship at Siemens medical technics, Amsterdam branch. Installing medical equiptment in hospitals around the country. Well I needed my German lessons at full.. Everything was in German language, from speaking to my chef to all the manuals. I improved my German in those 3 months very much. Even around the Commodore 64 era I bought German computer magazines because they were better then Dutch magazines.I still have no problem at all watching German TV, reading a German newspaper, reading German books or chatting with German people all over Europe while on holiday.
I wish could say that for my Dutch skills ;-) The Netherlands have great artist, great musicians and many things to offer.
It's always worth to enjoy a classic concert in the Concertgebouw.
dank uw wel
With your german skills you trapped into a false friend with the word chef. A chef in german is the boss but a chef in english is the cook.
Another aspect that always amazed me is the amount of "non-fiction" books available to even the youngest German kids. In French or Italian bookshops you might have a couple of options, but in German ones there's usually a huge section of picture books about everything from recycling to spaceships, trains and whatnot. And they are super detailed. At 3 my son would casually lecture me on the different types of fenders while walking around our street 🤓
I love reading that about your son! I hadn't really noticed that before, but yeah, there are many nonfiction books for kids.
I was shaking my head when you asked wether the day-to-day examples stay, because I didn't really remember and then five minutes later it hit me: in one exam in grade 12 on the topic of vector computations we actually had to calculate wether spider man, who was in position ABC was able to save his girlfriend in Position DEF from being killed by a chain saw moving from GIH to JKL at speed X. You know, every day stuff. That same teacher took us to a casino to teach us probabilities and in physics we had to analyse Lenkzeitenscheiben (little disks that show how long truck drivers are driving) and you can calculate down to wether they stuck to the speedlimit or not if you wanted to (of course the teacher wanted us to).
It was all too much for me.
I had a college professor like this too. On the exam we had to calculate the electric field inside the hole of a block of cheese, when the cheese is placed in an external field.
That sounds like it could be from the book "the physics of superheroes" ^^
Da wäre ich aber auch raus 😅, so etwas ist ja schon echt übertrieben. Ich habe eine bekannten der Macht gerade seine Doktorarbeit in Mathematik oder ist sogar schon fertig, da bin ich mir gerade nicht sicher, der könnte so was sehr wahrscheinlich leicht lösen, aber so hat doch jeder seine Stärken und Schwächen. Er hat dafür in der IT 0 Ahnung usw....
Ich denke genau deswegen brauchen wir Fachkräfte, damit alles am laufen bleibt
Welcome back! My pupils (mostly Gymnasium) will be pleased. I have recommended your channel to them for various reasons ( the clarity of your speech, the values you as a family represent, intelligent discussions around the content of your videos, the warmth and general wholesomeness emanating from your videos). They find it fascinating to see how foreigners experience the culture they've grown up with and take for granted. It prompts some really interesting discussions!
Oh wow! That’s so cool! Thank you! 💕
I know this is a reply to a very old comment, and i am not even German, but watching videos from people coming from outside the EU living in the Netherlands made me appreciate the things i took for granted. I guess it is the same for Germany.
I'm 50 and live in the Netherlands. I also grew up with the idea that a lot of engineering and math text books were in German. I didn't actually encounter this myself in my education. Upto high school all text books were in Dutch and by the time I got to university, English had taken over as the dominant language. But my dad was from the generation where German was still an important language in engineering. He had a lot of text books in German from his education. So that's why I was told that German is important if you're going to study engineering.
How cool! I hadn’t heard that learning German was important to be an engineer. Love that!
@@MyMerryMessyGermanLife In Japan for a long time the medicine text books were in German. (Well, after they opened their country to the West.) They still have learning German as part of medical studies in Japan.
@@MyMerryMessyGermanLife it had been centurys ago the languaga of science! Its a logik builded speech aslo perfekt for that!
When I was in college at University of Michigan, in my course catalogue, I noticed that for majoring in Math, Physics, Biology or Chemistry, they strongly recommended having a good reading knowledge of German. And it does not surprise me. I know several PhD recipients (even from US universities) that did postdoctoral work in Germany 🇩🇪.
@@franhunne8929 interestingly enough, as a podiatrist, I know that at least before COVID, podiatrists who underwent residency training in USA would go to Germany to do foot/ankle surgical fellowship training.
Interesting topic here. When I was a child in the 1970s, I excelled in math and could do everything in my head. After we moved to the United States, the teachers refused to allow me to do them in my head and forced me to do the long way (writing down the problem, crossing out and/or adding numbers, etc.). For instance, we could do 341:22=15,5 instead of the long division or 2.27323=75.009. When my parents showed my teachers how we did it in Germany, they were so flabbergasted, but they insisted on doing it the "American way". Afterwards, I despised the math so much that I wanted nothing to do with them for a very long time. I struggled to pass compulsory Math 101/102 at the university. I was so angry at the American educational system that focused on the hardest way to do the math problems than allowed us to do them in the head. Obviously, the American teachers have a very serious trust issues...
So great to see how excited Kevin is about all of this :)
One of his favorite topics! 😀
I'm a elementry school teacher in the Netherland. This is how math is tought here too. With a lot of realistic everyday context. My own kids are in high school and math is getting more and more abstract.
Great to know it’s also like this in the Netherlands! America has catching up to do with most of Europe, making the decision for us to move here easy. 😆
It's a EU guideline for schools... same in Italy. It's called "real life tasks". Teachers throughout the EU are all encouraged to assess students' skills and not only their theoretical knowledge. Some countries are much better at it than others, though.
Awesome seeing Kevin get all excited. Nothing beats having a professional talk about his/her profession 😆.
Honestly, I always thought Americans must be mathematical geniuses because of having to deal with the non-metric system. I‘m a carpenter and also into sewing and whenever I stumble across Americans on CZcams giving measurements for their projects I‘m like: „3 1/16 + 5 7/32 … WHYYY? 😭“ and I had advanced maths in Gymnasium and also some maths courses in Uni for Computer Science BA - so I really don’t mind numbers…
the imperial system is stupid. And the biggest joke: US got rid of british empire but not got rid of the british imperial system.
Yeah, I also had that Angst about Textaufgaben. 🤣 Because they weren't just calculations but required real thinking. Then there was the question:
Boiling 1 egg takes 5 minutes. How long does boiling 6 eggs for the whole family take?
Me: multiplied 5 minutes × 6 of course... 😬😭🤣
Also, absolutely LOVE it how Kevin shines and gets animated in this video. He almost climbed out of my screen and into my living room. 😆
Hahaha! Yes Kevin gets so excited about math!
Regarding the Würfelgebäude.
You mustn't forget that there are highly qualified apprenticeships in Germany. Just 10% of the students in Bavaria go to the Gymnasium.
Usually the apprentices start at the age of 16 and a CNC worker who writes his own programs needs a three-dimensional imagination.
I think that's one reason why the teaching of STEM content starts early.
It’s actually about 40% who go to gymnasium
@@therealannakonda Right, i had old numbers in mind. It changed the last few years a lot. I remember the highest quote was in Berlin with 30%.
The last three years of Gymnasium are usually called „Oberstufe“.
Maybe I am wrong, but I would think that at 5:13 you need to put in banknotes that actually exist, so 5, 10, 20, 50, 100, 200 or 500. Nice video as always.
Hope you enjoy this video where Kevin gets to GEEK 🤓 out about math and engineering! Does he give German math education a 👍 or 👎?
Geeks also make great wifes!
@@ThePixel1983 that’s right! Geeks are just awesome all around. 😍😀
At our Gymnasium I hated maths. In languages (German, Latin, English, Spanish) and history I always had a 1 or 2 without learning at home, but for maths I absolutely have no sense and only had a 5. If you solve a calculation together with me step by step it seems logical to me, but when I have to solve another calculation alone I simply cannot get it. Additionally I had problems with most of my maths teachers, because they always took it personally that I was so bad at maths. The worst was a maths-teacher who was a colonel in Bundeswehr (German Army) before he became a teacher. Two years I had war with this as*ho**....
@@janpracht6662
I think that especially in math, the kind of teacher that you have matters a lot.
Also, in higher grades in gymnasium, math becomes more and more abstract. At that point, I would have found it helpful if the math teachers were still able to explain how and where the math problem refers to a real world task. I think that it’s a lot harder to just learn formulas by heart, than it would be if there was given a reference, like the example from the above video with the baking recipe.
Of course, it helps if you have an engineer at home helping you with homework. 😊
And a combination of a geek husband and a creative and charming wife is the best. Especially if both love and respect each other's personality and don't want to change each other.
Hallo, In German we say " was Hänschen nicht lernt lernt Hans nimmermehr" When you something learn as a child mit is easyer then when you must lern it as a Man.
Ah okay! Great to learn this new German phrase. And it’s very true!
Ich habe in meiner ganzen Schullaufbahn keinen grafischen Taschenrechner benutzt. Als ich in der 10. Klasse mal nach Buffalo, NY, zur Schule ging, da war ich von grafischen Taschenrechner total verwirrt. Gleichzeitig stellte ich im Mathe und Physik Unterricht fest, dass die Verknüpfung von Experimenten oder neuen Lerninhalten mit dem bestehendem Wissen kaum vorhanden war. Ich war irritiert, warum in der 10./11. Klasse nicht aus einer Tabelle von Daten ein x/y Koordinaten System erstellen?
(ich stelle außerdem fest, dass ich den Kommentar auf englisch gedacht habe und der dadurch total befremdlich auf deutsch klingt xD)
The wonders of being multilingual, je sais, tu peux in mehreren Sprachen Worte vergessen. 😁
Ich habe 2005 Abitur gemacht und wir konnten im Vorfeld sogar abstimmen, ob wir die normalen oder die graphischen Taschenrechner benutzen wollen. Dem entsprechend hätte es im Abi dann natürlich andere Aufgaben gegeben. Das war allerdings im LK, nicht im Grundkurs und nachdem wir auch nur eine sehr dürftige Einführung in die Dinger bekommen haben, haben wir dankend abgelehnt 😅.
A lot of animal shelters in germany have volonteer programs, where you can take shelter dogs on walks.
Maybe a great opportunity to get to know a dog that is already house trained and in need of a good home.
Oh cool! Thanks for letting us know’
While - according to the tests I was very good at math ending up with a masters degree in university in Germany back in the early 90s, I have to admit I had partially a hard time helping / teaching my granddaugther a few years ago at highschool in her 10th grade. They learn so much more nowadays, using different approaches and obviously I also forgot alot. So be prepared, it will become increasingly challenging for you during the next years. 😂
I love Tetaufgaben like this: "One cubic meter of water costs 30 cents. You have a round pool with a diameter of 2.5 meters and a height of 80 centimeters. How much does it cost to fill up the pool?" If I didn't miscalculate, approx. 1.13 euros, but the point here is: You learn how to handle units, and how to read thoroughly. Give that to a class, and I bet there will be some who punch the 2.5 into their cylinder formula r^2*pi*h without minding that it's the diameter, not the radius.
So glad to see you have returned safely from your US vacation. Happy New Year! And about the dog, ask the cat first - lol.
Hahaha that’s right! Ask the cat! 😺😺
Happy New Year to all of you. I am glad to hear that you are safely back in German. Hope you had a great time in the States. Regarding the dog-you could consider adopting rather than buying a dog. You could adopt a young dog (age 1 or older) rather than a puppy. That makes home training a lot easier, too. Most rescue places test the dogs whether they are OK with cats before letting them go into a family with one or more cats. Cats are normally OK with dogs as long as the dogs know the cat is the boss. 😀 I currently share my life with 3 dogs and 4 cats-all rescues. Have a nice Sunday and a happy new week.
@@renate_c4h Rescue is my favourite breed!
I loved seeing Kevin get excited about this, especially since he has a unique perspective because of his education (Btw Kevin, if you ever play D&D with the kids again, why not throw some math and engineering challenges at them instead off riddles or fights?). Btw, Sara, since you seem interested about culture and history I can highly suggest the CZcams video "Facts about Germans never taught in School" from Thomas Sowell. Here is the link: czcams.com/video/AxKpoA23YWc/video.html. Have a nice sunday.
Thanks for the suggestion, Danilo! Kevin liked your comment about D&D 😉. He needs to play more of it with the boys now that they’re older!
@@lenaw.9405 Kevin mentioned in a reply to me in another video that he had played with the kids. I currently play in a D&D group 5th Edition and in another one 3.5 Edition (but that is put on hold at the moment). I used to play Magic the Gathering but mostly Commander (EDH) because it is less expensive. I started playing DSA when I was 10 and stopped when the 5th Edition came out. Over 90% of my tweets on Twitter are related to D&D, there's great interaction as long as it is on the topic.
@@MyMerryMessyGermanLife he really is a nerd. That face was priceless. Does he know series IT Crowds? I'm pretty sure he would love it as much as we, programming nerds working in Keenmate, love it.
Yes it continues in the Oberstufe (German high school equivalent). Even in your final exams (Abitur) EVERY question is based on a real problem. They can be unrealistic but still. For example we had a chart of the election results and hat so calculate the chances of what 5 random people voted or if they even voted and so on.
Also: I don’t know how it is in the US, but here in Germany you work with calculators from grade 8 onwards. So the questions are never just „calculate this“. And in the final exams there are small tests without calculators and the rest with them, so you still have do a little calculation in your head sometimes
I'm not sure what it's like now and it maybe different in different states, but when I was in school in Florida (1989-2002) you didn't get to use a calculator until you started Algebra. You could start Algebra at 14. It depended on how good in math you were. My brother was extremely good in math and started Algebra at 14. I didn't start until I was 15. All my math teachers said "you aren't going to carry a calculator with you everywhere you go." It's not like now where the whippersnappers have a cellphone with a calculator. When we did get to use calculators you had to write down everything you did. You couldn't say 4 when you typed in 8÷2 (I wouldn't type in something this easy. I would just do it in my head. It's just an easy example). To this day you aren't allowed to use a calculator for some state licensing exams. When I took my state licensing exam in physical therapy I wasn't allowed to use a calculator.
As I said a few times here. Every state even every city is different. There isn't a blanket rule on what you can and cannot do. The federal government leaves education up to states. It used to be the "rich" areas in a state have harder rules and school is harder than the poor areas. Now they did common core in a lot of states and instead of getting good teachers in the states at a lower level and bringing them upto the higher level they brought the states and cities with a good education down to the level of everyone else. Not all states participate in this. Florida finally dropped out of teaching common core. Unfortunately the "rich" areas are far far far better educated than the poor areas.
*Edit actually I think things have changed in Florida. I just thought of this. When I was about 25 a hurricane came and destroyed the transformers in my city. Since this happened we had no electricity. Stores were open, but you could only pay with cash. The 16 year olds didn't know how to make change when you handed them a 20 and the total was $6.30. My dad had a kid say to him "This is to much. I can't take this." This was a 🤦♀️ moment.
@@jessicaely2521 Wow that's sad, here in Germany we have standardized statewide exams since 2005 and there is a push for nationwide exams in recent years. This forces every school to teach the kids the same stuff for the final exams and if the school if constantly below average they face problems.
Our schools are also run by the districts, but the curricula and laws are handled by the state. The reason why we don't have "poor districts" with bad schools is, that rich districts have to help the poorer financially and the same goes for states. Furthermore the higher levels also helps them out financially. So a poor district will get Money from the richer districts and the state, while the state gets money from the richer states and the federal government. But I think America would write that off as Communism :)
In german (bavarian) gymnasium you may be allowed to use your calculator from 8th grade onwards but you won't really need it as you are mostly working with equations - also the part in the Abitur (maths and german are mandatory in Bavaria) where you mustn't use your calculator is relatively large
@@xyungeloest In Sweden we do have national test in Swedish, English and Math. The Math test is a two part test where the first part, making up about 2/3 of the test is without calculator where you have to write down your calculations and the second part is with a calculator. You still have to show the calculations, not just the answer.
@@leoe.5046 you mostly need it for physics in my experience
Kevin might also be interested in having a look at the questions of the "Bundeswettbewerb Mathematik". It's basically a German version of the math olympiad. The questions are demanding (you can find them online). They typically ask for proofs of some problems and are at least one or two levels above standard math classes.
But that's why the Bundeswettbewerb is quite prestigious. Managing to qualify for the advanced rounds of the Bundeswettbewerb certainly looks good on a CV. The Bundeswettbewerb also exists for other subjects such as coding, physics, languages and music, just in case your kids at some point are interested in getting (another) tough challenge. (However, sixth grade still seems to be a bit early for it.)
I had the "privilege" of "enjoying" the math course with Professor Baron, who in Austria was heavily involved with the math olympics. Everybody felt like the guy in the video: czcams.com/video/FUjKS4x8UD8/video.html And everybody pointed out in their CVs that they had "math with Baron".
I was used to Greek letters for angles when starting to study mathematics in Austria. What I was not prepared for was the utilization of the full Greek alphabet, and the use of old German handwritten letters (Kurrent) for vectors.
my math teacher in 12th and 13th grade used _Sütterlin_ (old German handwriting) letters for vectors and matrices... but then my math professors in university just wrote normal letters with an arrow above them for vectors.
Using Kurrent for vectors is outdated now, vectors are either not specially signed, or written blackboard bold, or underlined, or over-arrowed. However, Kurrent remains one of the standards for set systems in measure theory and probability (the other standard being to use calligraphic script letters), or for universes in set theory, or for models in model theory. I was able to read Frakturschrift when I was at school (my parents owned old editions of Goethe's and Schiller's works), but I had to learn Sütterlin-Kurrent within one week in order to be able to do the exercises and to follow the lectures of measure theory at university, which was a mandatory course of the third semester.
@@volldillo Re outdated: That was in 1988 and the Professor was nearing retirement.
Thank you very much for these insights.
As a teacher of a third grade let me tell you we worked with Würfelgebäude this week and kids love it. At this age even more with a plan than with imagination. To find out how many dices it takes or go around these buildings and draw it from every side is so much fun for these little professors. And it's fun for me to watch. I love this video a lot and maths a little more - thank you Kevin!
The same concept here in The Netherlands. As an example. From my school time. Johan, Mary and Peter go to xxx. Johan walks, Mary takes the train and Peter the car. The distance is ....etc. And everything by heart. Today one can use one's laptop. Progress???
Yeah it’ll be interesting as technology is already much smarter than we are…will we all get dumber or just get smarter about new things?
Another awesome video from you guys. Thanks for producing such high quality content 🙂 I love hearing your "reviews" and experiences.
This is fascinating. Thank you.
Thanks for the perspective. My godchild teaches Math in Elementry school but her university education was based on teaching university classes. And a small history fact: In Japan the engineers learned quite often German to read the textbooks (before WWII).
I just like watching your journey and find it very sympathetic how you are approaching everything and how you are doing what you are doing. Thank you very much for another very likeable and fun video :). It will not stay as it is in 4th grade concerning the "practicality" of the tasks, but yes they try to make it more experienceable instead of just telling you how to calculate an angle even in higher grades. Still, it will change after a while if it is just going to be harder to find easy real life examples.
Welcome back, good to see you healthy.
Many here say, "what do I need this for in life" when it comes to math. Good to hear things from the other side, that a lot of practical stuff is taught. By the way, I think a little statistics would have done one or the other quite well, in these strange times.
Thank you for sharing.
Just wow. Thank you for your assesement! I've also learned something.
In Grundschule math was no problem for me but in gymnasium it was one of the reasons I changed to Realschule after 7. grade. Not every geman child wants to become a engeneer. If you are not so talented in maths this system could be very hard. I always hated Textaufgaben. Even in Grundschule I never understood why I should learn stuff like this. As an adult I see the sense but as a child I didn't.
Like you said, math is like a new language. It took time for me to learn but in Gymnasium I didn't have enough time. In Realschule I had a little bit more time and I understood everything. It's not only geometry and algebra we learn in german schools. We learn logical thinking like finding a solution for a problem in your own way.
Funny story: after school I became a Erzieherin and thought I would never need maths anymore. After more than 20 years I had to change my profession for health reasons. Now I am a Fachinformatikerin and need math every day for programming. I am happy I learned logical thinking at school. You will never know what the future brings.
(in german we say "Logisches Denken". I don't know if logical thinking is the exact expression in englisch).
Welcome back !! FROHES NEUES JAHR!!! In today s Video I loved Kevins enthusiastic outburst on German school methods teaching Math ....That was great to see!!
Hi there. That was so nice to watch Kevin in his element there. He looked so excited talking about maths. Thanks for your great videos.
Happy New Year to all of you!
Hope you enjoy 2022 as much as the last year!
Thank you for all your vids. I love to watch them. Somehow they bring light in our mostly dark times.
I wish you and your family all the best for this year 🙂🙋♂️
Thank you so much. Wir wünschen auch Ihnen ein wunderbares Jahr! ❤️💕
I find this interesting, I struggled a lot with math, but was very good language wise. I took French at Realschule and during my term at Highschool in the UK, I noticed as well a gap in French. Even though being in Realschule they were doing stuff at Highschool and the pupils were struggling with it, which I had done two years ago in Germany. What I loved so, was the viarity in listening comprehension tasks and applying the language to real life situations. I once went to a language awareness meeting in French, and we had to make a movie about the city, explaining about the sights and characteristics of the city all in french. I really enjoyed that. Or I had to take a phone call and make a hotel booking all in french. I really was missing things like that in my school. Keep up the good work, always interesting to watch your perspective of things here in Germany. And as being a foreigner once myself I can relate to culture shocks and differences. But I took it always like a chance to broaden my horizons and was always curious to find out the reason, why something is done that way, or why people behave in a certain way.
Love your passion talking about teaching and engineering 👍👍👍
> Thank you very much for sharing this video!
I love how excited Kevin is for math! The kids are lucky he can help them understand. So impressive to see this level of work. Your kids are doing such excellent work, in a new language yet!
Yeah it really is amazing how you can accomplish so much in school without fully knowing German! And how fast our kids have learned the language is extraordinary. As it is with many children.
Aww, Kevin’s enthusiasm is so infectious! Hope you guys had a lovely time in the US! ☺️
Thank you! Yes we had a great time.
Thank you for sharing this video. I really enjoyed it.
The passion! Hahaha, so lovely to see! And definitely "ansteckend". 😊
Happy New Year for your family ! these tasks are called Sachaufgaben ore Textaufgaben
Thank you! Wir wünschen euch auch ein frohes neues Jahr!
I got my Abitur just 2 years ago and am now currently studying. It's very interesting to hear your perspective. Having grown up in Germany I never considered the way we were taught math to be looked upon as a special way. It definitely stays that way up in the higher levels/years of education in my opinion. What's funny is that in the higher years german students will also question why they have to learn certain topics in math. At least I used to constantly ask this as well and my classmates too.
I think the basics of math in Germany are logic and understanding the problem, the solution is important but the steps you do to get there are equally as - if not more important - in learning.
As an engineer/scientist I still think one of the most important and often neglected skills is the skill to understand the problem and then tackling it on that basis. A lot of people just jump on a problem or try to find a solution around a problem without really getting what the problem is.
I love your enthusiasm. I wish you continued joy on your journey :)
Thank you so much! ❤️
That insight into US maths teachings was interesting. Also the differences in regard to German maths classes. I knew that there are international differences e.g. in doing mathematical divisions, too. Like France or England.
we learned how functions like Fx (y) work, by calculating wich phone provider is the most profitable over wich period of time :)
didnt knew until now that this is a german thing :) great video!
Haha it's fun to see how excited Kevin is about this.
Very interesting and cool!!
Good morning from Rheinland-Pfalz. Once more a very interesting video with a new topic! Always a pleasure to see how you like (most) of what you experience here in Germany.
Hallo Peter! 👋🏼 Ich hoffe, du hast einen schönen Sonntag!
This was super interesting, thank you for this video!
I wasn’t aware all of these things were so different to the US, I went through the whole bavarian education system and am studying engineering now. It honestly still felt like I had to learn a whole new language in my first semester especially when it comes to mathematically correct proofs and such but I cannot imagine how that would have been if I wasn’t used to greek letters and the concept of counterproofs from a young age!
Yeah I wonder if you had come from the US if it would’ve been much harder! Best of luck in your studies!
Thanks for your great video, love you and your family!
❤️❤️❤️
Your video made me smile :) I never thought I would get to know someone who appreciates the Bavarian math curriculum as much as I do. I'm an engineer as well. My kids are in 5th and 7th grade and I was amazed as you are whenever I got a glimpse at their homework. It started in Grundschule when they had to interpret statistics or generate tables with all possible results to estimate the right answer like an approximation procedure.
I really enjoyed this video. My son attends a special needs school here in Germany and he also gets this type of math. It is interesting to see how much the education system is the same between his school and a regular gymnasium. If I had to guess I think he is in the real system. So far the only languages his school has taught him is German and English, but my son loves his school, much better than the American school he attended.
Wow that’s great to know the math education is similar in German special needs’ schools, also! Go Germany 🙌🏻
I remember my math teacher ending each class with Math fun. This was something for us to try beside the home work. The most impressive fun I remember was the multiplication of 1 numbers (11,111,1111,11111,...) either by itself or a smaller 1-number. It made math so much more interesting.
Love it! It’s always great when a teacher makes learning fun.
Really interesting video. I went to primary school in Scotland and secondary school in England and in both learnt Maths this way. I remember doing the building blocks in primary and using greek in secondary. I loved Maths 👍
Cool you made a shorter video with chapters! I really enjoyed that! 🙂
Good to know! Thanks for your feedback! I know our videos can get quite long 😆.
As an mechanic i use physics every day and i was so bad in school in physics. But my school time is more than 20 years ago and i think they changed the teaching methods a little bit.😁
Later at Gymnasium, this will probably not be the case anymore for most of the math stuff. I often asked myself what I'm even learning something for and where in my daily life I need that. But for calculating probabilities or geometry, they give you logical cases that you could actually use. For analysis, not so much.
Probably depends a lot on your teacher. I've been out of school for a while so a lot might have changed but I had an awesome math teacher from the 9th grade all the way up to my Abitur (and in some years he was also my physics teacher). A truly dedicated guy with a doctorate in mathematics who apparently spent a lot of his free time in the university library.
I will always remember that one day he was excited because he found an old text (of course in Latin) with a physics problem that was relevant to the math that we were currently studying. We translated it, formalized the problem (since it was written in some flowery language) and solved it in this class. And everybody could contribute something, whether they liked languages, physics or mathematics.
He always managed to tell us the story why the math we were currently studying is important.
I can remember some tasks that were inspired by physics or biology, e.g. about growth of bacteria or bank interest as examples of how to use exponential functions.
And on the other hand, analysis was pretty advanced - we talked about how to find maxima and minima of functions by using derivations (which is extremely helpful to know for scientific or technical tasks at university)
Wonderful to see how excited Kevin can get about Math!;) For me math was always quite the most disliked topic at school...but for both of my sisters ist was the same.My father, a trained and qualified engineer, was alway trying to help us as much as possible though
Welcome back, I hope, you had a wonderful holiday back with your family. As always, I enjoyed your video very much. And its absolutely cute, how Kevin gets excited. ;-) I like you guys. Great family.
Thank you so much 😍😍
It’s quite funny. Me and my partner are both engineers and we were discussing that we were missing the link to the real live for some mathematical areas. In school up to the 10th grade Textaufgaben were common, but afterwards, as well as in Uni, the application of the math was not clear anymore. Why did we needed to going through complex integral calculus? Yes it is important to know, that the integral is the area below a curve and do some calculations to understand the concept. When it is really getting complicated I start R and get the results immediately. Thanks for the video, It brings a new perspective on things that were so natural to me.
We learned to calculate the Stata output per hand and the parallel course just to interpret the results. Big difference
Ha! That homework sheet with the word problems had the old DM erased and a € sign pencilled in. 😁
Oh I didn’t even notice that! Haha it took us all a few months to stop writing $$ and write €€.
Super interessant. Vielen Dank für das Video! =)
Gerne! ❤️
Tolles Video 😀die Schulausbildung in Deutschland wird oft so schlecht gemacht,finde es schön das ihr es positiv sieht💐
5:13 you have some very interesting bills there ;)
(while the total sums are correct, the task was to figure out how to get to the sums with the actual bills - for example: 300 with four bills: 100+100+50+50)
Yeah it seems our son misunderstood the question! Language barrier…
Hi, I'm a 30 year old mother in Illinois, USA. I grew up using these unit blocks in elementary school. So has my son! He really appreciates math. Honestly I think he needs more challenge from his math classes. I do believe that America needs to reevaluate it's standards for youth education.
Yeah after seeing how far behind the USA is compared to the quality of education taught all over Europe.
Your openness and zest for new things with such a positive acceptance is so joyful to watch! Moving from Germany to the US we went kind of backwards in the education department for our kids! We are impressed with the creative subjects here in High School and the abundance of elective subjects and athletics! Our two oldest loved to be in theatre, tech and acting! Our youngest loves the sports!
What we also love is that they learn here already in Elementary to present projects and speak in front of an audience! I didn’t have to do it that much in my time in school in Germany and therefore have a problem to be confident, when I have to speak up or speak in front of an audience! Our sons though do it with such ease!
We moved to Mexico for two years and came back to Bavaria where our oldest attended Elementary! He wanted to do theatre and couldn‘t, because it was just around Christmas where they rehearsed for a play and not an ongoing Club or subject in school during the year!
That we llllllllove here!
Kids get here more encouraged to be creative and athletic than in Germany!
So, what is more important? Better academics or a better arts education? I wished there would be a good balance……but neither the US nor Germany has figured that out that for a well educated and good person in life both things are equally important!
I am still looking for that kind of school;)!
Nice to see you guys back in Bavaria. Hopefully you had a good time over there. Read you later!
Thank you! Yes we had a great time!
Welcome back Nice And inteligente famíly! 😘 Thank you for another interesting video. My grand daughters are in the 4th And 6th grades here in Portugal And I am curious to compare... The other grandmother is a math teacher in Gymnasium And my son in law is an engeneer, so I shared the video With trem And I am waiting for their coments, as They are the ones who Help the girls With their homework...
It would be interesting to see the differences in Portugal!
Would be interesting to see a similar video about foreign language teaching in Germany vs. the US.
Yes! We did talk quite a bit about that in our German Gymnasium video, actually, but it’d be great to make that a separate video.
You can't do a blanket statement like the US and foreign language. It depends where you are from in the US. If you are from someplace that has a lot of foreigners your chances of learning a foreign language at a young age is higher than someone who doesn't live in an area with a lot of foreigners. Its also more intensive in areas with a lot of foreigners. For example people who live in South Florida (Miami and Fort Lauderdale is here) have a completely different experience than someone in some small town in North Dakota. For example my cousin went to school in Massachusetts. She's 2 years younger than I. She didn't get a foreign language class until she was 16. I grew up in South Florida and my first foreign language class started when I was 7 and I continued until I was 17. I was the first class that started learning a foreign language so young. Now foreign language starts when a kid goes to Preschool in South Florida which is 4 (it's free to go to Preschool in the state of Florida). The reason behind kids learning a foreign language so early in South Florida is because there's a huge population of Spanish speaking people in South Florida. There are areas in South Florida you can't communicate with people unless you speak Spanish. My husband is screwed in parts of Miami when he isn't with me. He is Swiss with a greencard. His foreign language was French and then English. I need to say my Spanish definitely isn't perfect, but I can communicate and understand people.
You don't get into situations in Massachusetts where people only speak a foreign language.
@@jessicaely2521 Makes sense. In Germany in Kindergarten they do some songs in the language across the next border (France in my case). Without borders it defaults to English. And Schwyzerdütsch is considered German. First grade just continues with whatever you started with.
There is a problem though if you move during the first years: You may end up in an area where another language is the primary second language.
My favorite Question at School was in 4th Grade >Math
Thanks you for the detailed video. I just moved to Germany 3 months ago with two preschool kids.
We hope it’s going well for you! There are many big changes at first and we felt very overwhelmed for a long time. 😝 It’s getting easier now.
Very interesting 😍🙋♂
Happy new year! This is the traditional way the schools were separated. More or less Grundschule for manual labour and craftsmanship. There you learn things not tought in other schools. Real- or Mittelschule were for office related jobs, where you also learned typing etc., and Gymnasium prepared you for University. This also goes for foreign languages. Hauptschule English, Realschule or Mittelschule English and one other European language. In Gymnasium English, Latin or Greek and sometimes a third language. Although things have changed and continue to due so, this is the traditional reason for the different schools. Making a life decision at this early age charted your career, most times the same as your parents. One of the reasons for the changes that were made and change still continues.
Hope we can expect a follow up once physics lessons come into play 😉
Here is one example of what you can expect in 9th grade maths in Germany:
During vacation in the US Anna visits the St. Louis 'Gateway Arch'. She wants to know the buildings hight. She measures the span between the ends to be 192 m. She walks in a straight line between the endpoints. 0.5 m from each of the ends the arch is 2 m high. Calculate the highest point of the Gateway Arch.
If you want to know how a task in the final Abitur exam looks like, I recommend to take a look at the wikipedia article 'Oktaeder des Grauens' (Octahedron of Horror) which describes a task from the 2008 NRW Abitur. That is analytic geometry at a very high level!
Now this was a fun video seeing Kevin get excited over maths. And although I have not made it to engineer's level (maths at university became too hard for me 😅), I still like it and try to help my kids here. But as an addition for the future (ninth grade and on I think) I would like to recommend the YT channel MathemaTrick to you, because I think Susanne does a great job explaining and has a lot of videos for different math topics online.
And there are more good channels, I remember 'simpleclub math' when I had to help my boy. I couldn't have done without it 😉.....
Wow! Just checked that out. Thank you so much!
well. In germany a high percent of young people do not study at college when they leave the school but do so called Lehrjahre. there you learn a job where you already have to know how all those things work. You can't just start there with the basics in math as - especially if you do craft trades - you'll have to learn the things you need for this particullar job within a short time period. (mostly between 1 1/2 and 3 years)
and as no one can tell who is going to do what in his/her life they teach the basics to everyone at school. not only for math.
True!
That was really interesting, especially from Kevin's perspective who's an expert on the subject of math!
I think that the German school system in general focuses on teaching concepts instead of training kids to learn stuff by heart. I have a lot of concepts in my head, like grammar, mathematical concepts, biological and chemical processes and categories, understanding historical eras with respect to society, politics, music, literature, architecture and arts, and so on, and so on. Most of it I learned at school. And although I don't use most of it on a professional level, it does help me to understand the world.
By the way, some of the tasks from Griffin's math book you showed in the video were very different to the kind of tasks we had in school back then in the 90s. So I think that has changed a lot in Germany during the last 20-30 years, but I really like it! We did learn all those mathematical terms and concepts like natural numbers and Greek letters for angles and all that stuff, though. Fun fact: I'm studying Ancient Greek right now, and I remembered half of the letters from back at school! I remembered seeing a lot of them not only in maths class, but also in physics class. So you never know when that stuff from school might come in handy, even if you don't use it regularly in your profession!
what a cool video! :)
I went to school in the south of Germany in the Black forest. When I first heard about v = s/t in school (I was pretty young), I went to a Motocross race with a friend where we diligently timed every driver during the rounds, asked organisers for the total track length and calculated the average velocity of any driver etc. - we absolutely loved that. Presented the results at school and got huge positive feedback, something like this you'll never forget. School is all about encouraging curiosity - lovely to see you and your kids enjoy it too :)
Keep in mind that German school children have lots of free space in their brains for all that terminology because they don't have to learn how many ounces go in a gallon and how many inches go in a mile...
But we have to (in my case had to, or even were offered to) learn more foreign languages than the average US student.
well Textaufgaben oder word problems were also the stuff i liked least in Math class. I was good at math in general though. Interesting to hear how math is teached in the US though.
Sadly i remember very little of my math knowledge now and i had it as one of my focus courses (Leistungskurse) for the Abitur. I had the worst grade in math ever in my final written exam with a 5+. Saved it with the oral exam (a 2+) that was only done when the grade before final exam and the great of the final written exam were too different. That was in NRW in the year 2000 and that time the Abitur consisted of 4 classes, were you had to take an exam. 2 focus courses (Math and History for me) one basic course (German for me) and finally one course with only an oral exam (Philosophy for me).
The real world based examples are in highschool too. In our school (that's not common in other schools ) we went to an old castle in the woods for 3 weeks and our math teachers gave us theodolites and explained us how they work and we made a map of the area using trigonometry.
Sara and Kevin: Thanks for the video on German education, always an interesting subject for Americans.