*_Hope you enjoyed and let me know down there in the comments what you think about the exam! :)_* Also, if you appreciate me making this series, please make sure to support the cause over on my Patreon! www.patreon.com/mathable

Imagine finding out you failed from your Professor's KZfaq channel

I have read through the exam from the perspective of a student and have a few points I would like to criticize: 1) Part 1 task 1.4: The German version has a typo. Point d has the wrong sign. 2) Part 1 task 2: The text explaining the task is clear in itself. However, I think it could still be more idiot-proof and highlight a bit more that the students were supposed say which graphs do NOT match the given function description. It's normal to be nervous as a student during an exam and not read every assignment slowly and carefully. I can see that a student's first instinct after reading the function description is to directly search for the corresponding graph. I think a teacher should try to keep this in mind and formulate the assignments with some psychological reflection and benevolence. 3) Part 2 Task 1: The graph shown does not pass exactly through the point W(4|18). This makes it impossible for the students to draw exactly. I also think that the chosen scaling of the y-axis makes it unnecessarily inconvenient to draw the tangent (4 units correspond to 1.6 boxes on the y-axis). Also, you keep emphasizing how easy most of the tasks are. I think you should be careful with such statements in front of students, as they can be intimidating. Apart from all that, I like the exam. I think it checks for actual understanding of the topic and does not just ask you to do the same calculations a couple of times.

The file name is "test on derivatives" mashed into one word. When I first downloaded it, my tired arse somehow read "Tensor Derivatives" and my reaction was "yeah, I know why they all failed, that shit is boardeline incomprehensible sometimes " 😂😂

This has happened to me before. It's a humbling learning experience. Really forces you to analyze 1) where your students are at and 2) possible holes in your teaching methods.

In my experience working with students while I was a graduate student, it can't be overstated just how important the notation used is. It can mean the difference between students understanding something or not. Students can understand that a^2 + b^2 = c^2, but then if you start writing (alpha)^2 + (beta)^2 = (gamma)^2, suddenly they don't understand anymore. It's very easy to confuse students by being too formal. I've noticed it time and time again that, when I took something and made it less formal, the students almost always immediately knew what to do. Students early on are struggling to learn three things simultaneously: there's learning the mathematical formality and notation which is completely new and foreign, there's learning the actual mathematical concepts involved which are equally foreign, and then there's learning to problem solve which is also generally foreign. So, using Exercise 1.2 as an example, a student looking at that question might be simultaneously struggling to understand or remember what the big D_f symbol means, struggling to understand or remember what it means for a function f to have a zero, and also struggling with how to go about quickly solving mathematics problems. If one or more of those is too difficult, they'll struggle to finish. Based on the simplicity of the problems and concepts, the only thing I can think of where they'd be struggling is the formality and notation. Even I don't understand what "The intersection of G_f with the y-axis has coordinates I(0 | 3)" is supposed to mean. Hell, when I was in high school, I remember having the hardest time simply remembering the difference between "domain", "co-domain" and "range." That's my 69 cents, at least.

New fresh toadwalker video just dropped: 85% of german children cant solve this math exam!

If I gave an exam that 85% failed, then I was the one who failed them. However, I would consider both sides of this. Were the students really prepared, and did my teaching methods work? I had a situation where most of my students did poorly on a HW assignment, so I went back and changed my approach slightly - worked like a champ as they did better.

seems simple

I think for most of the time in school the students only worked with kochrezepte, where little understanding is needed. They are simply not trained in understanding things. And on the other side, there is often a lack of mechanical skills (like with fractures and rearrangeing equations).

I'm in my final year of PhD. I wish I dropped out of middle school and became a trashman.

I think the biggest issue with the exam is the formal wording of everything. Obviously, that's to be expected with math courses and should be taught well, but sometimes people can be confused on what the question is asking or focus too much on something said just for math completeness that doesn't have much bearing on the problem, even if they do know how to do it.

This is actually so easy and its multiple my calc teacher said and I quote “if it’s multiple choice it’s not a real test”

The exam can be easy for a lot of people here but if the avg is 2 out 15 and 85% failed it means the course did not prepare them for that test. I can see 30% not being attentive or making mistakes so they fail but this indicated either to few exercising and homework or lack of check of the homework for motivation or lacking quality of the lessons (to few hours for the lessons can also be a thing, in DE we have G and E courses so the exam should be made according to the course) More homework and more examples and a test with similar exercises to the homework sheets is what they need most students only do their homework not other thinks from the internet, you can't ask them something they did not see in class. But maybe they are just all lazy af idk Edit: not hating, actually love ur vids especially the hit or smash

Gerne mehr Videos über deine Klausuren ^^ Man sieht, dass du dir Mühe bei der Gestaltung deiner Aufgaben gibst. Gerade Aufgaben wie die Polynomrekonstruktion aus einem deiner letzten Videos finde ich gut, weil sie das Verständnis des Themas, in diesem Fall Differentialrechnung, auf eine doch eher spielerische und weniger schablonenhafte Art und Weise prüfen.

29:54 “I am a math fuckboi” lmfao xd A great video as always, appreciate your efforts!

Great video. Interesting that so many failed this exam! Also, looks like something is going on with the lighting continually changing - imo it would be a little better if it were just constant. Really enjoyed the video though, keep up the good work

Hallo Jens, bevor ich mir das Video nun gerade ansehe, habe ich vorhin deine Klausur heruntergeladen und durchgerechnet. Ohne Taschenrechner, Geogebra etc. habe ich für den hilfsmittelfreien Teil rund 11min und für die gesamte Klausur ziemlich exakt 45min gebraucht. Zugegeben studiere ich auch schon im 3. Semester Mechatronik an der Uni, bin daher natürlich mit Funktionen geübt und ich bekomme keinen Schrecken mehr bei sowas :) Insgesamt würde ich sagen, die Menge der Klausurthemen sind definitiv angebracht (auch darauf bezogen, an was ich mich noch von der Schule erinnere). Was die Zeit angeht, könnte ich mir vorstellen, dass es etwas zu sportlich war, gerade deshalb, weil die Klausur viel transferlastig war und ich mir vorstellen kann, dass Schüler, die noch nicht so viel Erfahrung mit Analysis haben, länger zum Nachdenken brauchen. Ich möchte hervorheben, dass ich das Konzept der Klausur aber super fand und mir die Klausur insgesamt (inwiefern es möglich ist😂) Spaß gemacht hat. Man merkt, dass es hier nicht um reines Rechnen ging, sondern darum, ob man (in dem Fall) Differentialrechnung verstanden hat. Liebe Grüße, Dennis aus Darmstadt :) PS: Ja, ich schäme mich ein wenig, dass mir der Fehler in 1.4 nicht aufgefallen ist, aber ayo, passiert denke ich mal😅.

Your students are lucky you teach them these concepts properly. The difficulty gap between highschool and university in my country is bad

My experience as a high school math teacher in California is similar. A few students - the ones who made an effort - do fine. The rest fail, shrug their shoulders, blame you for not making things easy (when in fact the assessment was painfully easy), complain that math gives them anxiety, and demand to know what you'll do to get them the superlative grade to which they feel entitled.

In the German Version in excercise 1.4 in the fourth option you mixed up the inequality sign (assuming the version shown at 10:55 is correct). Since then option 4 and 5 would be correct, contradicting the statement that exactly one option is correct at the beginning of the exam

that was a *brilliant* sponsor plug. bravo, shaking and crying rn

I don't know why but I felt you are the best maths teacher. I mean other maths teacher just copy paste questions from one standard book to another but you are putting efforts for your students. It's Great sir.

Such an Ehrenmann that he gave the exam for free out to every teacher.

I'm going to be completely honest here. I'm a final year physics student, so I have taken a couple of math and calculus classes, so I do understand that this exam is easy. But I'm still pretty sure that if I was one of those students, I would've failed as well. There's a couple of tricks you need to know in there to do these tasks quickly. And with the exam being pretty long, you don't have any time to ponder incase you don't know these tricks. From the fail rate I think it's pretty safe to say that they lacked the practice for this exam, since the only way to learn how to solve these problems quickly is by practice. Then again, I don't know what the lessons are like, so I have no authority to speak on this at all. Just my two cents

Don't let it get you down. You are great at math and I have learned a lot from you. Your students will eventually do the same.

h(x) = 3x^2(2-x)^3 + 6.9. Nice

Die einzige Matheklausur, die ich zur Schulzeiten verhauen habe, war über sinus und cosinus Funktionen mit parametern... war ein Albtraum, aber leider merkt man erst später das es doch eigentlich machbar ist

Thx for the video papa flammy, although I don't actually study based on your country's school curriculum, but It was interesting to try the exam for myself since im also a grade 12 student. this exam is actually not that hard, it just that ur students hasn't grasp the core concept of calculus yet, so don't feel so disappointed about it, in my country they don't even teach you the concept of calculus unless you learn it on ur own like i do, here we only do exercises with little to no comprehension of concept whatsoever. so which is why i appreciate that you actually teach the concepts to your student but i they need to work harder to understand it becuz most the test's material utilizes conceptual understanding . i understand the struggle you are facing but its okay, they'll learn if they work harder!

Flammable maths, can you make a video about what is typically seen in each year of high school math in Germany? That would be interesting for non Germans. I imagine the government tells you which subjects you must teach every year.

I'm not sure why they failed the first part, maybe time pressure? But for part two, the first question is a little tricky, and the second question is quite formal so it can be difficult to parse. I think you could just remove the subscript k and just say that k is another variable. And then for the later parts you can say consider the function with k = 2

love your videos and channel

The test seems pretty fair. For Freshmans with like 1 week of studying Calculus this must be hard.

Very nice test. Sadly my maths test tomorrow is about exponential functions, so it didn't help that much. I'm confident I would've passed your test, though with a few mistakes due to loosing focus. Also: thank you for not letting your students graph something, I hate these tasks, always did and always will.

Das gibt mir ja große Hoffnungen für mein Mathe GK Abitur demnächst. Sah jetzt wirklich nicht so schwer aus

At what rate does the thing in the background move? :O Thanks for the video.

I really liked this exam! When I was in 12th grade, they introduced that "Hilfsmittelfreier Teil" and I thought it was pretty intimidating. I kinda feel in the tests I had there were way more of those stupid calculation exercises. Your test can pretty much be done without any aids except pen and paper but Ig it can be hard for some ppl. whatever, don't get too demotivated by it. I'd love to have you as a teacher 😂

This is the "I just do exercises" syndrome being portrayed. When students are shown an almost entirely theoretical test, fail as f*.

19:30 This might sound a little pedantic, but I think it's important to those who are learning: you don't have 3 changes in curvature. You have 2 changes in curvature, and those are precisely the inflection points.

22:23 Part 2 Ex 1d I'm not following the answer given here. Why is the minimum the inflection point at (4, -4), when clearly the derivative function continues downwards towards -infinity?

i read the title and thought good luck at the parent conference day (elternsprechtag) papa flammy

There is a typo in the German version, making 2 of the given answers to 1.4 true.

do any questions contain possibility for partial credit? 15 points seems low/binary for a test of this magnitude. Not sure if it's a cultural thing but my math classes in the states always gave out tons of partial points for half-ass understanding where a clear effort was put into at least trying to answer correctly. obviously this doesn't address the core issue of the lack of understanding of the fundamentals but I was just curious.

I dislike the wording at 22:24 You should say the derivative has a LOCAL minimum, because it does NOT have an ABSOLUTE minimum if f(x) is a 4th degree polynomial that matches the graph. Edit: Your notation for points on the graph was different from what I have personally seen in US schools, examples being W(4|18) and (4|16k). In the US, I've always seen points written with a comma instead of a pipe symbol. Perhaps that is because in some other countries a comma is used for a decimal point instead of the period we use here?

Being a 12th grader myself, I tried the exercises before watching the video. I had no problem in doing the exercises except the first question in part 2, everything else was easy only took about 20ish minutes

I am a biology undergrad second year university student from Turkiye and here's my take on your situation: 1.Is 12th grade important for your country? Here, 12th grade is the year in which at the end we have our university exams, so for us 12th grade is very important. Usually, students flounder around in 10th-11th grade but study really hard on the 12th. This may be a factor for the lacking grades. 2. Is derivation a novel concept for them? Do the students learn derivation before 12th grade or were they just taught it? If they learned it beforehand and didn't learn it right, they may have coasted off of previous faulty knowledge for a while and gotten this result. 3. Is their teacher bad at explaining novel concepts to the uninitiated? If he is, he should consider thinking about math from the perspective of a layman who doesn't care much about math and only how it can be used. 4. Are the students under great stress from other lessons? If they are, they may have studied for those and disregarded the class with a less authoritative and strict teacher. (If this is the case of course) 5. Is this exam of consequence? If the exam wasn't very critical, the students may not have cared. 6. Are the students mentally challanged? I am serious. They had calculators and notes. In my country either of those is considered cheating in all but the most westernized private schools. If they potentially do have undiagnosed mental problems, the parents could be told about it. This is not likely at all, however; any student worth their salt knows how to sprinkle in a note or two in between formulas to know what to use and where to use them. If they failed to at least cheat with that arrangement I would consider them failures. Unless they are all very moral students, that is. These are all the points I wanted to make. If you read it and it manages to make a point that is useful to this situation I will be happy. Hope this can at least give a couple ideas on where one could go from a more student-y perspective. (^^)

How long have you been teaching for? Have you seen a failure rate that bad before for a test you made?

My guess is that a lot of people wasted time on part 2 exercise 1 and rushed/gave up on the rest

What if for the derivative of the volume of the sphere they put down V(r)' = A(r)

I'm judging you for giving them a multiple choice exam.

P2, Q1d strictly speaking is incorrect. The f' define in your solution is local minimum, but clearly not a global minimum. The latter would depend on the domain of f' as its unclear if G_f is implicitly defining the domain. HTH.

What is the passing score on the exam? I got most of them right just by doing them in my head (the others I didn't do because it is 03:42 in the morning here.) By "most" I mean about 85%.

Without knowing your class (but guessing this is first year of high school), I am gonna guess they lack the mathematical maturity to recognize expressions where constants are represented by symbols. If students have not worked explicity with this idea, it will fuck them up. I think they might experience the formulations as vague, and I sympathize to a certain degree, cause it almost seems that the focus of this test was to see who could understand that a constant is a constant, even if represented by the letter k

This exam is pretty ez. The only issue I can see happening is overcomplicating things somehow in part 1 and runing out of time

Hello Jens. I just wanted to let you know that there is a typo. In the german version, the fourth statement of 1.4 is different than in the english version. This makes the german problem have two correct solutions. I hope you see this!

one question i wanna ask: is it correct to say "the graph is increasing"? i'd rather say the value of the function is increasing, but the graph itself cannot do so since it's not some value. lmk if i'm making shit up, i don't study maths in english apart from watching some yt

On 1d, why isn't f' getting more negative as x increases, and hense there is no minimum?

Die Klausur ist definitv angemessen für ein K1 Basiskurs. Die Frage ist dann eher weshalb die Schüker so schlecht abgeschnitten haben... liegt es an der Klasse an sich, daran, dass die meisten zu wenig gelernt haben oder, dass der Unterrichtsstoff zu sehr von der Klausur abweicht. Vieleicht gab es aber auch im Unttericht zu wenige Fragen im Anforderungs Bereich3? Naja, dass du aber wahrscheinlich schon mit deiner Klasse durchgegeangen :)

Kannst du vielleicht eine Reaction oder Kommentierung von Prof Berhard Klötz machen? Falls du ihn nicht kennst, das ist ein Matheprof aus Paderborn der vor paar Monaten ein Video gemacht hat, wo er sich über Mathe an der Schule beschwert hat - das wir alle nix können und dumm sind. Wäre interessant dein input dazu zu kriegen, gern auch auf Englisch.

I love you papa, but definitely I think it's a you problem unless you work at the european equivalent of the chicago public school system(CPS) but also I think the solution to this is to give opportunity for test corrections. Make them do a page of deep problem solving for each question they got wrong and want to resubmit as a homework. Meaning the original question plus some stuff. If students do well on homework but not on exams. And the homework does reflect exams then I think it's an issue of time length/stress of exam or that they cheated on the homework. If they cheated on homework then fail them all and actively seek for it. But if you can objectively see that they do well in non timed contexts and not in times contexts then eliminate the difference. As well in the take home test corrections/extra questions sneak in some extra credit questions that require long written explanation that can't be easily found online. You will know right away if the students took the time to deeply understand/review their materials and thoughtfully explain or if they cobbled a few insights together off stack exchange

You should have used more latex.

When I was tutoring awhile back I noticed that Calc 1 students struggle the most in undergrad math. I think its because you chronically overthink problems and also don’t have a great ability to generalize problem steps yet. For example knowing how to solve x, 5x, but not cx

Wait wait... On the first graph of the 80min part you said in b) they cant use the saddle point as an argument, but in c) they suddenly have to use the saddle point? Yea I get it, you used the curves of the graph for b) and that basically implies a saddle point, but I font understand why they cant use that for b) then

I am a visiting instructor at a small liberal arts college. Your exam had a good mix of computations, theory, and visual exercises. The reality is that calculus is hard for high schoolers. But the response from the students should be to study harder, ask you for help on homework, and focus on doing their problems at a resonable pace. Dont beat yourself up too much. Dont lower your standards, either. Motivate your students to push themselves higher.

Isn't dividing by zero undefined? At 7:58 you mentioned that it goes to infinity.

multiplication isn't always commutative !! How is that ?can show that by example?

Honestly, I think most of the exam was really just basic algebra, with a little bit of calculus. The only hard part in my opinion was Part 2 Exersize 1 with the settle points and the proving the minimum. I would have expected 85% of the students to pass not fail. Its really sad. By the way, is the exam a midterm or just a weekly exam

So simple pahh! I laughed wickedly at that

Imagine having a KZfaqr as a professor and they’re just like, “Well, maybe you would’ve done better if you check out our class’s sponsor brilliant”. 10/10 would take Professor again

If these were university math questions then I probably wouldn't have any problem (only after I did my Engineering PhD though). In High school, the questions were always straight to the point about what I need to actually solve. No undetstanding of Math terminology like inflection point is required to formulate the problem. The tricky part was never in understanding the question but solving the problems requires combining multiple tricks and rules.

what level is this exam at? highschool?

Mathematics in lecture: find the derivative of the term Mathematics on homework: use fundamental theorem of calculus to find the area under the function Mathematics on test: from first principles, rederive the fundamental theorems of calculus

Oh I didn’t know papa was teaching my class!

I had Math LK during the Oberstufe and just looked over the exam and welp I don't think that was particularly hard. Definitely easier than the Analysis part of my Abitur exam 😅

I love your channel!

Which grade do you teach??

What grade are your students in?

T_T idk the exam seems so ez to me , didnt even need any support materials

I'm doing math too and I wish the exams were this easy

Hi Jens🤚 is there an email address where I can reach out to you? Thanks

Which exercises did most students get wrong? How many did they have to get wrong to fail?

damn. i wish this was my first calc 1 exam

This is the "Covid education lag", not your fault... once students are behind its hard to catch up. Covid came when i had 2 years left of my B.Eng in Mechanical. Some professors were unaffected in the online switch, but many were and saw a drop in grades.

I would like more collabs with andrew dotson if at all possible

That amount of failures is typically a problem with the teaching not the students

I imagine these kids are just coming out of trig or precalc. I wonder how much time they had to study for the exam. either way. I do think those 2 or three kids saw how nice of a teacher you are.. and maybe wanted some touchy touchy kissy kissy. just a little bit. because their personality is tangent to yours XD. nice video :)

Why do you all take multiple-choice tests in US?

Ich hab die Klausur mal verbessert, so wie ich mir eine Klausur an der Schule vorstellen würde. Kann man dir das irgendwie zukommen lassen? Ich finde die Aufgaben sind zwar alle an sich leicht aber du stellst sie so, wie sie an der Uni gestellt werden würden, und das macht es denke ich für Schüler unfassbar schwer überhaupt die Aufgabe zu greifen. Ich hab auf dem Verbesserungsvorschlag alles durchgestrichen, was ich in einer Schulmatheklausur für unnötig halte. An sich nicht schlecht, wenn man Mathematik von anfang an richtg beibringt, auch mit den Richtigen begriffen, aber dann muss man sich nicht wundern, wenn 90% der Leute dann nicht mehr durchblicken

I never understood ur shirt until today;)

Bro how are they failing this. If I got this test I'd be ecstatic

Please make a video about trigonometry 😢😢

that wasn't a hard exam what grade was this paper for? that looked so fun

When giving explanations for answers, you should avoid using the word "obviously" so much. The students are typically not going to have as much experience as you and its probably not obvious to them. Its really easy to forget that from a teachers pov, and irritating from a students pov.

I cannot find the background of the students from the video, maybe I missed. I assume they are non-Math major college students who required a basic Calculus course for their Major requirement. In that case, I do not think there are any major problem in the exam. Of course, a review for a more effective teaching is a good practice. However, for non-Math major students, they maynot put a reasonable time and effort to pass the exam as they are afraid of Maths.

Hi, ich glaube das Problem für die meisten Schüler ist, dass sie die grundsätzlichen „Vokabeln“ der Mathematik nicht verstanden haben. Wenn man Mathe als Sprache sieht, muss man erstmal Satzbau und wichtige Vokabeln können, um größere Probleme lösen zu können. Ich denke, die Rechenwege an sich sind einfach und einleuchtend, aber die meisten wussten nicht, was sie überhaupt machen müssen. Dafür könntest du etwas Zeit investieren und ihnen die dahinterliegende Sprache besser erklären, sowie ihnen tatsächlich Vokabeln aufgeben. Bsp: Ableitung = Steigung des Graphen = Tangente, Minimum /Maximum = Steigung =0 etc. Sodass sie zum Beispiel in der ersten Aufgabe sobald sie das Wort Steigung lesen sofort wissen: AHA Ableitung bilden, Ableitung muss 12 sein! Und vielleicht kannst du nicht einmal davon ausgehen, dass sie „sei f Element R“ einfach hinnehmen , sondern musst erstmal Abbildungen/ Funktionen und ihre Definitions und Wertebereiche sehr eingängig und bildlich erklären. Ich glaube, viele sind an dem Punkt schon raus. Ganz liebe Grüße ❤

6 years ago I would probably be in the 85% that failed this test, it's kind of demotivating for a teacher to be on youtube and repeatedly say how these questions are so easy with a condescending tone. If they're easy, why did the students fail? Did they not study, are they just stupid, or are they in the wrong class in the first place, and should be in a less advanced class? If everything is meant to be easy and they're meant to pass easily, what do you bring to the table to these kids as a teacher. You're pretty much killing hope and telling some of the students they are too stupid to do math instead of encouraging them. I almost gave up on math because of toxic teachers but luckily I found one that was incredibly patient with me and now I'm gonna have a Masters next year all because of them.

holy damn, i thought our 4.[something] NP test was bad 💀

It is piss easy. Suggests issues with class engagement.

Your students' failure is your failure. Edit: I don't mean to blame or ridicule Papa Flamming. I just mean that if 85% of your students don't understand the concepts, then you, as their teacher, need to find some way to reach them.

The exam looks very easy but I admit I would’ve gotten some wrong by doing silly mistakes or not reading the instructions carefully lmao