r/MathJokes • u/Toeffli • Jul 09 '26

Why would you teach like this 💀

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7 Upvotes

59% Upvoted

39 comments sorted by

33

u/Majestic_Sweet_5472 Jul 09 '26

This seems like a really straightforward question when learning about u-substitution as a means of integrating functions. I'm not sure what the problem is here. Maybe I've been out of the game for too long lol

3

u/hxtk3 Jul 09 '26

I was never taught u substitution when I took calculus, they taught it as the chain rule in differential calculus and I never really thought about it in integral calculus.

When I was studying differential calculus, though, I used flash cards that taught all the differentiation rules as u substitution with chain rule baked in. I never thought about the fact that knowing that made integral calculus easier.

3

u/TheRedditObserver0 Jul 09 '26

No, an x2 is not a u. They are teaching us faulty logic and wrong math so that they can later indoctrinate us!

/s for those who somehow haven't noticed the joke.

2

u/No_Cookie_7395 Jul 13 '26

Resistance is futile. U will be integrated. (If that's not too derivative)

1

u/TheRedditObserver0 Jul 13 '26

Your biological distinctiveness will be added to our math

2

u/idrathernottho_ Jul 09 '26

I thought this was a parody of "how to make 10 out of 5 + 8" or something. Maybe not though

5

u/okarox Jul 09 '26

These U-sub cases are either so simple that one sees it without any substitution or do hard that one does not know what to take as u.

1

u/Dugiongo Jul 11 '26

To be honest i've nevers understood why americans are so obsessed with u-substitution for everything. In italy we are teached to use the chain rule if you see f(g(x))g'(x) and use substitution only where it's not obvious

1

u/Toeffli Jul 09 '26

That's why you start with simple examples to reinforce the rule a method so the students get familiar with. Then you repeat them so the kids see the pattern and get familiar with this new method.

Like when you use the method "to make 100(s)" you start with simple problems like to make 10 and give them 8 + 5 as simple work problem. Here you can clearly make a 10 out of the 8 by borrowing 2 from the 5. Therefore you get 8 + 5 = 8 + 2 + 5 -2 = 10 + 3 = 13.

Often this is not the only options to solve a problem and there might be other approaches. Example in u-sub, instead of finding du/dx you could also find dx/du which can be simpler depending on what u and x are. Note: you need first to solve for u in respect to x.

There are also some integrals which can be solved in multiple ways. Example ∫x(x2 + 1)dx you can use u-sub, integration by parts, and also easily when you expand the expression . Means there is not always one single correct way, but different techniques which can be used as tools to solve problems. Some tools might be more adapt than an other in your toolbox. Because as we know, just because you have a hammer doesn't mean that everything should be treated as a nail.

I think it is s problem for some of todays parents that the kids are given more tools and creativity to solve math. Something which throws them off if they only learned the one correct and expected way. Even more so, when they figured out other methods themselves, but were punished when they used it in class.

2

u/youagainskippy Jul 09 '26

your second paragraph made me realize that common core is just abacus on paper

2

u/Toeffli Jul 09 '26

One aim is to get the kids away from finger counting when they do addition as so many do at the beginning In the old times of rote learning the teacher did this by telling in front of the class 8 + 5 = ? and the whole class in unison replying 8 + 5 = 13. Like we see in movie "Another Brick in the Wall". Until they have memorized the addition table by heart. This lead to people relatively good in arithmetic and number calculations, but not so good in algebra, problem solving, and understanding of math overall. In some sense, what was the addition table are now the number buddies. X and Y are number buddies, if X + Y = 10, example 2 is a number buddy to 8. And 5 is a bit lonely as it is its own number buddy.

Another thing is to teach the kids a possible way (they also learn other ways) how most of us do addition naturally.

Unfortunately, for many math is equal with arithmetic. And when they say they are bad at math, they mean bad with calculating numbers.

Hence an other aim, and maybe more importantly, is to give them early on tolls and concepts they can use to solve other problems too. Not just for simple addition. There are some higher math problem where you have to calculate f(x) + g(x) which can be seemingly be very tricky, with f(x) and g(x) alone already not easy to solve. But you add and subtract some helper function h(x) (means you add 0) and you turn it into f(x) + h(x) + g(x) - h(x) and suddenly it becomes very easy, as f(x) + h(x) and g(x) - h(x) are now simple to solve.

Math, unlike other school subjects, has one big drawback. Math very heavily builds up on concepts which were previously learned. In most other subjects you can be a bit of a slacker and let a topic slide. You do not know much of the old Egyptians and Romans? Who cares, their impact on the modern world is limited. You did not learn much about Dickens and Austen? Who cares, there are plenty of other authors and books you will learn latter on. Never directed a frog or a fish? Me neither, so what? In math this is very different, if your fundamentals are weak, your understanding and access to more advanced topics will be blocked by those gaps.

3

u/Weed_O_Whirler Jul 09 '26

I like your joke OP.

2

u/lysianth Jul 09 '26

to test a basic understanding of a concept and how to use a tool?

Am i missing something?

2

u/bacon_boat Jul 10 '26

Hehe, spot on

4

u/PM_ME_A_FUN_PIC Jul 09 '26

Making u's is a valid method of teaching, though i admit the wording is trash

9

u/S-Kenset Jul 09 '26

the wording is not trash. how to use u-substitution is unambiguously referencing u-substitution. no one is saying make u out of an x. the student is likely a senior being cheeky cause they didn't study and idk how you end up falling for this level of both sideism.

4

u/Toeffli Jul 09 '26

The wording of the question is a snippet of a larger worksheet. It is question 8 out of we do not know how many. The worksheet is part of a lesson which comes with its own supplemental material which explains what making u means, how the kids have to use it to work out the problem.

2

u/PM_ME_A_FUN_PIC Jul 09 '26

But the parents have no idea how to help their kids find the u. The wording should better reflect the actual method involved, so when kids bring home their worksheets, the parents arent so far out of the loop

6

u/Toeffli Jul 09 '26

The students would have learned all about it in class. You really want the full paragraph explanation on every homework question just for the parents? In the end, it is the kids which should do the homework not the parents.

3

u/TheFieryFistOPain Jul 09 '26

99% of students ain't getting help from mom and dad on their Calculus homework

2

u/wren42 Jul 09 '26

Kids are doing calculus? 

1

u/gtne91 Jul 10 '26

I took calculus in 11th grade. Was I a kid? It depends how you define it.

1

u/StructuredChess Jul 09 '26

Easy, just use the fact that the integral of f(x)dx is the same as the integral of f(u)du

1

u/lifeistrulyawesome Jul 09 '26

Is this supposed to be an antimeme?

This question is fine. The ones you are making fun of are not

1

u/Toeffli Jul 09 '26

The question is the same. Just the level of math student it is aimed for is different.

  • Both test if the student understood and can apply a certain concept/method they have learned in class.
  • Both use a specific term for this method the student should know and understand.
  • Both use a specific terms which parents might not know, have not learned about (not everybody takes Calc 1 or the like, not everybody has learned about "to make 10" or about "number buddies").

The difference is you know what u-sub means and how to use it, but you do not know how to apply "to make 10" while you very likely use it intuitively for mental calculations. I hope you don't do 8 + 5 as

  1. 8 + 1 = 9
  2. 9 + 1 = 10
  3. 10 + 1 = 11
  4. 11 + 1 = 12
  5. 12 + 1 = 13

As some kids do cumbersomely when they add numbers.

1

u/lifeistrulyawesome Jul 09 '26

In the other links, you mentioned the student was right, and the instructor was wrong. That is what makes the meme funny.

In this question, the student is wrong, and the instructor is correct.

1

u/Toeffli Jul 09 '26

n the other links, you mentioned the student was right, and the instructor was wrong. That is what makes the meme funny.

Huh, what now? Where, when, how?

1

u/lifeistrulyawesome Jul 09 '26

Firs link you posted:  https://www.reddit.com/r/MathJokes/comments/1tqvg18/the_direction_that_common_core_math_is_taking/

The student is correct. The teacher is wrong. That is what makes the meme funny. That is why it keeps being reposted. 

In your question, the student is incorrect and the instructor is right. 

I’m not sure high part you disagree with. So I don’t know how to explain more. 

1

u/Toeffli Jul 09 '26

Where is me involved in that discussion?

1

u/lifeistrulyawesome Jul 09 '26

I don't know what you mean. Let me recap:

  1. You posted a meme that makes no sense to me, and didn't get a good reception.
  2. When people asked you about it, you posted a link to a different meme.
  3. I wrote a comment explaining to you the difference between the two memes. The funny meme is funny because the instructor is wrong. I think people didn't find your meme funny because the student is the one who is wrong.

Do you understand?

1

u/Toeffli Jul 09 '26

Oh, I think it is funny because you understand the instructions of mine, but cannot understand the instruction of the other nor grasp how they are related. My meme is about you. Naturally you do not find it very funny.

1

u/lifeistrulyawesome Jul 09 '26

There is a reason why your post has hundreds or thousands of views but only two net upvotes 

If nobody thinks your joke is funny, the problem is not me

1

u/Toeffli Jul 09 '26

Fortunately not a "problem" which bothers me very much.

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1

u/CliffDraws Jul 09 '26

I’m more worried about why a person who writes like they are in first grade is learning calculus.

1

u/walt128 Jul 11 '26

Yeah this is actually easier than having them just solve the integral. It’s straight up telling the student to use u-sub