Is There Life after Flunking out of College?

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  • #26
Math_QED
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I just want to write an anecdote about Karl F. Gauss. One day he came from school and he was probably a kid of 9 or 10 years, hanaded a letter to his mother and said
“Mother, my teacher has given me this letter and told me to hand over it to you without reading it”.
His mother opened the letter and read it (in her mind, not loud out), after reading it she remain quiet for few minutes. Gauss asked her many times about what was written in the letter, finally she replied
“Your teacher has written that you have far more ability than what the school can offer and develop, so your teacher suggested you to leave the school and work on your own great mind, develop it by your own as no one is able enough to teach you my child”
After that, Gauss became an autodidact and did many charismatic works in Matheamtics. After many years when his mother died, he was just looking for her things, suddenly in her old box he found that same letter and read it, something like this was written in it
“We are sorry Mrs. Gauss but your son Karl F. Gauss is a very stupid kid and we cannot keep him in our school anymore.”
Gauss murmured “It’s my mother who has made me what I am, It’s only because of my mother that I have reached here in my life”.
Source of this "anecdote"? Wikipedia says the following:

"His mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension (which occurs 39 days after Easter). "

So reading a letter and being illiterate don't go well together. I hope you are not making things up.
 
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  • #27
etotheipi
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I was under the impression Gauss was some sort of mathematical wunderkind. Isn't he the subject of the famous anecdote about a primary school teacher asking the students to add 1+2+...+100 and him using the shortcut? Mind you this could be made up too :wink:
 
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  • #28
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I was under the impression Gauss was some sort of mathematical wunderkind. Isn't he the subject of the famous anecdote about a primary school teacher asking the students to add 1+2+...+100 and him using the shortcut? Mind you this could be made up too :wink:
This I believe is true. The wikipedia article gives 3 sources https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss#cite_note-:0-10
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss#cite_note-:0-11
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss#cite_note-:0-12
 
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  • #29
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On this, I'm with @jack action and strongly disagree with you
If you take a young child and give them enough encouragement and effective teaching methods and enough resources, far more people will be able to develop their mathematical skills.
@jack action's analogy was between the ability of humans to do mathematics vs. the ability of squirrels to make a living. A much better comparison, in my view, would be the ability of humans to do mathematics vs. their ability to play basketball at a professional level or to perform music in an orchestra. I don't think anyone would disagree that not everyone can become a member of a professional sports team or to play music at a professional level, but somehow, anyone can do mathematics at the level required by, say, electronics engineering, without any special abilities, given lots of encouragement. I don't buy this at all.

Of course, many students would be able to do mathematics at a higher level than they have attained, if they had had more encouragement or less discouragement along the way. I've run into countless older students who told me about one teacher in junior high or high school who so disparaged their work that they did not go further in mathematics courses. I'm not arguing that point at all. What I am saying is that most people have some innate limitation on their ability to think abstractly enough to be able to succeed at a level somewhere above arithmetic, just like they have a limitation on their physical and mental abilities to compete in professional sports.
I think you should carefully reflect on what you're saying above, because it frankly comes across like you have no empathy or compassion toward your fellow human beings.
What you quoted from me was taken completely out of context, as @Math_QED points out below.
I think you misinterpreted what @Mark44 was trying to say. I do not interpret his sentence this way. His response is a perfectly accurate one to the claim that was made earlier about the squirrels.
Exactly.
 
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So reading a letter and being illiterate don't go well together. I hope you are not making things up.
I will give you the source as soon as I will find it. Do you think I will think, analyse and become a story-writer only for this thread?
 
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  • #31
Drakkith
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As a tutor at a 'learning center' at a community college, I worked with many, many people who were struggling with math (the ones who weren't struggling didn't come to the learning center, or came there just to have a quiet place to work and to ask the occasional question). I tutored students in everything from below pre-algebra up through calculus 1 and I have worked with students who literally could not add without the assistance of a calculator. I agree with @Mark44 in that everyone has a 'skill cap' in mathematics, with some having a very low cap and some having a very, very high cap. While many people are far better at math (or could be) than they themselves think, this is true for practically every skill. I could be much better at sports, programming, math, and many other things if I put forth the effort and spent the time, but I will almost certainly never be top-tier in any of these.
 
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  • #32
etotheipi
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There are some good points from both sides of this thread.

I wonder what people think about the notion of a growth mindset? I find this interview between Sal Khan and Carol Dweck (Prof. Psychology at Stanford University) quite interesting, especially in terms of what sorts of cultural blinders we might have on in terms of how much intelligence is "fixed" (Sal uses an establishing example of how literacy rates have increased throughout history despite pessimistic predictions by past generations).

I'm no neuroscientist, but there's increasing evidence that the brain is very capable of plastic change, even into adulthood. This study indicated that the hippocampal volume in licensed London taxi drivers was significantly larger than in control subjects, and was correlated with time spent as a taxi driver. I know of no such study that has been performed pertaining to mathematical ability, however the hippocampus is associated with mathematical and spatial reasoning.

Of course, those with experience in education, like @Mark44, will have a better feel for this than I can have. However it seems to me that claims that some cannot progress to higher math should be treated with caution, even if there might be partial truth to it. We know so little about the brain as it stands that it appears to be too soon to make generalisations.

Even Feynman says:
"an ordinary person, by studying hard, would get to be able to imagine these things like I imagine them... I was an ordinary person who'd studied hard... there's no miracle people, it just happens they got interested in this thing and they learned all this stuff. There's no talent or special miracle ability to understand quantum mechanics or a miracle ability to imagine electromagnetic fields..." etc.
Then again, he might have been so talented that he didn't think it was possible for other people to not be able to see things like he did. So I don't know. But it's an interesting question!
 
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  • #33
russ_watters
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I think you have missed my point as well. I think you think some diplomas are worth more than others. I don't share that view. Because you need an engineering or medical degree to put food on the table as much as you need a degree in fine arts or in astronomy; i.e. the work you do with that degree has little to do with the basic needs of any living being....

One upon a time there was a guy living his life. He was gathering food and building a shelter for himself and his family. One day, in his leisure time, he look up to the sky and notice that stars were forming the same pattern that he noticed the previous night. He had just created the basis for astronomy that lead the future generations to walk on the moon.

The moral of the story is that nobody needs to know about astronomy to make a living. Because that guy could before he knew anything about it. He didn't look at the sky because he needed to, he did it for the fun of it. There are no ways that this is not true anymore.
I definitely think some diplomas are worth more than others. That is to say, I believe some degrees are worth less than the paper they're printed on -- for example, any degree in _________ Studies, where you can fill in the blank with any of a number of groups.
I suspect @jack action knows how "the system" works, he just doesn't like it. So he's consciously rejecting the financial definition of "worth" in favor of a personal fulfillment value, even though he knows the financial definition is a real thing that exists in our world. While also knowing that it isn't literally possible to be a hunter-gather-astronomer anymore. That may be a nice sentiment, but it won't help anyone who asks for advice here get out of or avoid poverty.

For my part, I realized an astronomy degree wasn't a viable path for me and I use my engineering salary in part to fund my astronomy.
I think you should carefully reflect on what you're saying above, because it frankly comes across like you have no empathy or compassion toward your fellow human beings.
I think there is empathy in truth-telling, even if it doesn't sound like it. I think telling people they should study a major that provides personal fulfillment, because it fits with a preferred worldview, which then results in an undesired life of poverty, is cruel.
 
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  • #34
Math_QED
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I will give you the source as soon as I will find it.
Waiting for that!
 
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I agree with @Mark44 in that everyone has a 'skill cap' in mathematics, with some having a very low cap and some having a very, very high cap. While many people are far better at math (or could be) than they themselves think, this is true for practically every skill. I could be much better at sports, programming, math, and many other things if I put forth the effort and spent the time, but I will almost certainly never be top-tier in any of these.
A few of the classes I taught were remedial classes, not at all college-credit classes, and some literally at the level of arithmetic. A number of students that I had were older students returning to school a number of years after they had last attended high school. There were quite a few who were pleasantly surprised that they could do well, because they had been under the impression that they were "bad at math." People can get usually get better at some activity if they work at it, and spend the time practicing it. But the idea of a 'skill cap' as you mentioned is a very real thing, in my experience.
 
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  • #37
etotheipi
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But the idea of a 'skill cap' as you mentioned is a very real thing, in my experience.
I'm not saying this is wrong (I have no experience, so I cannot make a counter-claim), but I wondered if you could flesh this out a little? To me the idea of a video-game like "progress bar" with a skill cap that means that when you reach, say, having gained fluency with 1000 mathematical theorems you can go no further seems too oversimplified (sorry if I misunderstand!).

If there is a cap, I would suspect it be at a much higher level than one would imagine. The more fundamental issue IMO is a lack of interest/motivation that might hold people back.
 
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  • #38
vela
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To me the idea of a video-game like "progress bar" with a skill cap that means that when you reach, say, having gained fluency with 1000 mathematical theorems you can go no further seems too oversimplified (sorry if I misunderstand!).
As opposed to oversimplified just enough? :wink:
 
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  • #39
jack action
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I don't think anyone would disagree that not everyone can become a member of a professional sports team or to play music at a professional level,
So you consider someone cannot play basketball because he cannot play at a professional level? You can't play music because you're not playing in a symphonic orchestra?

A lion doesn't have to be the best hunter to be considered 'able to hunt'. If it runs after a gazelle, if it gets one from time to time, it can hunt. So, yes, a human can do math.

Most people don't manage math because they don't use it in their daily life. They don't do it because they're constantly told they don't need it or only special people can do it. My stairway anecdote - that I told in another thread - is a real good example of this. Funny thing, there is an update to this stairway story. In another building he bought recently, he finally did a winder staircase completely from scratch, all by himself.

I use math in my everyday life almost on a daily basis. People often laugh at me for it. They think I do too much for simple jobs. They don't understand how it prepares me for bigger jobs. I see mathematical relationships everywhere, all the time, and I have to figure them out. Some do crosswords or sudokus, I do that. If I didn't do that, I would be like everyone else and forget everything about what I was thought.
but somehow, anyone can do mathematics at the level required by, say, electronics engineering, without any special abilities, given lots of encouragement. I don't buy this at all.
When attending university, I've personally sit by someone for 4 years who graduated the same as me in mechanical engineering who didn't understand integrals. Didn't know what they meant; Couldn't work them out. Yes, he passed all of his courses. It's not necessarily because he wasn't able to do the work, just because he didn't care. I think he simply got off on tricking others. It is awful to think that this guy is an engineer. Between him and students who were perfectly managing the engineering math, there is an array of shades of grey in the student community.

Again, someone who knows how to use the system, he can pass right under any teacher's (or boss) nose without him seeing anything. It's even easier when the teacher keeps his eyes closed voluntarily. (Yes, lots of those too)

So, yeah, not that impress by people going through engineering. I've done it. I've seen a few talented people do it. And I've seen a lot of people who couldn't give a crap about it doing it.
 
  • #40
Drakkith
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I'm not saying this is wrong (I have no experience, so I cannot make a counter-claim), but I wondered if you could flesh this out a little? To me the idea of a video-game like "progress bar" with a skill cap that means that when you reach, say, having gained fluency with 1000 mathematical theorems you can go no further seems too oversimplified (sorry if I misunderstand!).

If there is a cap, I would suspect it be at a much higher level than one would imagine. The more fundamental issue IMO is a lack of interest/motivation that might hold people back.
It's not really a 'hard cap' in my opinion. Not usually at least. It's more the idea that as your skill level improves, it takes more and more effort and time to improve further. I like to imagine different lines on a graph representing the time&effort vs skill of a person. Some might have a near-linear graph. But others look more like a logarithm, where even spending 10x more time and effort only nets them a very small increase in their skill.

The more I think about it, the more I like this viewpoint. It removes the black and white, can or can't, binary viewpoint, which isn't realistic in my opinion. The young man I tutored who couldn't add without a calculator, who had severe difficulty understanding even the most basic mathematical concepts, I can't say that he will never understand calculus, but I can confidently say it will take him so long to do so that he'll probably have grey hair by then.
 
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  • #41
etotheipi
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It's not really a 'hard cap' in my opinion. Not usually at least. It's more the idea that as your skill level improves, it takes more and more effort and time to improve further.
I see; thank you for clarifying!
 
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I don't think anyone would disagree that not everyone can become a member of a professional sports team or to play music at a professional level,
So you consider someone cannot play basketball because he cannot play at a professional level? You can't play music because you're not playing in a symphonic orchestra?
Please reread what I wrote more carefully. What you wrote is nowhere close to what I actually said.
When attending university, I've personally sit by someone for 4 years who graduated the same as me in mechanical engineering who didn't understand integrals.
Different engineering disciplines require different levels of mathematical prerequisites, at least according to the standards at the University of Washington, where many of my students transferred to. The discipline that required the least number of lower-division (first two years of college) mathematics courses before admission to the program was Civil Engineering. Next lower was Mech. Engineering. At the top (meaning most math courses required prior to admission) were Electrical Engineering and Electronics Engineering. Somewhere in the middle, but closer to the top was Aeronautical Engineering.

From your description of your fellow student, it sounds like he wouldn't have been admitted to the UW Mech. Eng. program.
 
  • #43
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, and perhaps Mark44 still expects his students to give an effort and therefore his experience does push his opinion to what it is. If children into adolescence into adult become students of Mathematics (not as major field) and became discouraged and remain so, that is not Mark44's fault. When these students go into university and college enrollment and enter Mathematics courses, THEIR effort is necessary. The teacher (or professor), cannot make it up for them; he can only try to encourage them to give the effort. Maybe Mark44 does this, but his main goal is, review the material in a systematic way and conduct assessment.
I agree with you that adult students of math classes in university need to put effort to understand the material. And I also agree that teachers or professors can only try to encourage them to give the effort (on top of teaching on the material). The point I'm making is that the foundation to understand mathematics lies far before adulthood, and often involves resources invested in the young child.
 
  • #44
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@jack action's analogy was between the ability of humans to do mathematics vs. the ability of squirrels to make a living. A much better comparison, in my view, would be the ability of humans to do mathematics vs. their ability to play basketball at a professional level or to perform music in an orchestra. I don't think anyone would disagree that not everyone can become a member of a professional sports team or to play music at a professional level, but somehow, anyone can do mathematics at the level required by, say, electronics engineering, without any special abilities, given lots of encouragement. I don't buy this at all.

Of course, many students would be able to do mathematics at a higher level than they have attained, if they had had more encouragement or less discouragement along the way. I've run into countless older students who told me about one teacher in junior high or high school who so disparaged their work that they did not go further in mathematics courses. I'm not arguing that point at all. What I am saying is that most people have some innate limitation on their ability to think abstractly enough to be able to succeed at a level somewhere above arithmetic, just like they have a limitation on their physical and mental abilities to compete in professional sports.
The analogy between mathematics and professional sports or music is not a good one, as I've argued many times before on this forum. Ability in professional sports is partly based on physiological features of the human body. Ability to grasp abstract thinking is inherent within the capabilities of most humans who do not suffer learning or developmental disabilities, and is a skill that can be acquired and nurtured through training and practice, particularly through early training in childhood onwards.

And even in professional sports, simply having the right physiological features is not enough. To play at the elite level also involve dedication and practice as well as resources to hone the skills of the players.

What you quoted from me was taken completely out of context, as @Math_QED points out below.
You wrote the following:

"The ones who lack certain abilities get eaten... "

For someone coming in "fresh" to this forum, and this thread in particular, it is very hard not to see this statement as suggesting a lack of empathy. I have read enough of your past posts to know that was not what you intended, but I was concerned that your message will be misconstrued.

Let me ask you this -- do you feel that I am being unfair to you by pointing this out?
 
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  • #45
StatGuy2000
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I think there is empathy in truth-telling, even if it doesn't sound like it. I think telling people they should study a major that provides personal fulfillment, because it fits with a preferred worldview, which then results in an undesired life of poverty, is cruel.
I don't disagree with you about the value in truth-telling (I've done plenty of that here on PF, or sought to do so, as you are very well aware).

My issue with @Mark44 (as you saw in my subsequent reply) was that the message he was trying to impart wasn't necessarily clear, particularly to those coming "fresh" to this thread, and may give the impression of callousness, which I know was not his intention.
 
  • #46
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Let me ask you this -- do you feel that I am being unfair to you by pointing this out?
Yes. Here is the full context of what you commented on.

Right outside my window, there are plenty of birds and squirrels. I don't really notice that one squirrel or bird has different abilities compared to another one. If one can do it, most likely the other one can too. There is nothing special about someone who can do mathematics.​
Mark44 said:
The ones who lack certain abilities get eaten...
It ought to be obvious that I was talking about the squirrels and birds.
Anyone coming in fresh to the forum should be cautious about quoting other members out of context.

The analogy between mathematics and professional sports or music is not a good one, as I've argued many times before on this forum.
It was a much better analogy than comparing humans with or without mathematical abilities to the abilities of birds and squirrels.
Ability in professional sports is partly based on physiological features of the human body. Ability to grasp abstract thinking is inherent within the capabilities of most humans who do not suffer learning or developmental disabilities, and is a skill that can be acquired and nurtured through training and practice, particularly through early training in childhood onwards.
That's a very broad brush, "abstract thinking."
And even in professional sports, simply having the right physiological features is not enough. To play at the elite level also involve dedication and practice as well as resources to hone the skills of the players.
No argument there, but I believe that proficiency at elite athletic levels depends on both practice/training and on innate abilities. IOW, both nature and nurture. It seems unrealistic to me to hold that nurture alone is sufficient for the more intellectual abilities, such as are being discussed in this thread.
 
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  • #47
StatGuy2000
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Yes. Here is the full context of what you commented on.


It ought to be obvious that I was talking about the squirrels and birds.
Anyone coming in fresh to the forum should be cautious about quoting other members out of context.
Yes, now I see the context in which you made the quote. For some reason this escaped me while I was going through the thread and your statement came across to me as more callous than was intended. My apologies.
 
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symbolipoint
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Anyone coming in fresh to the forum should be cautious about quoting other members out of context.
GoodLuck with that.
 
  • #49
jack action
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It seems unrealistic to me to hold that nurture alone is sufficient for the more intellectual abilities, such as are being discussed in this thread.
We're gonna have to agree to disagree on that point.

My personal view on the way humans should be educated (which goes against what is conveyed by the actual education system) is well resumed in this article about learning to read, which could easily be applied to math or any other "abstract thinking" as defined by @StatGuy2000 . The best way to resume this article is going through its list of subtitles:

https://www.psychologytoday.com/ca/blog/freedom-learn/201002/children-teach-themselves-read said:
Children Teach Themselves to Read

Seven Principles of Learning to Read Without Schooling

1. For non-schooled children there is no critical period or best age for learning to read.

2. Motivated children can go from apparent non-reading to fluent reading very quickly.

3. Attempts to push reading can backfire.

4. Children learn to read when reading becomes, to them, a means to some valued end or ends.

5. Reading, like many other skills, is learned socially through shared participation.

6. Some children become interested in writing before reading, and they learn to read as they learn to write.

7. There is no predictable "course" through which children learn to read.
If you don't follow these principles, you can destroy a human for life, i.e. he will seem to have no or limited intellectual abilities.
 
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  • #50
TeethWhitener
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For many years, the colleges and universities in my country, the US, have been churning out graduates with degrees that qualify them for jobs as baristas, if that. Obviously, they weren't interested in competing for wealth, but they probably didn't realize that when they were studying Medieval Dance Theory.
I suspect @jack action knows how "the system" works, he just doesn't like it. So he's consciously rejecting the financial definition of "worth" in favor of a personal fulfillment value, even though he knows the financial definition is a real thing that exists in our world. While also knowing that it isn't literally possible to be a hunter-gather-astronomer anymore. That may be a nice sentiment, but it won't help anyone who asks for advice here get out of or avoid poverty.

For my part, I realized an astronomy degree wasn't a viable path for me and I use my engineering salary in part to fund my astronomy.

I think there is empathy in truth-telling, even if it doesn't sound like it. I think telling people they should study a major that provides personal fulfillment, because it fits with a preferred worldview, which then results in an undesired life of poverty, is cruel.
Just for some context, this “problem” of useless degrees isn’t nearly as bad as it’s perennially made out to be:
https://www.google.com/amp/s/fiveth...t-most-colleges-dont-pick-useless-majors/amp/
It’s also worthwhile noting that, while the overall poverty rate in the US is about 12%, the poverty rate among people who completed a Bachelor’s degree (any major) is closer to 4%.
 
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