An observation on homework problems

[coppice]

Tell me and I will forget.
Show me and I will remember.
Let me do it and I will understand.

A lot of people who struggle to understand even simple things are remarkably good at pure memory activities.

[paulca]

Tell me and I will forget.
Show me and I will remember.
Let me do it and I will understand.

A lot of people who struggle to understand even simple things are remarkably good at pure memory activities.

It's funny.  I take the completely opposite approach.  I can't remember facts so I don't try.  I only remember the logical reasoning steps to get from one bit of information to the other.... or I recall how I could find the information again when I actually need it. 

Random contrived example, the statement "Cats fall".  There is no point remembering anything.  Cats exist and so does gravity, so the statement is useless.  I literally just drop everything that comes into that category.  It can be derived from other information I already have with sane reasoning.

The other category is.  "Makes sense, I understand it, don't need it right now, so only going to remember it makes sense and that I can derive or find it later should I need it."

It's like you don't need to remember the road map of England to cross it in a car.  You can derive it fairly easily on the fly.

Eventually of course the common nodes of this derivation tree become ingrained with use to become instant recall.  Others sadly atrophy away with lack of use.  The worst are when those weak atrophying paths get tangled with another and you get false recall or bullshit.  Which I don't doubt will become worse as I get older and end up demented or stuck in a loop in my own bullshit tree. LOL 

[tggzzz]

Tell me and I will forget.
Show me and I will remember.
Let me do it and I will understand.

A lot of people who struggle to understand even simple things are remarkably good at pure memory activities.

It's funny.  I take the completely opposite approach.  I can't remember facts so I don't try.  I only remember the logical reasoning steps to get from one bit of information to the other.... or I recall how I could find the information again when I actually need it. 

Random contrived example, the statement "Cats fall".  There is no point remembering anything.  Cats exist and so does gravity, so the statement is useless.  I literally just drop everything that comes into that category.  It can be derived from other information I already have with sane reasoning.

The other category is.  "Makes sense, I understand it, don't need it right now, so only going to remember it makes sense and that I can derive or find it later should I need it."

It's like you don't need to remember the road map of England to cross it in a car.  You can derive it fairly easily on the fly.

Eventually of course the common nodes of this derivation tree become ingrained with use to become instant recall.  Others sadly atrophy away with lack of use.  The worst are when those weak atrophying paths get tangled with another and you get false recall or bullshit.  Which I don't doubt will become worse as I get older and end up demented or stuck in a loop in my own bullshit tree. LOL 

That's why I was never much good at languages where you have to remember arbitrary associations between two words.

Ditto street names and road numbers. Some people navigate by following familiar street name. I navigate by knowing the direction I want to go in, and finding a road to fit.

Ditto which button to push on an IDE or word processor etc.

[jh15]

Remember the old joke about the technician that repaired a car by hitting it with a hammer[1]. The customer objected to the £10 invoice for one thwack. The technician agreed it was wrong, and changed it to "Thwack: £1. Knowing where and how hard to thwack: £9".

[1] I've done just that, to a starter motor
[/quote]

The perfect tool for that is the heel of your shoe.

[coppice]

Asimov's old story "Profession" significantly shaped my career choices. The points are as true today as they were in the 50s. Hence it is still worth speed-reading it at https://www.abelard.org/asimov.php (Even though the page's style is stuck in the geocities era )

I've just re-read it, and come to realise it anticipates modern consultancy practices, the decline of apprenticeships, and typical training courses.

I just read it for the first time. He presents interesting ideas, in a framework reminiscent of Arthur C Clark's The City And The Stars, or Brave New World. I don't understand some of his plot choices, though. Why did he make the children learn to read as late as 8? Why did he make the number of creative people so small? Real creativity is not common, but its not as rare as that story implies. Is the implication that people have been purposefully dumbed down, so they now need to hunt for the few outliers?

I seem to remember another story where the "House for the Feeble Minded" turns out to be the "Centre for Advanced Research". Did Asimov, or others, reuse that idea?

[0culus]

my favorite gripe.  PROVE THAT (A+B)^2 IS A^2 + B^2 + 2AB

WHY ? This was proven thousands of years ago by some dude with a grey beard and a toga . It possible was also proven earlier by some dude from a place in the indus valley ( today's india) . All these years we have had millions of students posting the same proof.
Ar you as a math teacher still unsure about it that you need to ask your students to prove it once again ? IF you are so desperate why don't you prove it ?

That is not learning. That is solving crossword puzzles and sudoku's.
Of course you need to know that formula. And it is nice to prove it while you are  explaining it. But mindnumbingly asking the student to repeat that is parrot work. That equation can be looked up in a second. Teach them the applications !
Exams should be done by giving the student a book with all formulas. There is no reason to memorise all that stuff. There are students with bad memory skills that have excellent reasoning skills. They fail cause they can remember if it was Bob or Pete that came up with something. That is just plain wrong. Reasoning skill is waaaaay more important that being able to recant the coursebook letter for letter.

Feynman called that Cargocult Science. Go through the motions and you get the paper. But you are still the worlds biggest Moron.

Proving theorems that are already proved is an essential exercise that trains you how to think as a beginning math student learning how to reason through proofs. You can't very well assign all the Millennium Problems as homework and expect students new to mathematical thinking to get anywhere (unless one of them happens to be the next Terence Tao, or Grothendieck, or what have you).

I do agree that you should never memorize what you can look up (eventually you will internalize the information that is important), and time pressure exams prove nothing except who is able to function in that environment. In fact, all of the advanced (some grad level) mathematics I took in my BS in Math used take home exams only. I ended up not doing math in grad school, but I learned a huge amount of very useful reasoning skills by suffering through that second undergrad degree (I also did computer science) with some great professors.

[tggzzz]

Asimov's old story "Profession" significantly shaped my career choices. The points are as true today as they were in the 50s. Hence it is still worth speed-reading it at https://www.abelard.org/asimov.php (Even though the page's style is stuck in the geocities era )

I've just re-read it, and come to realise it anticipates modern consultancy practices, the decline of apprenticeships, and typical training courses.

I just read it for the first time. He presents interesting ideas, in a framework reminiscent of Arthur C Clark's The City And The Stars, or Brave New World. I don't understand some of his plot choices, though. Why did he make the children learn to read as late as 8? Why did he make the number of creative people so small? Real creativity is not common, but its not as rare as that story implies. Is the implication that people have been purposefully dumbed down, so they now need to hunt for the few outliers?

I seem to remember another story where the "House for the Feeble Minded" turns out to be the "Centre for Advanced Research". Did Asimov, or others, reuse that idea?

I wouldn't over-analyse the plot choices an author uses to lead readers to the key points!

I'd also apply that to Kurt Vonnegut's "Harrison Bergeron" http://www.tnellen.com/cybereng/harrison.html

Or, if you are channelling Harrison Bergeron, you can read the "Cliffs Notes" on the story

[coppice]

Asimov's old story "Profession" significantly shaped my career choices. The points are as true today as they were in the 50s. Hence it is still worth speed-reading it at https://www.abelard.org/asimov.php (Even though the page's style is stuck in the geocities era )

I've just re-read it, and come to realise it anticipates modern consultancy practices, the decline of apprenticeships, and typical training courses.

I just read it for the first time. He presents interesting ideas, in a framework reminiscent of Arthur C Clark's The City And The Stars, or Brave New World. I don't understand some of his plot choices, though. Why did he make the children learn to read as late as 8? Why did he make the number of creative people so small? Real creativity is not common, but its not as rare as that story implies. Is the implication that people have been purposefully dumbed down, so they now need to hunt for the few outliers?

I seem to remember another story where the "House for the Feeble Minded" turns out to be the "Centre for Advanced Research". Did Asimov, or others, reuse that idea?

I wouldn't over-analyse the plot choices an author uses to lead readers to the key points!

He could have talked about reading day being in early childhood, but instead specifically made it at 8 years of age. I assume there was a reason. Asimov normally has a reason for each of his plot points.

I'd also apply that to Kurt Vonnegut's "Harrison Bergeron" http://www.tnellen.com/cybereng/harrison.html

Or, if you are channelling Harrison Bergeron, you can read the "Cliffs Notes" on the story

Harrison Bergeron is not to be taken too literally. It uses too much humour for that.  In reality there would have to be a ruling elite of the most capable people running such a handicapping system, and Harrison would have been recruited into that. This is the route at least one movie inspired by Harrison Bergeron took -

[pgo]

As an educator I am often amazed and how much effort students will go through to remember things rather than understand them.
Personally I have a poor memory so unconnected facts are hard to remember.
Connected reasoning is much easier.

[coppice]

As an educator I am often amazed and how much effort students will go through to remember things rather than understand them.
Personally I have a poor memory so unconnected facts are hard to remember.
Connected reasoning is much easier.

You might be focussing on the students you can't relate to - the ones with a terrific memory, but poor critical thinking.

[tggzzz]

As an educator I am often amazed and how much effort students will go through to remember things rather than understand them.
Personally I have a poor memory so unconnected facts are hard to remember.
Connected reasoning is much easier.

Yes.

It helps such students in the long term if (at the beginning of the course) they can be forced to realise that job interviewers look for that - and avoid such candidates.

[coppice]

As an educator I am often amazed and how much effort students will go through to remember things rather than understand them.
Personally I have a poor memory so unconnected facts are hard to remember.
Connected reasoning is much easier.

Yes.

It helps such students in the long term if (at the beginning of the course) they can be forced to realise that job interviewers look for that - and avoid such candidates.

Good interviewers probe understanding, but most don't because they are part of strong memory/weak thinking cohort. Many interviewers are actually intimidated by someone who clearly has deep understanding, which they lack. Overall, life is richer when you understand, but people can progress surprisingly well understanding very little.

[free_electron]

i wish i had this guy as a teacher !.

[b_force]

Personally I think it highly depends what type of learner someone is.
One person is very practical and really learns fast an quickly by doing stuff, others learn by (theoretical) repetition etc
Most important is that there is no good or wrong in it, neither is one more smart or not.
It's just nothing more than just having a preference.

Unfortunately on schools/universities only one kind is being taught and (therefor) only being taken serious.
The fast majority is only done with repetition, and even one of a very limited kind.
This doesn't train peoples brains to understand the problem, but just repeat the solution.
Result; after a month or two people totally forget what everything was about and move on.
Or in other words, people are trained to remember things like (useless) facts, not to understand things and being trained in logical reasoning.
Let alone understanding the meaning of it and seeing how that can be implemented on a wider/bigger scale or bigger picture.

In fact, I have seen multiple people with a cum laude degree as well as a PhD but weren't able to understand not only some basics but also failed in very similar problems but with a different context.
When I am coaching interns, I always let them focus on basically 4 things; statistics, error analyses, control theory and Fermi problems.
With these four plus a little bit of base knowledge and logical thinking you can tackle a lot of problems that or sometimes not even close to your working field.

I really never bother about facts, nowadays there is Google as well as YouTube.
Rather safe time, energy and effort (= hard-disk space in the brain) in understanding things.
For an engineering/scientist tackling new unknown problems is far more important.

[tggzzz]

As an educator I am often amazed and how much effort students will go through to remember things rather than understand them.
Personally I have a poor memory so unconnected facts are hard to remember.
Connected reasoning is much easier.

Yes.

It helps such students in the long term if (at the beginning of the course) they can be forced to realise that job interviewers look for that - and avoid such candidates.

Good interviewers probe understanding, but most don't because they are part of strong memory/weak thinking cohort. Many interviewers are actually intimidated by someone who clearly had deep understanding, which they lack. Overall, life is richer when you understand, but people can progress surprisingly well understanding very little.

Hey, I'm trying to be optimistic here! That's either or depending on mood.

[tggzzz]

I really never bother about facts, nowadays there is Google as well as YouTube.
Rather safe time, energy and effort (= hard-disk space in the brain) in understanding things.
For an engineering/scientist tackling new unknown problems is far more important.

Feynman used to have a hack at medical students, who had to remember the names of all the bones etc. He wondered why they didn't just consult "a map of the body" when they needed to.

Apart from that, many "simple facts" are very transient in nature, e.g. which button to press in FroobleApp v3.5 to cause the splodger to be faddled. You know, the kind of stuff that fills stackechange and similarly boring sites.

[b_force]

I really never bother about facts, nowadays there is Google as well as YouTube.
Rather safe time, energy and effort (= hard-disk space in the brain) in understanding things.
For an engineering/scientist tackling new unknown problems is far more important.

Feynman used to have a hack at medical students, who had to remember the names of all the bones etc. He wondered why they didn't just consult "a map of the body" when they needed to.

Apart from that, many "simple facts" are very transient in nature, e.g. which button to press in FroobleApp v3.5 to cause the splodger to be faddled. You know, the kind of stuff that fills stackechange and similarly boring sites.

hahaha, yes very typical.

Mostly also with math for example, something like differential equations or similar.
After doing 10 of them you get the point and what it's for and what it can (and can't) do, so why doing another 2000? 
Especially the weird ones that don't have ANY practical value, except for staying busy and being bothered about it.

Second, raise an hand who does this by hand on a daily basis?  (sound of crickets)

You just fill those things into your math calculator of choice and let it ramble while you do actual serious work or get some coffee.

[tggzzz]

You just fill those things into your math calculator of choice and let it ramble while you do actual serious work or get some coffee.

I do like to see candidates that know the correct answer to "what is 1+2*3?" I don't mind if they prompt me to say "using the normal laws of arithmetic". If they don't know "BEDMAS" or equivalent, then they need some other truly outstanding characteristics

[ucanel]

I am an EE.
First year of the collage at the C lessons
i think that the first thing that i will fail at my education life will be the programming,
indeed that happened, i failed,
at the summer school exams i memorised 10 pages of programs that likely to be asked,
i passed the exams knowing nothing about programming.

Now i am an embedded programmer,
i love programming, i love problem solving.

[b_force]

at school exams i memorised 10 pages of programs that likely to be asked,
i passed the exams knowing nothing about programming.

And that, ladies and gentlemen, is a perfect way to get ACTUALLY a degree without knowing anything.

No offence towards you obviously, happy you found something you like 

[tggzzz]

I am an EE.
First year of the collage at the C lessons
i think that the first thing that i will fail at my education life will be the programming,
indeed that happened, i failed,
at the summer school exams i memorised 10 pages of programs that likely to be asked,
i passed the exams knowing nothing about programming.

Now i am an embedded programmer,
i love programming, i love problem solving.

That is possible for a technician, not an engineer.

You should read "Profession" by Isaac Asimov, since it is directly relevant to that. I've previously posted a link to it.

[tggzzz]

at school exams i memorised 10 pages of programs that likely to be asked,
i passed the exams knowing nothing about programming.

And that, ladies and gentlemen, is a perfect way to get ACTUALLY a degree without knowing anything.

No offence towards you obviously, happy you found something you like 

And that, ladies and gentlemen, is why some institutions and degrees are more valued than others.

[b_force]

at school exams i memorised 10 pages of programs that likely to be asked,
i passed the exams knowing nothing about programming.

And that, ladies and gentlemen, is a perfect way to get ACTUALLY a degree without knowing anything.

No offence towards you obviously, happy you found something you like 

And that, ladies and gentlemen, is why some institutions and degrees are more valued than others.

Maybe in the UK, but I have never seen people bothering about it.
As long as you have a Master of Bachelor of Engineering/Science people believe and assume you have some knowledge.

[coppice]

at school exams i memorised 10 pages of programs that likely to be asked,
i passed the exams knowing nothing about programming.

And that, ladies and gentlemen, is a perfect way to get ACTUALLY a degree without knowing anything.

No offence towards you obviously, happy you found something you like 

And that, ladies and gentlemen, is why some institutions and degrees are more valued than others.

Maybe in the UK, but I have never seen people bothering about it.
As long as you have a Master of Bachelor of Engineering/Science people believe and assume you have some knowledge.

People have always wanted to know where you got your degree in some countries, like the US. There was a time when people in the UK didn't focus much on where you got your degree. They were mostly interested in whether you got a 1st, upper 2nd, etc. Now people do want to know where you studied in the UK. Anyone that didn't attend a Russell Group university (a group of about 40 old and trusted universities) is treated with great skepticism.

[b_force]

People have always wanted to know where you got your degree in some countries, like the US. There was a time when people in the UK didn't focus much on where you got your degree. They were mostly interested in whether you got a 1st, upper 2nd, etc. Now people do want to know where you studied in the UK. Anyone that didn't attend a Russell Group university (a group of about 40 old and trusted universities) is treated with great skepticism.

Interesting, never came across these experiences, nor other people I know

Personally when I look for candidates I don't even bother looking for a degree anymore.
I just haven't seen any correlation between having a degree vs knowledge, work mentality and skills.
Well obviously you're also not going to just take a random person, but what I am trying to say (also with my earlier posts), is that are other ways to gain knowledge
For some people it's even more just a prestige thing than anything else.