An observation on homework problems

[Mr. Scram]

No it is not and most threads can not be put in pre-labeled boxes, if you do you are the one doing the filtering with a preconception which says more about you than the thread. Can we continue on content.

Irony is saying this in a thread more than one is using to confirm his own preconceived notions.

[Kjelt]

Isn't that what a discussion is all about? Checking ones view on a subject and discuss it with others?
There is no need or request to label the discussion only to participate.

[rhb]

All of this is very far from my original point that the purpose of homework is to solidify the student's understanding of the subject by having them apply what they have been taught in the form of solving problems.  And that the benefit of homework is in direct proportion to the amount of effort the student puts into solving the problem without outside assistance.

I have this ridiculous expectation that an educated individual will understand logic at the subtlety of Plato, Locke, Hume, Kant and Camus, have mastery of applied mathematics such as differential equations and integral transforms and have a basic knowledge of chemistry, geology, biology and physics as taught in a 2-3 semester sequence in each making full use of mathematics where appropriate.

Furthermore, have the ability to write clearly and grammatically with proper punctuation and spelling, and not be so deluded as to think that they are right and everyone who disagrees with them is automatically wrong without any discussion.

That is the essence of a good liberal arts education.  University  has been degraded into an expensive vocational training program.  It is still possible to get an education, but it now takes a lot more  effort swimming against the current.  How can anyone acquire the ability to make a critical analysis if opposing viewpoints are not permitted lest some poor soul be traumatized by exposure to a different viewpoint.

Engineers in particular, are inclined to sneer at liberal arts graduates.  Certainly, there are many who receive liberal arts degrees without learning anything.  Tertiary education is now a scam to defraud young people with false promises and convince them to enslave themselves with debt.

But:

We all get what we deserve whether we want it or not, either as individuals or as members of a group.  Sometimes this is as punishment and sometimes it's a blessing.  Which is always ambiguous and depends entirely on what we do next.

I rather suspect that a lot of university faculty and administrators will be quite dismayed when they discover that their pensions are dependent upon the financial well being of the students they have defrauded.  As the saying goes, what goes around, comes around.

[coppice]

You have no idea how well you have learned a subject until you come to apply your knowledge. Applying might be a matter of working through some homework problems, working through some real world problems, or teaching the topic to other people. The smartest in the class acting as tutor to the middling students in the class usually benefits both groups - the smartest find the gaps in their understanding, and can fill them in. The middling students get a better basic understanding of the topic. This tutoring idea has its limits, though. If the smartest try mentoring the weakest students it can end up wasting both group's time (depending on how big the spread of ability and education on the course might be).

I have found that homework generally works best when you don't spend an excessive amount of time trying to solve difficult problems on your own. It you find a problem that hard, you probably lack a piece of knowledge needed to solve it. Working in peer groups after a moderate amount of time on your own is a good step for efficient learning. Different people in the group typically have different gaps in their knowledge, and together they can get to a solution, benefiting all. Unless the peer group is really lacking in some area, going beyond the peer group for a solution should really be a last resort.

[Mr. Scram]

All of this is very far from my original point that the purpose of homework is to solidify the student's understanding of the subject by having them apply what they have been taught in the form of solving problems.  And that the benefit of homework is in direct proportion to the amount of effort the student puts into solving the problem without outside assistance.

I have this ridiculous expectation that an educated individual will understand logic at the subtlety of Plato, Locke, Hume, Kant and Camus, have mastery of applied mathematics such as differential equations and integral transforms and have a basic knowledge of chemistry, geology, biology and physics as taught in a 2-3 semester sequence in each making full use of mathematics where appropriate.

Furthermore, have the ability to write clearly and grammatically with proper punctuation and spelling, and not be so deluded as to think that they are right and everyone who disagrees with them is automatically wrong without any discussion.

That is the essence of a good liberal arts education.  University  has been degraded into an expensive vocational training program.  It is still possible to get an education, but it now takes a lot more  effort swimming against the current.  How can anyone acquire the ability to make a critical analysis if opposing viewpoints are not permitted lest some poor soul be traumatized by exposure to a different viewpoint.

Engineers in particular, are inclined to sneer at liberal arts graduates.  Certainly, there are many who receive liberal arts degrees without learning anything.  Tertiary education is now a scam to defraud young people with false promises and convince them to enslave themselves with debt.

But:

We all get what we deserve whether we want it or not, either as individuals or as members of a group.  Sometimes this is as punishment and sometimes it's a blessing.  Which is always ambiguous and depends entirely on what we do next.

I rather suspect that a lot of university faculty and administrators will be quite dismayed when they discover that their pensions are dependent upon the financial well being of the students they have defrauded.  As the saying goes, what goes around, comes around.

I agree with your idea that homework or exercises are supposed to solidify someone's understanding by having them apply it, but I don't think the notion that the benefits being proportional to the amount of effort the student puts in has been demonstrated or proven. It may very well be that students dwelling on subjects too long will miss out in other areas. As science advances, education has to provide knowledge about much more subjects and going all out with every single one isn't possible. Doing what worked 40 years ago isn't realistic or sensible. Instead the focus is more on giving students tools with which they can develop themselves into whatever is required.

Research indicates that modern day students are better communicators than their older peers. It's one of the perks of living in the era of information. Don't let badly written Twitter and Facebook messages fool you.

I don't agree with your fairly negative assessment of everything being worse than it used to be. The world has changed, and education has too. Students have much more information at their disposal, and need to develop different strategies to be successful in today's world. I don't see modern education producing students less prepared or able than it used to and thinking it is may be a sign one has fallen behind to the point of no longer understanding how things work. At that point it's best to move over and leave things to the next generation.

[rhb]

@coppice

I think that is sound.  In the case I cited at the beginning, the class hotshot from my Cal I class and I were not looking at the problem properly.  We had gotten too good at applying certain methods and failed to step back and rexamine the problem.  Once the TA pointed out how to approach it we were off and running.

In that case, the 4 hours each of us had spent beating on the problem didn't teach us anything about solving that problem.  It should have taught us that sometimes the best way to solve a problem is to step back, do something else and then take another try.  We were a little too good at it for our own good and not yet mature enough to back off.

Later in life I had many instances where I was trying to find an error in a program for several hours without success, looked up and saw it was close to time to go home.  As I was a contractor I came and went when I pleased.  So I did not sit around until 8 hours had passed. 

About 5 minutes from the office there was an overpass where US 59 connects to beltway 8.  I came to refer to the crest of that overpass as "the point of epiphany" because of the number of times that when I reached that point I realized what the problem was.  I'd go in the next morning and fix it in a few minutes.

@Mr. Scram

It the current college students are better communicators I'd like to know on what basis that is.  I don't see even basic command of English. We are living through a repeat of the Tower of Babel story.

There is certainly a lot more material that must be mastered to be competent in today's world.  I don't think a BS in EE today is anything but a technician's degree.  Geology, even 80 years ago required an MS for professional status.  In geology you had to look at a lot of geology.  The problem today for engineering is you have to master about 30-35 semester hours of mathematics.  I would not suggest anyone go into engineering today as a profession without getting an MS. I think that the students would be far better served by having time to actually learn the mathematics well rather than pressing through it as quickly as possible. 

The plain fact of the matter is that after you graduate from school, even with an MS or PhD, you really don't know very much.  You've been exposed to a large range of ideas, hopefully have acquired some skills, but knowledge, the ability to use information to solve problems, really doesn't come until you have done it for several years on a daily basis.

[tornados]

Wow! Good job! I got 80, and I was very proud of myself

[paulca]

If I had to do my day job without being able to google stuff.... it would take 10-100 times longer to get anything done.

What I learnt at Uni is still partly valid, but significantly out of date.  On a day by day basis I have to deal with problems that weren't even defined a month ago using technology that didn't exist a year ago. 

The real painful ones are the ones so new, or so industry bespoke that you can't google them.  Sometimes they don't even have proper documentation and your only course of action is to read the code.

This is to say that you can't learn everything in advance, what you need to have is a good problem solving strategy and be expecting to learn new things each and every day.

The really painful part in my trade is that resource managers take this a few steps too far.  It's is extremely unpleasant to be assigned to a project as a consultant, the customer being charge $1000+ a day for your expertise when... in all reality, you didn't even know what technology existed until your manager told you what your next project would be.

[paulca]

Oh and a small story.

In the penultimate year of high school my attendance was around 15% and my presence in the "Technology" class was, literally 2 classes in that year.  I showed up to the end of year exam and when marked it was 84%.  The class went nuts and cried foul.  How could I get 85% when I was never in school and had only attended 2 classes out about maybe 35?  They demanded my paper be remarked.  So... they remarked it, a different teacher gave me 86%.  I didn't do a shred of homework or even a shred of class work.  The material was just plainly obvious to me.

It was around the time I kinda realised where my career should be pointed.

[tggzzz]

If I had to do my day job without being able to google stuff.... it would take 10-100 times longer to get anything done.

What I learnt at Uni is still partly valid, but significantly out of date.  On a day by day basis I have to deal with problems that weren't even defined a month ago using technology that didn't exist a year ago. 

Yebbut, there is little real fundamental change; it is mostly variations on a theme with some semantic sugar and a colour change.

Software language examples: C# is Java, Delphi is Pascal, Go's channels are from Hoare's CSP, Objective-C is Smalltalk.

Hardware examples: the myriad different MCUs, all programmed in C.

The real painful ones are the ones so new, or so industry bespoke that you can't google them.  Sometimes they don't even have proper documentation and your only course of action is to read the code.

Those are the fun ones. There you have to think of the fundamentals, and apply techniques first used in other domains.

Example: to reduce noise I needed a narrowband filter, so I used a technique described 20 years earlier to make a filter with a Q of 4000 using 10% components.

Fast forward 30 years, and always wanted to revisit that N-path filter to do something new. I was most irked to find Tayloe had already got there with his mixer

This is to say that you can't learn everything in advance, what you need to have is a good problem solving strategy and be expecting to learn new things each and every day.

Precisely.

The really painful part in my trade is that resource managers take this a few steps too far.  It's is extremely unpleasant to be assigned to a project as a consultant, the customer being charge $1000+ a day for your expertise when... in all reality, you didn't even know what technology existed until your manager told you what your next project would be.

Not so precisely . The customer is paying for your expertise in bringing previous experience to bear. Part of that experience is knowing how to rapidly become the local expert in the tech and the customer's problem domain. (Plus being able to spot the customer has asked for an inappropriate solution because they asked the wrong question.)

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

[tggzzz]

Oh and a small story.

In the penultimate year of high school my attendance was around 15% and my presence in the "Technology" class was, literally 2 classes in that year.  I showed up to the end of year exam and when marked it was 84%.  The class went nuts and cried foul.  How could I get 85% when I was never in school and had only attended 2 classes out about maybe 35?  They demanded my paper be remarked.  So... they remarked it, a different teacher gave me 86%.  I didn't do a shred of homework or even a shred of class work.  The material was just plainly obvious to me.

It was around the time I kinda realised where my career should be pointed.

I passed an English Literature exam witha respectable grade after 1 hours revision. I wasn't interested in the subject, and that confirmed my opinion.

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.

[paulca]

Yebbut, there is little real fundamental change; it is mostly variations on a theme with some semantic sugar and a colour change.

Software language examples: C# is Java, Delphi is Pascal, Go's channels are from Hoare's CSP, Objective-C is Smalltalk.

Hardware examples: the myriad different MCUs, all programmed in C.

No offence but this sounds like an opinion from the perspective of a low level programmer.  No that domain hasn't changed much I agree.  No matter what paradigm or trendy language you use it all boils down to basic Jackson structured programming at the end of the day.

The difficulties I am more referring to is the higher levels.  Frameworks, platforms, AaaS, SaaS, PaaS, Cloud, Big Data, Clustering etc.  Your education and experience allows you to read the documentation and be much faster at knowing what exactly to google and when, but each of these technologies introduces a lot of complexities and bespoke processes and nomenclature.

For example, if you were an experienced coder in C or Java and I sat you down to a project and said it was in a Big Data cluster using Kubernetes and Docker, running on a Hadoop cluster utilising Spark.  There is very little a basic set of core programming experience will help you with there.  Nothing is quite as it seems anymore and there is a whole new glossary of terms... trying to use it like a normal local application node will lead to pain.

[tggzzz]

Yebbut, there is little real fundamental change; it is mostly variations on a theme with some semantic sugar and a colour change.

Software language examples: C# is Java, Delphi is Pascal, Go's channels are from Hoare's CSP, Objective-C is Smalltalk.

Hardware examples: the myriad different MCUs, all programmed in C.

No offence but this sounds like an opinion from the perspective of a low level programmer.  No that domain hasn't changed much I agree.  No matter what paradigm or trendy language you use it all boils down to basic Jackson structured programming at the end of the day.

You couldn't be more wrong, about me and about JSP.

I investigated JSP (and the other contemporary techniques) in the mid 80s, and rejected it as boring and not the way forward. My decisions and choices at that time have been proven correct.

The difficulties I am more referring to is the higher levels.  Frameworks, platforms, AaaS, SaaS, PaaS, Cloud, Big Data, Clustering etc.  Your education and experience allows you to read the documentation and be much faster at knowing what exactly to google and when, but each of these technologies introduces a lot of complexities and bespoke processes and nomenclature.

Been there, done some of those, some in HPLabs, some in other companies. Always at the bleeding edge where there were no available training courses.

I got sick of seeing async protocols layered on top of sync protocols layered on top of async protocols layered on top of async protocols for at least five different layers.

And still people don't understand the "fallicies of distributed computing". They think because the framework documentation omits to mention them, the problems have been solved. Ha.

As for people understanding the limits defined by Lamport, or the Byzantine General's problems, or the split brain problem, they have no clue. They think FSMs are something to do with compilers.

For example, if you were an experienced coder in C or Java and I sat you down to a project and said it was in a Big Data cluster using Kubernetes and Docker, running on a Hadoop cluster utilising Spark.  There is very little a basic set of core programming experience will help you with there.  Nothing is quite as it seems anymore and there is a whole new glossary of terms... trying to use it like a normal local application node will lead to pain.

Well, I have archtected several high-availability soft real-time distributed systems, so I do have a clue about the "large scale" problems and how they can be ameliorated (not solved).

[coppice]

You couldn't be more wrong, about me and about JSP.

I investigated JSP (and the other contemporary techniques) in the mid 80s, and rejected it as boring and not the way forward. My decisions and choices at that time have been proven correct.

JSP was just another cult. People came back from the JSP courses like religious converts, but later realised they'd got very little from it. The mid 80s was a little late to be looking at Jackson, Yourdon, etc. They had already passed peak BS by then.

[tggzzz]

You couldn't be more wrong, about me and about JSP.

I investigated JSP (and the other contemporary techniques) in the mid 80s, and rejected it as boring and not the way forward. My decisions and choices at that time have been proven correct.

JSP was just another cult. People came back from the JSP courses like religious converts, but later realised they'd got very little from it. The mid 80s was a little late to be looking at Jackson, Yourdon, etc. They had already passed peak BS by then.

Since I picked up JSP from a book comparing all the techniques, it was late.

Once I figured out that JSP was a mechanical limited version of what I'd been doing naturally for several years, I was unimpressed.

I never knew any practitioners of any of the techniques, so I can't comment on religious conversion I, and everybody I've worked with, have always picked apart techniques and technologies to find what is good and, um, less good.

[paulca]

You couldn't be more wrong, about me and about JSP.

I investigated JSP (and the other contemporary techniques) in the mid 80s, and rejected it as boring and not the way forward. My decisions and choices at that time have been proven correct.

JSP was just another cult. People came back from the JSP courses like religious converts, but later realised they'd got very little from it. The mid 80s was a little late to be looking at Jackson, Yourdon, etc. They had already passed peak BS by then.

Em.  All CPUs still function purely on JSP. 
Sequence, selection, iteration.

At least that's what I took from my exposure to JSP.

Even a concept as ingrained as a C function has no real model in a CPU.  The stack and branch operations required to deliver it in assembler are fabricated into sequence, selection and iteration operations.

That is what I meant by it not mattering what paradigm or language you use, it all ends up at basic JSP anyway.

Granted there is the rest of JSP stuff.  It's been decades since I looked into it.  Was it not just top down design?  Modularise, divide and sub divide into smaller chunks to work with?

[paulca]

And still people don't understand the "fallicies of distributed computing". They think because the framework documentation omits to mention them, the problems have been solved. Ha.

As for people understanding the limits defined by Lamport, or the Byzantine General's problems, or the split brain problem, they have no clue. They think FSMs are something to do with compilers.

I suppose it depends on what you want to achieve by using distributed computing.

If you are simply in the "compute" space aiming for speed/throughput/latency it would be completely different to the scalability requirements and presenting dynamic platforms to allow basically architecture as a service.  aka Kubernetes.

Similarly, the Big Data concepts in distributed computing have allowed data mining and processing on a different level which simply was not achievable until recently.

Maybe you mean the age old confusion that management might have that if 1 machine takes an hour to do a job that 2 machines will take half an hour.  That's just management being fucking dumb.  I don't think I have met a manager with a degree in anything related to management, so I normally treat them with caution ... tolerate them or use them to my advantage.

[tggzzz]

You couldn't be more wrong, about me and about JSP.

I investigated JSP (and the other contemporary techniques) in the mid 80s, and rejected it as boring and not the way forward. My decisions and choices at that time have been proven correct.

JSP was just another cult. People came back from the JSP courses like religious converts, but later realised they'd got very little from it. The mid 80s was a little late to be looking at Jackson, Yourdon, etc. They had already passed peak BS by then.

Em.  All CPUs still function purely on JSP. 
Sequence, selection, iteration.

At least that's what I took from my exposure to JSP.

Even a concept as ingrained as a C function has no real model in a CPU.  The stack and branch operations required to deliver it in assembler are fabricated into sequence, selection and iteration operations.

That is what I meant by it not mattering what paradigm or language you use, it all ends up at basic JSP anyway.

Granted there is the rest of JSP stuff.  It's been decades since I looked into it.  Was it not just top down design?  Modularise, divide and sub divide into smaller chunks to work with?

Looking at https://en.wikipedia.org/wiki/Jackson_structured_programming#JSP_and_object-oriented_design it does look boring and trivial, and it looks like you are right.

It seems as if I may have been thinking of JSD https://en.wikipedia.org/wiki/Jackson_system_development

It has been a long time, and I've no regrets purging them from my memory

[tggzzz]

And still people don't understand the "fallicies of distributed computing". They think because the framework documentation omits to mention them, the problems have been solved. Ha.

As for people understanding the limits defined by Lamport, or the Byzantine General's problems, or the split brain problem, they have no clue. They think FSMs are something to do with compilers.

I suppose it depends on what you want to achieve by using distributed computing.

If you are simply in the "compute" space aiming for speed/throughput/latency it would be completely different to the scalability requirements and presenting dynamic platforms to allow basically architecture as a service.  aka Kubernetes.

It always depends

I've never bothered to look at kubernetes, so I can't comment on that.

However, one system I architected in 98/99 presumed globally distributed order fulfillment with rapidly evolving products and fulfillment mechanisms.

Others were telecom systems, where latency, horizontal scalability and availability are key. And the telco system changes without notice - even the network operators know they don't know what's in their system, let alone other companies' systems

Yes, that did involve evaluating and implementing both clustered frameworks and platforms (J2EE, Spring, JAIN SLEE), and custom coded servers.

Similarly, the Big Data concepts in distributed computing have allowed data mining and processing on a different level which simply was not achievable until recently.

Indeed, but there have been very few fundamental advances there.

Maybe you mean the age old confusion that management might have that if 1 machine takes an hour to do a job that 2 machines will take half an hour.  That's just management being fucking dumb.  I don't think I have met a manager with a degree in anything related to management, so I normally treat them with caution ... tolerate them or use them to my advantage.

I've seen all sorts of dumbness, technical and managerial. I'm glad I'm out of all that!

[coppice]

Looking at https://en.wikipedia.org/wiki/Jackson_structured_programming#JSP_and_object-oriented_design it does look boring and trivial, and it looks like you are right.

It seems as if I may have been thinking of JSD https://en.wikipedia.org/wiki/Jackson_system_development

It has been a long time, and I've no regrets purging them from my memory

I think JSD was just something they cooked up when the business from JSP was tailing off. The essence of these things is to be profitable, not useful.

[schmitt trigger]

  It's just like building muscle.  No exercise, no muscle.

Or as physical trainers like to say: No pain, No gain.

[free_electron]

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.

[tggzzz]

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 ?

You really should read (or re-read) Asmov's "Profession" - he addresses that point and others. The key points are just as valid as when it was written. https://www.abelard.org/asimov.php and try to ignore the geocities colour scheme

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.

Agreed.

[coppice]

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.

A lot of this is a scam that lets low ability people get high marks in exams, by being drilled for hours in expensive private tuition, to turn a thinking task into a simple memory one. When these formulae are derived in class, and you work through where they come from, they are a genuine learning exercise. Reducing them to a memory exercise is a perversion of learning.

[paulca]

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