An observation on homework problems

[rhb]

Almost 40 years ago, I was told by an EE undergrad sitting next to me that I would never pass Physics II, EM, because I had a degree in English lit and "This is where they weed out the engineers."

I had the highest score on the final, an 89.  The class average was 45.

This led to the following observation:

Of the people I knew, the ones who made an A would beat on homework problems until they solved them and only sought help after 4 or more hours of failure.  Those who made a B went for help after 3 hours.  Those who made a C sought help after 2 hours.  The D and F students sought help after only an hour or less of effort.

The point of homework problems is to develop skills by exercising.  It's just like building muscle.  No exercise, no muscle.  There are no shortcuts.  You may get a sheet of paper, but without the exercise it has no value.

[golden_labels]

Hmm… were you exercising for 40 years to pass the exam? That would confirm their assessment! </JOKE>

Of course there is no way to score good marks without exercises. It’s not only about acquiring knowledge. It is about speed. The time on an exam is limited and one is usually working under stress. Even if the student knows the subject perfectly, they will fail to recognize the path needed to solve a problem. Exercises make you automatically match partial solutions to typical situations in the blink of an eye.

The years of exercises made me sensitive to some of the fallancies related to statistics, like concluding causation from correlation. In this particular case the students, who got worse grades, might have asked for help earlier because of the common factor that caused both the low score and the need for help.

[rhb]

Correlation does not imply causation.  David Hume showed that.  No statistics required.   Just logic.

I worked physics problems 3-4 hrs/day 3-4 days/wk all semester.  I had the great advantage over my classmates that I was a grad student and only had to carry 12 hours.  So I had the time. The extra 3-4 hours the engineering students had to take made it impossible for most to put in the same amount of time on physics.  I was working on an MS in geology.  By the end of the 6th week I had read all my geology textbooks cover to cover.  So I was just attending class to review what I had learned and ask questions.  I'd sit in class and sometimes eat an orange while everyone else was taking notes.  This led one instructor to pepper me with questions for the first 3-4 weeks of class.  I always knew the answers so eventually he moved on to the other students.

I was failing Calculus I at the start, 17 out of 100 on the first quiz.  I  was advised to take Precalculus.  I took that for my BA math requirement and was so bored I did not do any homework and got a C.  I'd taught myself algebra in 6th grade and trig in the 8th.  No way I was taking Precalculus  a 2nd time.

I did calculus problems 3-4 hrs/day 5-6 days/wk.  I went from 2 out of 20 on the weekly quiz to 18 or 19 at the end of the semester.  The person that triggered the inference was the class hotshot from my Cal I class.  We were sitting waiting for the physics TA to show up.  We had both spent 4+ hours on the same problem the day before.

My comment is really an extension of the common phenomenum of people giving up without even trying.

I was barely a B student overall.  I never cared about grades.  My focus was on learning.  If I thought something was important, that got the bulk of my attention.  If the instructor thought something else was more important and I missed that on an exam, I did not care.

I have a close friend who had a 4.0 GPA for is PhD work at Austin.  We took several courses together.  There have been a number of instances where I had to explain to him some basic facet of what we had both studied some years after we finished the course. That never happened often, but I was always quite surprised.  The real shocker was the nature of the Cristoffel symbol in tensor analysis.  I had to drop the class because I simply could not spend enough time on it.  But a year or two later I was explaining to him that it was the derivative of one coordinate system in relation to another.  Very basic.

The real world is not an exam.  It requires solving problems for which there may not be clear answers.  It is  experience trying multiple techniques for attacking a problem that matters in real life.

The reduction of university education into job training has littered the landscape with "professionals" who are utterly incompetent.

What do you call a scientist who took remedial classes?  An engineer. 

Most of engineering is a few courses in physics and a lot of mathematics.  The rest is an ocean of details which one needs to know to work quickly, but which are not essential prior knowledge for solving a problem.

[HighVoltage]

In the last few years I come more and more across students in the field of science and engineering that believe that homework is a ridicules invention of the past generation. These students want to pass tests without ever doing any serious training and just look at problem shortly. And with many new rules, that you can pass with 39% of correct answers, some of these students even pass their test and proof to me that I was wrong.

 

[rhb]

Most exemplified by:

"If I need to know that I'll look it up on the internet."

I usually respond by saying I am not good at predicting the future.  So I learn everything I can just in case I need the knowledge.  In fact, we only understand things in the context of what we already know.  The advantage of age and experience is we acquire an ever greater range of contextual knowledge.  Or at least, some of us do.

[HighVoltage]

Exactly!
It can all be looked up within seconds.

I have been looked at very strangely, when I use basics and develop a formula for something in physics.
One very simple example would be the formula for the oscillating pendulum: t = 2 * PI * SQRT (l/g)
It took me many hours as a student to do it myself and I was very much exited about it. These days, students get bored, when I try to show them the solution step by step.

Of course, not all students are like this but the trend is definitely going in this direction.

[nctnico]

Most exemplified by:

"If I need to know that I'll look it up on the internet."

I usually respond by saying I am not good at predicting the future.  So I learn everything I can just in case I need the knowledge.  In fact, we only understand things in the context of what we already know.  The advantage of age and experience is we acquire an ever greater range of contextual knowledge.  Or at least, some of us do.

The problem is that in today's world you are likely not to have enough time to learn everything. The complexity is just too big. So instead it makes more sense to built from existing building blocks. Kind of like using software libraries.

[rhb]

The problem is that in today's world you are likely not to have enough time to learn everything. The complexity is just too big. So instead it makes more sense to built from existing building blocks. Kind of like using software libraries.

There has *never* been a time when it was possible to learn everything.  The complexity is *exactly* why a thorough grounding in the fundamentals is so important.  Much of the complexity in today's world is the consequence of very bad decisions which ignore the impact of complexity.

If you're young enough, you may get to see the consequences of the philosophy you espoused above.  It will not be pleasant and you have less than a 10% chance of surviving the event.  After that technology will slowly regress to neolithic levels over the course of a few hundred years.  And at some point the human species will become extinct as have the majority of the species which have ever populated the earth.

We have stripped the earth of all the resources which are accessible to small groups with limited technology.  What is left requires tens of thousands of people working in an organized society to access.  After the die off, neither the technology nor the level of organization required will exist.  And most of the knowledge needed will be gone along with the means to power it.  The technological regression is an inevitable  consequence of the staggering waste of natural resources over the last 200 years.

When that will happen and what the proximate cause will be no one knows.  But I could list plausible causes for a week.  None of which involve contemporaneous human actions.  Just natural changes in the environment of the earth.  A Yellowstone caldera collapse, or a Deccan Traps basalt flood.  An no one has come up with a satisfactory explanation of the major extinction events which form the boundaries of geological time.

My MS focus was minerals, so I developed an acute sense of the distribution of metals and other elements like rare earths.  For lack of such work I went into the oil industry from which I developed an equal understanding of fossil fuels.

Those who do not know history are shocked and amazed when the inevitable occurs.

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 upon what we do next.

[Buriedcode]

You're assuming that how "good" someone is at a subject is down to their effort.  Often with mathematics some students don't "get it" at all when something is initially explained.  It isn't some nice linear thing where they just keep chipping away at a problem - what if they don't even know how to approach it?  That is why we have teachers to explain things in different ways, accommodating for different students.  And of course, there are varying degree's of interest - some will put more effort in because they enjoy it, others will hate it, so will do the bare minimum.

I'm not sure what this topic is about.  Is it an observation that homework "these days" is easier? or there's less of it? or that younger generation is less knowledgeable?  The internet has indeed changed things - but it is still more important to know how to find something out than it is to memorize it.  After all that is mostly what general education is about - teaching people how to learn, absorb information and ideas to make them useful.  If people have become reliant on it, well, so be it.  Before the internet there were books.  In some ways I think it has gone too far, like spell-check for example - I know some who really can't spell at all because they just run spell-check rather than learning correct spelling.  What's worse though are those who can't spell but don't even use spell check - there is no excuse for that.

It's all well and good memorizing, or becoming knowledgeable in many fields, but ultimately, it's your time.  I agree that engineers, and of course, scientists, should have a grasp of all the fundamentals - so one understands the underlying principles, but that doesn't meant to say all engineers should work from first principles all the time - thats just a waste of everyone's time. 

[rhb]

I'd like to return to the original topic, homework exercises.

The purpose of these is to build proficiency in extending what you know beyond your current boundaries of knowledge.  Good instructors and authors put a lot of effort into crafting exercises which are a small step from what you have been shown into things you have not been shown.  It is impossible to show you everything and pointless as that would require a perfect memory.  The purpose is to build the ability to go from what you do know into areas you do not know.  The PhD is the culmination of that to the highest level.  At least it is for those who "get it".  There are far too many PhDs who  only got their degree because their supervisor couldn't justify tossing them out.

Those who seek assistance too soon defeat that purpose.  They may get a certificate proclaiming their knowledge, but the certificate is just a piece of paper.  It is not the skill to move from the known to the unlnown.

[Kjelt]

You don't know what you don't know, so solving homework on subjects that have not been taught are making this generation just to google to find the answers, so it is pointless IMO. That is homework of previous generations where the answers could only be found in the library, or further on in the books.

My observation of the new geberations of students is impatience. They want something, they want it now, not in hours of trial and error. It is the arduino generation and does it matter actually how they make it work in he end, as long as they make it work? Same with homework, I am glad if they do it instead if having to s of excuses to not have it.

[IanB]

I'm not sure what this topic is about.
...
It's all well and good memorizing, or becoming knowledgeable in many fields, but ultimately, it's your time.  I agree that engineers, and of course, scientists, should have a grasp of all the fundamentals - so one understands the underlying principles, but that doesn't meant to say all engineers should work from first principles all the time - thats just a waste of everyone's time.

I agree, I don't think you have quite understood what this topic is about.

It is not about memorizing, or becoming knowledgeable (i.e. "knowing facts"). It is about exercising the brain muscle.

In the real world of engineering there is a need to solve problems. Problem solving is a skill that has to be learned, it's about recognizing patterns and situations, about being able to "fill in the gaps" with appropriately learned intuition, and knowing what are the right things to do in what order to unlock the puzzle and find a solution.

These are all skills that take practice and effort and dedication. They don't come from books and the internet. They can't be taught in class (but they might be coached by a tutor).

There is an analogy here with sports and many other pursuits. To excel at any given sport you have to practice every day and work hard on your skills. Someone can't make you into a competitive tennis player just by telling you how to play each shot in a classroom. You can't make yourself into a competitive tennis player just by reading books or by watching other people play. To get better at tennis you have to put time in on the court, learning by doing. You have to work at it.

(Edited for clarification)

[rhb]

You don't know what you don't know, so solving homework on subjects that have not been taught are making this generation just to google to find the answers, so it is pointless IMO. That is homework of previous generations where the answers could only be found in the library, or further on in the books.

My observation of the new geberations of students is impatience. They want something, they want it now, not in hours of trial and error. It is the arduino generation and does it matter actually how they make it work in he end, as long as they make it work? Same with homework, I am glad if they do it instead if having to s of excuses to not have it.

The hallmark of a well trained PhD *is* knowing what they don't know.  Knowing *very* precisely what you know and what you don't know, the exact location of the boundary, is essential to the process of discovery.

Today we have a lot of PhDs who cannot separate facts from hypotheses.  Some of them are Nobel laureates.

A very common homework problem asks the student something they have been taught, but places it in a different context so they have to look for the relationship. The most common problem simply asks the student to apply the information they have been given to solving a problem.

I was trained as a scientist, not an engineer.  So I am more accustomed to reframing the question in terms of first principles.  Good engineers do the same thing.  Poor ones are helpless if they encounter something they've not memorized.  Hence all the hand wringing about becoming obsolete 10 years after graduation.  Good engineers become obsolete when they die, not before.

The reframing is for the purpose of identifying the problem.  Then I consider what I already know and whether I already know how to find the answer or if it is something new.  I have had countless people come in my office at work asking that I write a program for them.  Nearly always after I asked a few questions they said, "Oh, I know how to do that." and ran off.

IanB got my point very precisely.  I'd quibble with his usage of "knowledge", but that's a very minor point.  I define "knowledge" as the ability to apply information to resolve a problem or question.  A consequence of 5 years spent getting a liberal arts degree in English literature.

Practice is required even if you have already mastered something.  I was skilled at drywall and concrete work.  I did a lot of that to pay for my MS.  The trowel trades depend on your sense of touch.  If you don't do it for a long time, you lose the feel and it will take at a minimum several days to get it back. Playing a musical instrument is the same way.  If you don't play every day your skills diminish rapidly.  There is a 3-4 minute guitar piece I wrote which I cannot play.  And as I am musically illiterate, it takes a huge struggle over several days just to remember it.  Even when I can remember it, it's quite difficult and took me a month to learn to play when I wrote it.

If you still doubt the importance of actually *doing* things, pull out a calculus book and solve some integrals or differential equations.

[IanMacdonald]

The problem is that in today's world you are likely not to have enough time to learn everything. The complexity is just too big. So instead it makes more sense to built from existing building blocks. Kind of like using software libraries.

The problem with this approach is that you become an 'appliance user' - Never understanding how anything you use works. That, and you end up using 0.001% of each of ten different 1GB software libraries to do a job that could be done with 1KB of proper code. This is basically why Windows 7 and 10 are so bloated compared to Windows XP.

You see the same thing on the Web, where someone wants to start a website but has little knowledge of how to, so they start by installing WordPress or the like. Because, it seems like it will make the process 'automatic' -or something. The consequence is that to create anything original they now need to understand not just a simple and easily learned markup like HTML, but labyrinthine object-oriented PHP code with deeply nested functions, plus bespoke markup for theme definitions etc.  Since they realise they are never going to understand this, they instead start searching for ready-written themes or plugins that will do what they want,  find that most of them are junk, and of the few that aren't junk, some have nasty security vulns.

If they added up the time spent on this process they'd probably be surprised to find that they could have learned the basics of HTML a lot more quickly than it's taken. Plus, learning HTML is an ongoing process, and as they learn more they can do more, whereas with the 'appliance-user' approach of searching for CMS plugins it's basically like rolling dice over and over again and hoping you get a six this time. A skill which doesn't actually improve with time spent doing it.

[rhb]

A very nice summary of where we are today and why.  Thank you.

[nctnico]

A very nice summary of where we are today and why.  Thank you.

No, it is old people 'everything used to be better' thinking. Re-inventing the wheel to understand how the wheel works isn't a good use of time. Just know what kind of wheel you need for a certain situation and order that wheel off-the-shelve is a much better use of time. Let a wheel specialist figure out how to design & make the wheel.

[tpowell1830]

As nctnico observed, this does sound a bit like 'everything used to be better' thinking. However, as a person that did not get the level of education that RHB has, I have found that the key to all of my successful completion of all my projects was focus.

Focus can be learned, and although working those problems for hours is an exercise, as RHB put it, the key was focus. As I have mentioned in the past, I am an old fart at 65, but my accumulated knowledge is a result of working the problem in a focused manner. Albeit I have good intuition for how things work, sometimes it is not obvious and that is where things grind down to a slower pace.

I do agree that the problems that are already solved are there for the picking, but we should always look at things with a critical eye to be sure that what we see is optimized, and don't take the word of the original designer/engineer. Also, ask the hard questions whether it is best optimized for our solution in the project.

Again, there is a lot of ageism out there where young people don't trust old people, but there are gems out here that can be utilized if needed. I never said that older people are always right, but, we do have a lot of experience that we can share for the right person and situation. We are what we are, no more, no less.

my 2 cents...

[nctnico]

As nctnico observed, this does sound a bit like 'everything used to be better' thinking. However, as a person that did not get the level of education that RHB has, I have found that the key to all of my successful completion of all my projects was focus.

Focus can be learned, and although working those problems for hours is an exercise, as RHB put it, the key was focus. As I have mentioned in the past, I am an old fart at 65, but my accumulated knowledge is a result of working the problem in a focused manner. Albeit I have good intuition for how things work, sometimes it is not obvious and that is where things grind down to a slower pace.

I do agree that the problems that are already solved are there for the picking, but we should always look at things with a critical eye to be sure that what we see is optimized, and don't take the word of the original designer/engineer. Also, ask the hard questions whether it is best optimized for our solution in the project.

Agreed. I think it is more important to be able to analyse a problem and recognise a good solution rather than being able to master every detail of the solution. The latter can actually be counter productive because it is easy to loose sight of the big picture.

[Kjelt]

A very common homework problem asks the student something they have been taught, but places it in a different context so they have to look for the relationship. The most common problem simply asks the student to apply the information they have been given to solving a problem.

Actually IMO many math and physics highschool homework asignments are nowadays just comprehensive reading asignments where the student has to extract the parameters for the formulas from the "story".
I already had a different topic about this so will not elaborate here.

I agree with most part you wrote after that.

Playing a musical instrument is the same way.  If you don't play every day your skills diminish rapidly.

I played piano for years, stopped a few years and picked it up now and then. The oldest pieces I played for a long time are still there, I believe they are somewhere embedded in my subconsciousness , if I rationaly try to think what key I need to play and when, it is gone, if I just do it, it is all still there. Strange how the human brain works. I must admit it takes time to regain the speed and precision but ut will probably never be gone.
Just like swimming or riding a bicycle.
I agree that practice makes the master, what was it 10000 hours to master any subject ofcourse if not limited by physical ability and/or brainpower.

[rhb]

FWIW I have 1 hour of WATFIV FORTRAN as my sole computer related credential.

I've gone from a BA in English lit to an MS in hard rock geology to reflection seismology, which makes the DSP that most EEs do look like an afternoon nap.

I fear complexity for the same reason Ken Thompson feared complexity.  We are now dependent upon things that no single person is able to understand.  I spent a lot of time fixing bugs in million line code bases.   I share Thompson's discomfort with anything over 10-20 thousand lines.  I just learned to swim through the mess.

@kjelt the real world doesn't give you the formula.  What you get is a bunch of information which is often incomplete and much of which is extraneous.   Quickly determining if you have enough information is valuable.  I'd loved to give examples from geology, but I'd get banned again if I did.

[tooki]

In the last few years I come more and more across students in the field of science and engineering that believe that homework is a ridicules invention of the past generation. These students want to pass tests without ever doing any serious training and just look at problem shortly. And with many new rules, that you can pass with 39% of correct answers, some of these students even pass their test and proof to me that I was wrong.

I think part of the problem is that until university, a lot of the homework is genuinely useless. We know from studies that the amount of homework assigned to kids doesn't make a big difference in knowledge acquisition, so it's clear that at least in some subjects, the homework is actually a waste of time. I can't blame students for thinking homework is ridiculous when (as I often experienced it myself) it didn't actually help them learn.

And on the other hand, I absolutely agree that practice is essential.

A very common homework problem asks the student something they have been taught, but places it in a different context so they have to look for the relationship. The most common problem simply asks the student to apply the information they have been given to solving a problem.

Actually IMO many math and physics highschool homework asignments are nowadays just comprehensive reading asignments where the student has to extract the parameters for the formulas from the "story".

While I find the "stories" to often be contrived, I think this approach does fundamentally make a lot of sense, because one of the huge disconnects between school and the workplace, IMHO, is that people have no idea when and how to apply the math they've learned in school. I mean, look at how many people learned algebra, yet can't even begin to apply it to real-world situations?

[rhb]

A major reason why kids in high school struggle with algebra, geometry and trig is that their teachers have no clue how to apply the skills.  The story problems would be much better if the authors and teachers had some real world experience of using them.

With the exception of mechanical and electrical repair, they are essential to all the skilled trades.  The high school math subjects are routinely used in carpentry, plumbing, machining, etc on a daily basis.

Without a concrete explanation of what the tools are used for it is small wonder that the kids are not interested.  I enrolled in Advanced Applied which was a quick summary of linear algebra and integral transforms when I was getting my MS in geology.  I had not a clue how to use the material at the time, so I dropped the course because it was eating up so much time.

My experience over the course of my career was that if I could get the problem into the appropriate mathematical form I could find a solution quite easily.    The really hard part was figuring out what the appropriate form was.  This is especially a problem for me with differential equations.  I pretty much know how to solve the wave equation and that's it.  For everything else I hunt through my books for a problem that matches mine.

Of course, the kids are told that they should go deeply into debt for a completely useless piece of paper.  The shameless exploitation of the students by the faculty and administration is appalling, but best left for another time.

[Echo88]

"I'd loved to give examples from geology, but I'd get banned again if I did."
Why?

[Mr. Scram]

Is this another thread of old men yelling at clouds? Because it sounds an awful lot like it. The world has changed and information has become much more readily available. You'll still need to practice your skills, but ignoring this fundamental change means you're woefully inefficient compared to those that adapt. Research indicates that younger folks retain less information than they used to but are more efficient at filtering and finding what they need from large volume of information, which is just what this era of copious amounts of available information requires.

[Kjelt]

Is this another thread of old men yelling at clouds?

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.