General > General Technical Chat
An observation on homework problems
0culus:
--- Quote from: free_electron on August 13, 2020, 03:25:04 pm ---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.
--- End quote ---
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:
--- Quote from: coppice on August 16, 2020, 01:49:45 am ---
--- Quote from: tggzzz on August 13, 2020, 12:12:54 pm ---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.
--- End quote ---
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?
--- End quote ---
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:
--- Quote from: tggzzz on August 16, 2020, 08:19:45 am ---
--- Quote from: coppice on August 16, 2020, 01:49:45 am ---
--- Quote from: tggzzz on August 13, 2020, 12:12:54 pm ---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.
--- End quote ---
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?
--- End quote ---
I wouldn't over-analyse the plot choices an author uses to lead readers to the key points!
--- End quote ---
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.
--- Quote from: tggzzz on August 16, 2020, 08:19:45 am ---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 :)
--- End quote ---
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:
--- Quote from: pgo on August 17, 2020, 09:52:04 am ---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.
--- End quote ---
You might be focussing on the students you can't relate to - the ones with a terrific memory, but poor critical thinking.
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