Debate: Grades VS Knowledge

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Ralith The Third
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Re: Debate: Grades VS Knowledge

Postby Ralith The Third » Tue Mar 17, 2009 9:56 pm UTC

Rilian wrote:
Ixtellor wrote:I personally would love to lecture every day,


There's a teacher at my school who says lecturing should be avoided, because people don't learn from it. Actually, there are quite a few teachers in the math department who say that.

and they learned math HOW?
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Dwarph
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Re: Debate: Grades VS Knowledge

Postby Dwarph » Wed Mar 18, 2009 1:20 am UTC

Ok here is my theory on grades. They take away from the real reason we go to school. School is supposed to be about learning. If you ask me the point of school, I will say, to get good grades. Why do I want good grades? To get into college, so I can get more good grades. Then those good grades will get me a job and I'll learn how to do that job. When I'm sitting in school, every assignment that is presented to me I think, does this directly affect my grade? If the answer is no, the assignment isn't going to get done or at least done with any substantial thought. Sure, I might have to learn or memorize a few things to do well on tests. My point is that I go to school not to learn, but to get good grades.

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Re: Debate: Grades VS Knowledge

Postby Rilian » Wed Mar 18, 2009 2:47 am UTC

Ralith The Third wrote:
Rilian wrote:
Ixtellor wrote:I personally would love to lecture every day,


There's a teacher at my school who says lecturing should be avoided, because people don't learn from it. Actually, there are quite a few teachers in the math department who say that.

and they learned math HOW?

They probably learned it through investigation, like everyone does.
And I'm -2.

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Re: Debate: Grades VS Knowledge

Postby Ralith The Third » Wed Mar 18, 2009 11:53 am UTC

Rilian wrote:
Ralith The Third wrote:
Rilian wrote:
Ixtellor wrote:I personally would love to lecture every day,


There's a teacher at my school who says lecturing should be avoided, because people don't learn from it. Actually, there are quite a few teachers in the math department who say that.

and they learned math HOW?

They probably learned it through investigation, like everyone does.

I might be wrong here, but aren't college classes generally required for teaching jobs, and aren't they generally in lecture form?
Omni.

cathrl
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Re: Debate: Grades VS Knowledge

Postby cathrl » Wed Mar 18, 2009 1:53 pm UTC

achan1058 wrote:I think I have a solution to this problem:

An insanely hard take home final that you have 2 weeks to complete. Surely, you won't be limited by time, nor will you be regurgitating answers. You can make all question test for knowledge and skills if you desire, and that is not difficult to do if you are not bounded on the difficulty. There is no test of memorization, as they will have their notes in front of them. You are even allowed to use Maple if desired. (in fact, if it is a computational course, make questions to force them to use it is a good idea) If it is difficult enough, no one will cheat. (since the people who knows stuff won't want to get their grade lowered when it comes down to the curving, and the people who don't, it doesn't matter) The only issue is that you will probably be giving 0's to 3/4 of the class, depending on how nastily difficult you make it.

(I have take home's before, but nothing this bad. 24 hours and moderate difficulty. I did heard about a hard 1 week take home from some other people, and how the prof for another course was commenting that they will probably need all that time, though.)


I guarantee you my kids will both get top grades on one of those. Even though one of them is only 9.

So will all the other kids of parents with higher degrees and/or professional qualifications in the subject you are testing. Your "no one will cheat" rather naively assumes that no one has access to people with a significantly higher level of knowledge and ability than the course they are doing is aiming at. There are plenty of people out there for whom even undergraduate final level is not "hard".

Someone else mentioned vivas. We used to have one per term, after an exam, where we'd be grilled on our answers and lack of answers. It was a saving grace if you'd made a howling mess of something, because you could discuss that you knew you'd made a howling mess, what you'd got wrong, and why.

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Re: Debate: Grades VS Knowledge

Postby achan1058 » Wed Mar 18, 2009 2:24 pm UTC

cathrl wrote:I guarantee you my kids will both get top grades on one of those. Even though one of them is only 9.

So will all the other kids of parents with higher degrees and/or professional qualifications in the subject you are testing. Your "no one will cheat" rather naively assumes that no one has access to people with a significantly higher level of knowledge and ability than the course they are doing is aiming at. There are plenty of people out there for whom even undergraduate final level is not "hard".
Well, I guess we just need to make it harder than that Putnam! As long as it is difficult enough, no one can cheat. Though I suppose the number of student which will get 0 will approach 100%. More realistically, an "explain your work" session afterwards should work reasonably well in detecting cheaters like that.
Last edited by achan1058 on Wed Mar 18, 2009 2:27 pm UTC, edited 2 times in total.

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Re: Debate: Grades VS Knowledge

Postby Ixtellor » Wed Mar 18, 2009 2:24 pm UTC

Rilian wrote:
Ixtellor wrote:I personally would love to lecture every day,


There's a teacher at my school who says lecturing should be avoided, because people don't learn from it. Actually, there are quite a few teachers in the math department who say that.


There is a lot of information on what % of information people retain compared to how it was given.

Straight lecture has the lowest retention bonus of any other method and this is mostly undisputable.

Here is why I like lecture:

1) It is my firm belief that there is no 1 perfect way to teach. I think teachers should do whatever works best for them. Lecture happens to be my forte.

2) Lecture works well when it goes like this:
Students read material on their own then come to class.
The teacher goes into detail, fleshes out the subject matter, answer questions, and goes into depth for understanding.
Teacher gives a test on the material that holds students responsible for mastering the subject matter and they study for the test.
This gives students exposure to the same material at least 3 times.

Furthurmore, I use a brief outline that helps students focus on the most important information AND I use a lot of visual aids and representations so they get exposed to new materials in another fashion.

3) Clearly students are going to skip or not due 'their part' but this will usually be reflected in their grades. I suppose I have kind of accepted the fact that students are going to learn everything in my courses in a long term fashion. But I generally try to distinguish from things that are really really really important like Keynesian economic principles and worry less about things like limited partnerships and Buckley v Valero. I realize not every student is going to be an economics or poly sci major and/or be a business owner. And if they are, they will see all this material again.
My main goal is going to be making sure they do recall the very important "big picture" stuff and in AP classes that they PWN the test.

Ixtellor
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Re: Debate: Grades VS Knowledge

Postby TheKrikkitWars » Thu Mar 19, 2009 2:38 am UTC

Jorpho wrote:
ThomasS wrote:I noticed how the book kept talking about all these experiments that were done and I found those sections rather dull and pointless. Those stories become a lot more compelling when you start to realize what the researchers had to start with and what you have to do, even today, in order to reproduce those results.
Have you never had the chance to do a long and tedious experiment yourself? Do you actually think it would be exciting to spend a few hours staring at tiny charged drops of oil, or counting scintillation flashes? Would you rather have students complaining about having to do dull and pointless work to derive an equation they could have just read about?


At least they learnt something out of it, If they read it in a book then spend the rest of the hour copying said book down, then their time is being wasted even more.

My entire Sixthform maths and further maths courses were taught in a work from first principles, lets all try to generate a proof for... kind of way, it sticks really well compared to other styles of learning.

With reference to dull experiments, I just spent my day making up 30 odd erlenmeyer flasks of 10cc 0.1M phenol soln, 10cc 1M KBr Soln 3 drops of methyl orange, adding 25cc of varying concentrations of H2SO4 at various temperatures and measuring the time taken for the solution to turn colourless. All in order to create a calibration chart for some kinetics work, it was unavoidable and tedious with some flasks taking upto 2.5 hrs. But I did learn something from it.
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Re: Debate: Grades VS Knowledge

Postby Jorpho » Thu Mar 19, 2009 3:39 am UTC

TheKrikkitWars wrote:With reference to dull experiments, I just spent my day making up 30 odd erlenmeyer flasks of 10cc 0.1M phenol soln, 10cc 1M KBr Soln 3 drops of methyl orange, adding 25cc of varying concentrations of H2SO4 at various temperatures and measuring the time taken for the solution to turn colourless. All in order to create a calibration chart for some kinetics work, it was unavoidable and tedious with some flasks taking upto 2.5 hrs. But I did learn something from it.
And you're saying it's quite impossible that you could have spent all that time in some other way and learned something more valuable (however you care to define value) ?

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Re: Debate: Grades VS Knowledge

Postby Ralith The Third » Thu Mar 19, 2009 10:37 pm UTC

Ixtellor wrote:
Rilian wrote:
Ixtellor wrote:I personally would love to lecture every day,


There's a teacher at my school who says lecturing should be avoided, because people don't learn from it. Actually, there are quite a few teachers in the math department who say that.


There is a lot of information on what % of information people retain compared to how it was given.

Straight lecture has the lowest retention bonus of any other method and this is mostly undisputable.

Here is why I like lecture:

1) It is my firm belief that there is no 1 perfect way to teach. I think teachers should do whatever works best for them. Lecture happens to be my forte.

2) Lecture works well when it goes like this:
Students read material on their own then come to class.
The teacher goes into detail, fleshes out the subject matter, answer questions, and goes into depth for understanding.
Teacher gives a test on the material that holds students responsible for mastering the subject matter and they study for the test.
This gives students exposure to the same material at least 3 times.

Furthurmore, I use a brief outline that helps students focus on the most important information AND I use a lot of visual aids and representations so they get exposed to new materials in another fashion.

3) Clearly students are going to skip or not due 'their part' but this will usually be reflected in their grades. I suppose I have kind of accepted the fact that students are going to learn everything in my courses in a long term fashion. But I generally try to distinguish from things that are really really really important like Keynesian economic principles and worry less about things like limited partnerships and Buckley v Valero. I realize not every student is going to be an economics or poly sci major and/or be a business owner. And if they are, they will see all this material again.
My main goal is going to be making sure they do recall the very important "big picture" stuff and in AP classes that they PWN the test.

Ixtellor

With math concepts, many books, at least before college, SUCK at imparting knowledge, so I end up having the lecture, then look over it myself, then ask questions, then homework/test.
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Re: Debate: Grades VS Knowledge

Postby Rilian » Thu Mar 19, 2009 11:05 pm UTC

Ralith The Third wrote:
Rilian wrote:
Ralith The Third wrote:
Rilian wrote:
Ixtellor wrote:I personally would love to lecture every day,


There's a teacher at my school who says lecturing should be avoided, because people don't learn from it. Actually, there are quite a few teachers in the math department who say that.

and they learned math HOW?

They probably learned it through investigation, like everyone does.

I might be wrong here, but aren't college classes generally required for teaching jobs, and aren't they generally in lecture form?

The poor ones are. It's better to learn by experiment and practice. I like it when teachers do it that way.
And I'm -2.

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Re: Debate: Grades VS Knowledge

Postby Ralith The Third » Fri Mar 20, 2009 1:33 am UTC

Rilian wrote:
Ralith The Third wrote:
Rilian wrote:
Ralith The Third wrote:
Rilian wrote:
Ixtellor wrote:I personally would love to lecture every day,


There's a teacher at my school who says lecturing should be avoided, because people don't learn from it. Actually, there are quite a few teachers in the math department who say that.

and they learned math HOW?

They probably learned it through investigation, like everyone does.

I might be wrong here, but aren't college classes generally required for teaching jobs, and aren't they generally in lecture form?

The poor ones are. It's better to learn by experiment and practice. I like it when teachers do it that way.

Math teacher.
I may be wrong, but in terms of doing math, you have to be taught the formulas first, and I've yet to run across a good textbook for teaching such.
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Re: Debate: Grades VS Knowledge

Postby TheKrikkitWars » Fri Mar 20, 2009 3:05 am UTC

Jorpho wrote:
TheKrikkitWars wrote:With reference to dull experiments, I just spent my day making up 30 odd erlenmeyer flasks of 10cc 0.1M phenol soln, 10cc 1M KBr Soln 3 drops of methyl orange, adding 25cc of varying concentrations of H2SO4 at various temperatures and measuring the time taken for the solution to turn colourless. All in order to create a calibration chart for some kinetics work, it was unavoidable and tedious with some flasks taking upto 2.5 hrs. But I did learn something from it.
And you're saying it's quite impossible that you could have spent all that time in some other way and learned something more valuable (however you care to define value) ?


Indeed, I wouldn't have the calibration charts I required, and so couldn't get on with more interesting science. Sometimes we do dull things because we have to.
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Re: Debate: Grades VS Knowledge

Postby Jorpho » Fri Mar 20, 2009 3:16 am UTC

TheKrikkitWars wrote:
Jorpho wrote:
TheKrikkitWars wrote:With reference to dull experiments, I just spent my day making up 30 odd erlenmeyer flasks of 10cc 0.1M phenol soln, 10cc 1M KBr Soln 3 drops of methyl orange, adding 25cc of varying concentrations of H2SO4 at various temperatures and measuring the time taken for the solution to turn colourless. All in order to create a calibration chart for some kinetics work, it was unavoidable and tedious with some flasks taking upto 2.5 hrs. But I did learn something from it.
And you're saying it's quite impossible that you could have spent all that time in some other way and learned something more valuable (however you care to define value) ?
Indeed, I wouldn't have the calibration charts I required, and so couldn't get on with more interesting science. Sometimes we do dull things because we have to.
Okay, if you had someone else to do this dull work of making these calibration charts, could you have spent all that time in some other way and learned something etc?

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Re: Debate: Grades VS Knowledge

Postby Rilian » Fri Mar 20, 2009 5:06 am UTC

Ralith The Third wrote:I may be wrong, but in terms of doing math, you have to be taught the formulas first,

You're wrong. Or maybe communication fails.
And I'm -2.

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Re: Debate: Grades VS Knowledge

Postby achan1058 » Fri Mar 20, 2009 5:24 am UTC

Ralith The Third wrote:I may be wrong, but in terms of doing math, you have to be taught the formulas first, and I've yet to run across a good textbook for teaching such.
Formula != math. Formula = human interpreters. We have computers, there's no need to train humans on how to run algorithms using poorly written pseudo code. In fact, if you know the definitions and what you are trying to solve and do, you can derive all the formula from scratch. (Well, it might be a bad idea to attempt to derive something that involves multiple summations, but it can be done.) By the way, this might surprise you, there are branches of mathematics with little or no formula. For example, much of graph theory.

In fact, formula drilling should be reserved for the most uninterested and unmotivated kids. (If they can't learn the interesting bits of math, they need to at least know how to compute.)

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Re: Debate: Grades VS Knowledge

Postby Ralith The Third » Fri Mar 20, 2009 11:09 am UTC

achan1058 wrote:
Ralith The Third wrote:I may be wrong, but in terms of doing math, you have to be taught the formulas first, and I've yet to run across a good textbook for teaching such.
Formula != math. Formula = human interpreters. We have computers, there's no need to train humans on how to run algorithms using poorly written pseudo code. In fact, if you know the definitions and what you are trying to solve and do, you can derive all the formula from scratch. (Well, it might be a bad idea to attempt to derive something that involves multiple summations, but it can be done.) By the way, this might surprise you, there are branches of mathematics with little or no formula. For example, much of graph theory.

In fact, formula drilling should be reserved for the most uninterested and unmotivated kids. (If they can't learn the interesting bits of math, they need to at least know how to compute.)

Whatever, I guess I'm just screwed up because I'm still in Algebra.
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Re: Debate: Grades VS Knowledge

Postby TheKrikkitWars » Fri Mar 20, 2009 11:44 am UTC

Jorpho wrote:
TheKrikkitWars wrote:
Jorpho wrote:
TheKrikkitWars wrote:With reference to dull experiments, I just spent my day making up 30 odd erlenmeyer flasks of 10cc 0.1M phenol soln, 10cc 1M KBr Soln 3 drops of methyl orange, adding 25cc of varying concentrations of H2SO4 at various temperatures and measuring the time taken for the solution to turn colourless. All in order to create a calibration chart for some kinetics work, it was unavoidable and tedious with some flasks taking upto 2.5 hrs. But I did learn something from it.
And you're saying it's quite impossible that you could have spent all that time in some other way and learned something more valuable (however you care to define value) ?
Indeed, I wouldn't have the calibration charts I required, and so couldn't get on with more interesting science. Sometimes we do dull things because we have to.
Okay, if you had someone else to do this dull work of making these calibration charts, could you have spent all that time in some other way and learned something etc?


Then I'd be a tenured professor!
Doing real science, investigating new things, or even re-investigating things done before, is neccessarily boring sometimes... The fact that I might have learned more in that time doing something else is ireleivent as its *_very_* important to my scientific "apprenticeship" that I develop the practical skills to do that sort of thing.
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Re: Debate: Grades VS Knowledge

Postby Jorpho » Fri Mar 20, 2009 6:00 pm UTC

TheKrikkitWars wrote:Then I'd be a tenured professor!
Or it could be in a book.
Doing real science, investigating new things, or even re-investigating things done before, is neccessarily boring sometimes... The fact that I might have learned more in that time doing something else is ireleivent as its *_very_* important to my scientific "apprenticeship" that I develop the practical skills to do that sort of thing.
Aha! Can the same philosophy not be applied to all the dull schoolwork you regard as "busywork" ?

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Re: Debate: Grades VS Knowledge

Postby ThomasS » Fri Mar 20, 2009 6:09 pm UTC

Jorpho wrote:
Doing real science, investigating new things, or even re-investigating things done before, is neccessarily boring sometimes... The fact that I might have learned more in that time doing something else is ireleivent as its *_very_* important to my scientific "apprenticeship" that I develop the practical skills to do that sort of thing.
Aha! Can the same philosophy not be applied to all the dull schoolwork you regard as "busywork" ?

Scales are dull, but help people to improve as musicians. There honestly isn't a lot of point to playing them if you don't also turn around and also play music. Telling people to play scales without ever letting them play, or even hear music probably should be labeled as busywork. I once heard it claimed that Mozart was offended when somebody made a comment about how lucky it was that music came so easy to him. He became upset at the suggestion that he didn't work hard. He did work hard, but he enjoyed it and/or was driven to do it, because he enjoyed music.

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Re: Debate: Grades VS Knowledge

Postby mathangelist » Fri Mar 20, 2009 9:20 pm UTC

Ralith The Third wrote:
achan1058 wrote:
Ralith The Third wrote:I may be wrong, but in terms of doing math, you have to be taught the formulas first, and I've yet to run across a good textbook for teaching such.
Formula != math. Formula = human interpreters. We have computers, there's no need to train humans on how to run algorithms using poorly written pseudo code. In fact, if you know the definitions and what you are trying to solve and do, you can derive all the formula from scratch. (Well, it might be a bad idea to attempt to derive something that involves multiple summations, but it can be done.) By the way, this might surprise you, there are branches of mathematics with little or no formula. For example, much of graph theory.

In fact, formula drilling should be reserved for the most uninterested and unmotivated kids. (If they can't learn the interesting bits of math, they need to at least know how to compute.)

Whatever, I guess I'm just screwed up because I'm still in Algebra.


You might be interested in http://en.wikipedia.org/wiki/Moore_method for an idea of not lecture based methods.

Though I do still think there is some need to teach people algorithms-- though you need a conceptual understanding (which I would say is the most important part from simply a education point of veiw) knowing how to use the algorithms is also important-- as my algebra professor put it, there are plenty of PhD's who get through with a good theoretical understanding of math but not of how to apply it, and that this leads to trouble (a favorite story is of an algebraist who proved some really nice theorems about group, but it ended up being that because he didn't check to see if any groups met the requirements it only applied to the trivial group. Not quite the same thing, but the overall idea of being able to apply math and not just understand the theory).

Also, I would argue there are lots of formulas in graph theory (Though I defiantly agree math != formulas, I am just squabbling over details...)

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Re: Debate: Grades VS Knowledge

Postby achan1058 » Fri Mar 20, 2009 10:43 pm UTC

mathangelist wrote:as my algebra professor put it, there are plenty of PhD's who get through with a good theoretical understanding of math but not of how to apply it, and that this leads to trouble (a favorite story is of an algebraist who proved some really nice theorems about group, but it ended up being that because he didn't check to see if any groups met the requirements it only applied to the trivial group.
Ouch!!
mathangelist wrote:Also, I would argue there are lots of formulas in graph theory (Though I defiantly agree math != formulas, I am just squabbling over details...)
Some parts of it, yes. I am taking algebraic graph theory right now, and we are getting spammed by lots of formula from linear algebra. Not so for my pure graph theory courses that I have taken in the past. It's relatively formula free except for the really basic counting formula and Euler's formula. There are a few numerical bounds here and there, but I don't consider them as formula.

Anyways, I am all for teaching how to use algorithms, since I have a CS/math major, which means applying known algorithms is a major part of my education. I am mostly against drilling on how to run an algorithm by hand, since I can always program it onto my computer.


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