Debate: Grades VS Knowledge

[codebliss]

I recently made it into my future college's honors program through a great interview. The question I'm quite sure that pushed me past the line asked "What do you attribute to your low GPA of 3.66?" I basically answered how I'm a hard worker who has a passion for learning and nothing else. I'm wondering what other people think.

Do you think there are classes where it is a large war to fight for the A? Do these classes cut out possible learning just to please the grading system?

I've had some classes (generally those that accept almost every type of student, like history and general education classes) that follow the "fight for an A" philosophy. I honestly learn almost nothing in these classes.

Do you think that modern generations are settling for mediocrity? Are standards lowering?

Discuss.

[AnotherUser]

Do you mean high GPA? Or do you go to some absolutely insane college where 3.66 is low?

[codebliss]

Oh. I'm sorry. I'm a senior in high school. I HATE doing nothing in class, and wasting time making teachers happy. All I like to do is learn, screw the grading system. This is why I started taking college classes in highschool, I got 42 credits completed entering freshman via PSEO.

But this topic isn't to talk about me. I'm wondering what you guys think about highschool classes being about grades and not learning?

[LaserGuy]

This is a complicated question. I'll try to break things down a bit as I see it:

Assessment is an absolutely necessary component in learning. Students need to be given a metric that shows them their progress and how well they grasp a particular concept. This does not have to be a numerical score or a letter grade per se; these are really just a short-hand for a particular standard of evaluation. Giving these metrics some intrinsic value as a grade can act as an incentive for students to perform better than they would otherwise. Eg, in a pass-fail system, students will, on average, put in the amount of work required to get a marginal pass, but will rarely put in significantly more effort to do so. Assigning a value to effort beyond a pass then can help motivate students to excel.

The problems with grading in its current form are unfortunately, quite numerous. The first is that many schools use too many categories. Research suggests that the extra precision granted by giving students an B+ versus A- is generally not warranted, and certainly not the level of precision required to have a percentage scale of precision. Under conventional systems, the best would probably have A,B,C,F levels--although this still leaves the problem of the arbitrary cutoffs for the scale. Why is an 79% a B and 80% an A? Cross-comparisons between grades in schools are pretty much useless, since an A in one school might be a B in another, and some schools then re-weight their systems so that their students end up with super-inflated grades (eg. >4 GPAs in the US), which have somewhat non-sensical meanings. A bigger problem that stems from that is whether or not an A actually represents the fact that the student has mastered the material, or, as you allude to, simply has learned what the teacher likes to hear. How well letter grades actually translate to working knowledge is pretty dubious.

The system that I've taken a liking to is one called Mastery-based education. It is essentially a pass-fail system, except that the bar is set very, very high... probably at an A or A+ range. Functionally, it works more like skills testing than school testing. Think of taking a driving exam. You learn the background theory. You practice a lot. You take the test. If you fail, then you get more help with what you have problems with, and are free to retake the test. Drivers who fail their first time are not penalized if they succeed on their second or third try. So, say a class was getting taught an unit on fractions. The teacher would do lessons essentially as normal, and then the students would write the test. The students who get a high enough mark to get Mastery in fractions, then are given time to pursue some other project of interest, and the teacher also spends time helping the students who didn't master the first time, and then write the test again. This cycles through each unit in the course, and student's report cards simply report which topics have been mastered, and which have not. This system emphasizes a necessarily high level of excellence in all subjects, but also doesn't have the same problems wrt cutoffs or inflation that typical grades do.

[Cadvin]

Grades: It's complete lunacy. Say you took a test, and got a 50/100, being a fail. That doesn't necessarily(God I hate my spellchecker... I struggled with this word for five minutes, only to figure out it was correct...) mean you have not mastered the subject, it means you may have had some errors actually doing them, or you didn't have time to finish. What they need to do, is ask you how you do it, on every sort of subject you've learned, and maybe do an example, and then you're done. MUCH more accurate as to what you've learned.

[codebliss]

Thanks for the facts and opinions guys. I understand that a form of crowd control is necessary when it comes to assessment, but its ridiculous how some teachers teach to please the assessment system rather than enlightening a generation.

[BlackMesa]

The system that I've taken a liking to is one called Mastery-based education. It is essentially a pass-fail system, except that the bar is set very, very high... probably at an A or A+ range. Functionally, it works more like skills testing than school testing. Think of taking a driving exam. You learn the background theory. You practice a lot. You take the test. If you fail, then you get more help with what you have problems with, and are free to retake the test. Drivers who fail their first time are not penalized if they succeed on their second or third try. So, say a class was getting taught an unit on fractions. The teacher would do lessons essentially as normal, and then the students would write the test. The students who get a high enough mark to get Mastery in fractions, then are given time to pursue some other project of interest, and the teacher also spends time helping the students who didn't master the first time, and then write the test again. This cycles through each unit in the course, and student's report cards simply report which topics have been mastered, and which have not. This system emphasizes a necessarily high level of excellence in all subjects, but also doesn't have the same problems wrt cutoffs or inflation that typical grades do.

I really like this system, but there are some problems that make it difficult. First, I dont think teachers would be able to handle it. They wouldnt be able to keep track of mutiple studendts at potentially different places and be able to meet mutiple studendts individual needs. There just arent that many teachers. Now in this system it is possible that good studendts could function without a teacher at all and just teach themselves (i would support that). However, i dont think that would be allowed (they dont trust us that much). Also, the teachers attention is primarily focoused on those who are most behind, so one studendt could prevent the entire class from getting help until they finally pass that unit. However, the current grading system is useless and horrible and doesnt reinforce learning. It forces studendts to waste their time instead of focousing on what matters. There is really very little support for it. So although the proposed one is not perfect (mostly due to a lack of resources) it is still much, much better.

[LaserGuy]

The system that I've taken a liking to is one called Mastery-based education....

I really like this system, but there are some problems that make it difficult. First, I dont think teachers would be able to handle it. They wouldnt be able to keep track of mutiple studendts at potentially different places and be able to meet mutiple studendts individual needs. There just arent that many teachers. Now in this system it is possible that good studendts could function without a teacher at all and just teach themselves (i would support that). However, i dont think that would be allowed (they dont trust us that much). Also, the teachers attention is primarily focoused on those who are most behind, so one studendt could prevent the entire class from getting help until they finally pass that unit. However, the current grading system is useless and horrible and doesnt reinforce learning. It forces studendts to waste their time instead of focousing on what matters. There is really very little support for it. So although the proposed one is not perfect (mostly due to a lack of resources) it is still much, much better.

Yes, obviously teaching time factors significantly into how successful this would be, and of course teachers would need to be properly trained to teach such a system. I don't know if it has ever been tested for general education, but as I alluded to, such systems are common in a variety of applied programs where grades are not appropriate (surgeons, pilots, driving tests, etc. often use variants of this system). I don't think the bookkeeping of each student's progress would really be a problem, since teachers do a lot of that anyway in the current system by means of grades.

A quick misconception to correct though... the system doesn't advocate that one student would hold the entire class back, necessarily. Typically, each unit would have two cycles. The first cycle everyone is taught the same material, then the mastery test is taken, and the second cycle, the group who have mastered that material are given time to spend on some other activity, while the group who have not mastered the material are given additional instruction. After the second cycle, the teacher would move on to a new unit, even if there were some people who hadn't mastered it yet (if the cohort was large enough, the teacher might do a third cycle, but this would be mostly discretionary). Those students would otherwise need to get additional help on their own time if they wanted to master the topic, or their final report would simply record that topic as unmastered, and it would be up to the school, parents, and teacher to decide whether or not that student could advance to the next grade without that topic at a high enough level. Ideally, each class would have a teacher and an assistant, so that each group of students always has adequete supervision and instruction.

Whether or not the current system (or any other, for that matter) is effective really hinges on the questions that I feel are often forgotten: What exactly is the purpose of the education we are giving our students? What do we want them to get out of it? What skills do they need to know?

[BlackMesa]

A quick misconception to correct though... the system doesn't advocate that one student would hold the entire class back, necessarily. Typically, each unit would have two cycles. The first cycle everyone is taught the same material, then the mastery test is taken, and the second cycle, the group who have mastered that material are given time to spend on some other activity, while the group who have not mastered the material are given additional instruction. After the second cycle, the teacher would move on to a new unit, even if there were some people who hadn't mastered it yet (if the cohort was large enough, the teacher might do a third cycle, but this would be mostly discretionary). Those students would otherwise need to get additional help on their own time if they wanted to master the topic, or their final report would simply record that topic as unmastered, and it would be up to the school, parents, and teacher to decide whether or not that student could advance to the next grade without that topic at a high enough level. Ideally, each class would have a teacher and an assistant, so that each group of students always has adequete supervision and instruction.

Whether or not the current system (or any other, for that matter) is effective really hinges on the questions that I feel are often forgotten: What exactly is the purpose of the education we are giving our students? What do we want them to get out of it? What skills do they need to know?

Oh, I see. I think that could work well. I think that the purpouse of education is to prepare studendts to enter the 'real world' and be productive members of society. They need to learn whatever is necessary for their profession. This would be supported by your system. However, the current system makes you go through alot of classes that are useless in this respect. It is primarily focoused on getting high test scores and filling people with useless information. My dentist doesnt need to know about star formation. The proposed system would allow for focous on a particular area and it would be able to make sure most people had a sufficcent mastery of everything. As you said this is the system used to ensure that people are up to standards in many areas, so we see that i can work for focous and is what is used in the 'real world', where it seems to be working. Overall I think it would work well. So in relation to the original topic, it doesnt appear necessary that grades per se are necessary or useful.

[codebliss]

A quick misconception to correct though... the system doesn't advocate that one student would hold the entire class back, necessarily. Typically, each unit would have two cycles. The first cycle everyone is taught the same material, then the mastery test is taken, and the second cycle, the group who have mastered that material are given time to spend on some other activity, while the group who have not mastered the material are given additional instruction. After the second cycle, the teacher would move on to a new unit, even if there were some people who hadn't mastered it yet (if the cohort was large enough, the teacher might do a third cycle, but this would be mostly discretionary). Those students would otherwise need to get additional help on their own time if they wanted to master the topic, or their final report would simply record that topic as unmastered, and it would be up to the school, parents, and teacher to decide whether or not that student could advance to the next grade without that topic at a high enough level. Ideally, each class would have a teacher and an assistant, so that each group of students always has adequete supervision and instruction.

Whether or not the current system (or any other, for that matter) is effective really hinges on the questions that I feel are often forgotten: What exactly is the purpose of the education we are giving our students? What do we want them to get out of it? What skills do they need to know?

Oh, I see. I think that could work well. I think that the purpouse of education is to prepare studendts to enter the 'real world' and be productive members of society. They need to learn whatever is necessary for their profession. This would be supported by your system. However, the current system makes you go through alot of classes that are useless in this respect. It is primarily focoused on getting high test scores and filling people with useless information. My dentist doesnt need to know about star formation. The proposed system would allow for focous on a particular area and it would be able to make sure most people had a sufficcent mastery of everything. As you said this is the system used to ensure that people are up to standards in many areas, so we see that i can work for focous and is what is used in the 'real world', where it seems to be working. Overall I think it would work well. So in relation to the original topic, it doesnt appear necessary that grades per se are necessary or useful.

I mostly agree with you guys. To Black Mesa, I understand where you're coming from, although I do think that taking some of those "useless" classes make you a more well-rounded person. There's many things that aren't important to my career that I'm interested in, and wouldn't have been if I had not taken those classes.

But yes there still are some just utterly useless classes. Thanks guys.

[ThomasS]

First of all, we have used the current system for so long that most of the datapoints that people see all regard the same sort of school. Within the basic model where people sit in class and listen to a lecturer talk there is a lot of variation. Standardized tests seem to be a cheap and easy way to recognize particularly troubled schools and instructors.

However, it has been argued that there are some downsides to this basic approach. In addition, I have studied enough math to find the arguments in Lockhart's Lament rather convincing, and I wonder in how many other fields standardization helps to prevent real education. There is a certain amount of intrinsic value in learning the basics of a number of fields, and trying to ensure that a certain amount of exposure happens is probably good. However, especially in light of Lockhart's arguments, I think that the best things for students to learn about math have nothing to do with standardized test questions and everything to do with understanding why proofs so excited the cult of Pythagoras and affected western philosophy.

One common reaction to all this is that we simply don't have anything else which works. Yet, both the Sudbury Valley School and the unschooling movement do report a certain amount of success both in producing well rounded individuals, and in seeing them continue their education with or without college. As a result I often find myself wondering about the real truth behind a lot of the statements which have been made in this thread.

[Ixtellor]

However, the current system makes you go through alot of classes that are useless in this respect. It is primarily focoused on getting high test scores and filling people with useless information. My dentist doesnt need to know about star formation.

1) We call this a 'liberal' education.

2) Taking a variety of classes you won't use directly in your profession, will still make you smarter. You will understand the millions of allusions and references that we commonly use in our society. "Big brother is watching" "Osmosis" ""We are all made of Stars" "tis the rub" "why we don't say the name of a certain play Hint: M"

3) Exposing HS kids to a variety of classes might make them 'discover' a career path they might never have been exposed too.

Ixtellor

[idlehandsrome18]

My major beef with grades is that they are too based on tests, especially multiple choice tests. In college, your grade in a class is normally more than 75% tests, with some exceptions. The problem with tests is that they don't ONLY measure knowledge about a subject, there is a skill to taking tests. What this means is someone who is less knowledgeable about the topic could score higher on a test than someone who knows more if they are a better test taker. This variability means that the grades are an untrustworthy indicator of a student's aptitude in a certain area. Further, curving by making the average score a 'C' takes value away from questions that were answered based on knowledge and adds value to questions that were answered based on guessing. Consider a class that received a very hard multiple choice test and the average score was less than 50%. Curving the score to this value may seem like a good way to even out the grades, but the problem is that random guessers get rewarded while someone who tried to work out the problem and got caught in a pitfall gets screwed relative to the entire class.

Classes should be based more on projects and performance over ability to take tests. That's why I'm a CS major I guess....

[TheKrikkitWars]

Classes should be based more on projects and performance over ability to take tests. That's why I'm a CS major I guess....

Personally, I'd like to see university level assesment and grading based on yearly, individual, viva voce assesments by a board of professors...

[idlehandsrome18]

Classes should be based more on projects and performance over ability to take tests. That's why I'm a CS major I guess....

Personally, I'd like to see university level assesment and grading based on yearly, individual, viva voce assesments by a board of professors...

Don't PhD students have to go through something like this? The PhD student evaluation is probably much more rigorous than what you are suggesting.

[TheKrikkitWars]

Classes should be based more on projects and performance over ability to take tests. That's why I'm a CS major I guess....

Personally, I'd like to see university level assesment and grading based on yearly, individual, viva voce assesments by a board of professors...

Don't PhD students have to go through something like this? The PhD student evaluation is probably much more rigorous than what you are suggesting.

Anyone who is assessessed by dissertation takes a Viva Voce on the subject of their dissertation/thesis, so all MSc/MA and PhD/DPhil students will go through exactly what I suggested (it happens to be partially where the idea came from).

I think viva voce is a better vehicle for determining the real level of knowlege in a candidate at any level, but doing one for each of 60 undergrads in each of 4 years would be very time consuming and involved for the lecturers and professors, hence it being confined primeraly to postgraduate study.

[Jorpho]

A bigger problem that stems from that is whether or not an A actually represents the fact that the student has mastered the material, or, as you allude to, simply has learned what the teacher likes to hear.

What is this idea of "telling the teacher what (s)he wants to hear" ? In math or science there are objective answers to questions, and if you're not telling the teacher what he wants to hear, you're probably wrong, and no amount of sillybollocks is going to make you right! This also applies to a considerable extent in things like history or English - facts are facts, grammar is grammar, and if you can get that much down and write a coherent argument you're most of the way to a decent grade anyway - even if what you finally have to say isn't "what the teacher wants to hear", whatever that means.

[ThomasS]

What is this idea of "telling the teacher what (s)he wants to hear" ? In math or science there are objective answers to questions, and if you're not telling the teacher what he wants to hear, you're probably wrong, and no amount of sillybollocks is going to make you right!

Objective answers are the least interesting part of math and science. If you really want to know how a person thinks, if you really want to evaluate their potential, watch them work on a problem which is new to them. Right or wrong, their approach and mindset is far more important than being able to recite \pi or even the equations which use it.

[Jorpho]

Objective answers are the least interesting part of math and science.

I guess much of math and science is uninteresting, then.

If you really want to know how a person thinks, if you really want to evaluate their potential, watch them work on a problem which is new to them. Right or wrong, their approach and mindset is far more important than being able to recite \pi or even the equations which use it.

And if they happen to forget the objective facts along the way, suddenly that's okay?

[ThomasS]

I guess much of math and science is uninteresting, then.

If you've never experience the joy of puzzle solving that is math, if you cannot imagine the joy of discovery that is science, then you have my sympathy. But yeah, compared to those things, a pile of disconnected math or science facts is uninteresting, and useless to boot.

Real math books include proofs, and by real math books I mean both those modern yellow bound tombs that scare graduate students and Euclid's Elements. There certainly is some value in knowing the facts which those proofs demonstrate. However, the value of Euclid's postulates as mathematical entities pale in comparison to value of the mindset and organizational principles which his work helped to popularize. As the wikipedia article mentions, Abraham Lincoln read it in order to strengthen his ability as a lawyer. Similarly, mathematicians study proofs in journals and yellow tombs not because they doubt their correctness (or at least, not just because they doubt their correctness) but because they hope to find inspiration for their own proofs.

And if they happen to forget the objective facts along the way, suddenly that's okay?

Objective facts can be found in reference books. What is far more important than a perfect memory is an understanding of how to look facts up and put them together creatively. What is far more important than rote memorization is a desire for discovery. Yes to discover new things you end up researching and learning old things. However, until you have a purpose for these facts, until you have a puzzle that matters, their value is limited. Trying to convince students otherwise can make the smart ones mad.

The real question is whether you trust yourself to recognize the spark that is a person approaching problems in a creative and useful manner. Without that, trying to evaluate somebody's mathematical ability is a bit like a tone deaf person trying to evaluate somebody's musical ability.

[Jorpho]

If you've never experience the joy of puzzle solving that is math, if you cannot imagine the joy of discovery that is science, then you have my sympathy.

And if you think math is all joyous puzzle solving and science is primarily the joy of discovery, you have much to learn.

Real math books include proofs, and by real math books I mean both those modern yellow bound tombs that scare graduate students and Euclid's Elements.

Have you considered that there might be a good reason that they scare graduate students? And if they scare graduate students, how can you ever expect to get away with teaching anything remotely like that to the typical disinterested high school student!?

Objective facts can be found in reference books. What is far more important than a perfect memory is an understanding of how to look facts up and put them together creatively.

That's like saying there's no need to learn how to multiply in your head or do long division, because all the answers are right there in your calculator!

[TheKrikkitWars]

Real math books include proofs, and by real math books I mean both those modern yellow bound tombs that scare graduate students and Euclid's Elements.

Have you considered that there might be a good reason that they scare graduate students? And if they scare graduate students, how can you ever expect to get away with teaching anything remotely like that to the typical disinterested high school student!?

With passion, commitment, personal understanding of both the students and the material... also the students need to be fairly bright (the interest is less essential).

Objective facts can be found in reference books. What is far more important than a perfect memory is an understanding of how to look facts up and put them together creatively.

That's like saying there's no need to learn how to multiply in your head or do long division, because all the answers are right there in your calculator!

It isn't, long division is a process to carry out on known information, its always the same. The answer to a given question is not neccearily always the same, nor is the process of finding it. In my current degree, more emphasis is being put on researching and referencing than on memorising key facts, a good conceptual grasp, some key operations/processes, and a strong research method are the best way to achieve at a graduate level.

Ignoring the boons of the information age whilst using a computer, is like buying a washing machine to support your washtub and mangle.

[Ralith The Third]

Grades are only affected by knowledge when you're intelligent (If you put any stock in IQ tests, mine is 142-144) except in that it tells you to try some, or if you are in a higher math track. Grades are not an indicator as to how intelligent you are- good grades just mean you have a work ethic or parents who help you way too much, and that you're not (seriously) retarded.

[ThomasS]

And if you think math is all joyous puzzle solving and science is primarily the joy of discovery, you have much to learn.

Well, puzzles and discovery can be addictive, and this can have you waking up in the middle of the night because you are thinking too hard. There is a dark insane obsession lurking behind real math, and real science, but it normally comes after the joyous stage and probably isn't what you are describing.

It seems more likely that you are describing what Lockhart refers to as a "hollow shell" that people mistake for math instruction. I survived a bit of this soul draining irrelevance in my youth, and in some ways I think that I'm still working to recover from the trauma. I have also taught a few Calculus courses and I'm ashamed to admit that I propagated this system in them. Now, using the keywords from a previous post it wasn't hard to find a story of a grade school student learning the multiplication table because she wanted to. In addition to Gatto's essay it is possible to hear him give testimony which includes some interesting comments about the education of Einstein, Tesla, and our founding fathers.

It seems to me that we have these stories of people choosing to learn math and other topics because they were given the space to see for themselves the value and relevance, and that your response is just "well, you have much to learn about math". Perhaps you are right, if nothing else I should go get back to work on my thesis.

[Jorpho]

Real math books include proofs, and by real math books I mean both those modern yellow bound tombs that scare graduate students and Euclid's Elements.

Have you considered that there might be a good reason that they scare graduate students? And if they scare graduate students, how can you ever expect to get away with teaching anything remotely like that to the typical disinterested high school student!?

With passion, commitment, personal understanding of both the students and the material... also the students need to be fairly bright (the interest is less essential).

Sir, you say they scare graduate students. I would argue it is quite impossible to begin teaching something like that to students who do not have a thorough, ingrained grasp of basic concepts that does not come from running to a reference book every time they need to know something.

Objective facts can be found in reference books. What is far more important than a perfect memory is an understanding of how to look facts up and put them together creatively.

That's like saying there's no need to learn how to multiply in your head or do long division, because all the answers are right there in your calculator!

It isn't, long division is a process to carry out on known information, its always the same. The answer to a given question is not neccearily always the same, nor is the process of finding it.

A lot of the questions you're likely to encounter in high school (and even most of undergrad) do in fact have answers that are always the same. I am not speaking of graduate level education here; certainly, few would agree that grades matter at all at that point.

And if you think math is all joyous puzzle solving and science is primarily the joy of discovery, you have much to learn.

Well, puzzles and discovery can be addictive, and this can have you waking up in the middle of the night because you are thinking too hard. There is a dark insane obsession lurking behind real math, and real science, but it normally comes after the joyous stage and probably isn't what you are describing.

I admit that I can't really speak for math, but a good part of science comes down to endless repetition, testing and re-testing, experiment after experiment with slightly-tweaked conditions, and maybe after years and a certain amount of good fortune, maybe in the end you end up with a pretty looking-graph and some small amount of the "joy of discovery".

It seems to me that we have these stories of people choosing to learn math and other topics because they were given the space to see for themselves the value and relevance, and that your response is just "well, you have much to learn about math". Perhaps you are right, if nothing else I should go get back to work on my thesis.

If students got to choose exactly what they wanted to learn on the basis of what they considered "valuable and relevant", methinks a lot of students wouldn't learn anything, certainly not about things that they might find they enjoy after further investigation despite initial impressions.

And I already finished my thesis. Nyah nyah!

[ThomasS]

Have you considered that there might be a good reason that they scare graduate students? And if they scare graduate students, how can you ever expect to get away with teaching anything remotely like that to the typical disinterested high school student!?

The modern yellow book comment was meant to be one extreme. Another data point was Euclid, and I thought that Lockhart did a rather good job of arguing that elementary school students wouldn't be nearly so disinterested in arguments about lines and circles if they were presented correctly. Perhaps I should have come up with some other data points. The best college math course I ever took was a relatively elementary topology class from a book that had no proofs, just theorems. Every day a different student was assigned to present to the class some of the theorems (with proof).

If students got to choose exactly what they wanted to learn on the basis of what they considered "valuable and relevant", methinks a lot of students wouldn't learn anything, certainly not about things that they might find they enjoy after further investigation despite initial impressions.

And I already finished my thesis. Nyah nyah!

You think that they would learn nothing, but have you done the experiment? Isn't the dangers of anecdotal reasoning one of the things that you are suppose to learn about in graduate school?

I'll accept that your anecdotal experience tells you to expect one thing, but history books do mention rather successful people who had poor grades or who didn't finish college. Furthermore, my personal experience is that nothing spoils a student for a topic like giving them irrelevant busy work under the guise of teaching them about it. You can teach facts about physics all day without calculus, but one of my favorite physics teachers once said that you can't teach physics without calculus, you can only teach about physics.

[Jorpho]

I'll accept that your anecdotal experience tells you to expect one thing, but history books do mention rather successful people who had poor grades or who didn't finish college.

Oh, come on! Who's relying on anecdotes here? History books aren't going to bother mentioning the millions upon millions of thoroughly unsuccessful people who had poor grades or who didn't finish college!

[Rilian]

Most of my non-A's were due to the fact that the assignments were beneath me.

But really, it's quite obvious that a person can know things and still get bad grades. And a person can memorize things for a test, regurgitate, and then purge.

[ThomasS]

I had a few more thoughts on the science side of things, so apologies for going back a bit, but...

I admit that I can't really speak for math, but a good part of science comes down to endless repetition, testing and re-testing, experiment after experiment with slightly-tweaked conditions, and maybe after years and a certain amount of good fortune, maybe in the end you end up with a pretty looking-graph and some small amount of the "joy of discovery".

Imagine if you will, two possible science courses, populated with students who may or may not be in high school:

In course A, the instructor maybe drops something on the ground, makes a rhetorical question about how long it took, and then proceeds to write the free fall equation up on the board, maybe talks a bit about how it comes about through calculus, or maybe comes up with stories about ramps and marbles, and the challenges newton had because clocks were very poor in those days. Then he proceeds to work out a whole bunch of the standard types of free fall problems. Most of the calculations seem unrelated to real situations, and even the computations that don't seem unrealistic wouldn't necessarily be that accurate because of things like air resistance.

In course B, the instructor stands up there with, say, a pencil and a feather, drops both, and declares that he wants to know how much faster heavy items fall than light items. He then opens a closet with a range of items - items "obvious" to instructor like ramps, scales, and marbles of various materials, but also less obvious items like erector sets, string and springs. The class proceeds with the instructor encouraging them to guess a possibility and then come up with a way to check the guess.

Course B might require multiple meetings to get to anything resembling the free fall equation, but I believe that course B is far more likely to teach both the truth behind the scientific method and the way in which science is about experiment and discovery. And I consider those things to be far more important than knowing x(t)=\frac{1}{2}a t^2 +v_0 t + x_0, or any similar formula, whether or not the students will become scientists in any professional sense. Them needing to look it up bothers me far less than them not understanding in their bones how and why we believe it. I'm a firm believer that if people had a stronger sense of what science is, then fake science like creationism would not gain so much traction, and the mob which is America would be just a little bit better at making evidence based decisions.

[Jorpho]

That sounds alarmingly like "whole math". I will leave you to Google that and read about what a complete and unmitigated disaster it was. There's some non-anecdotal evidence for you!

I'm a firm believer that if people had a stronger sense of what science is, then fake science like creationism would not gain so much traction, and the mob which is America would be just a little bit better at making evidence based decisions.

Oh, I agree. But odd as it may sound, I would question whether teaching such a thing in a Physics class is a good use of Physics class time. Physics is a pretty broad subject and if it takes "multiple meetings" to teach each concept you'd be at it for years. I had an utterly amazing critical thinking and epistemology course to hit the true lessons of science home for me.

[achan1058]

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.)

Speaking of which, what yellow tomes? Springer's grad texts? Personally I haven't had much of those myself in my studies, though I have had a few very dense books from other sources. Besides, if they actually scare them grads, they shouldn't be in grad school.

[Ralith The Third]

Most of my non-A's were due to the fact that the assignments were beneath me.

But really, it's quite obvious that a person can know things and still get bad grades. And a person can memorize things for a test, regurgitate, and then purge.

Yeah, pretty much. There's several kids who do better than me gradewise, but when I try to talk to them about say... electromagnetism, which hasn't been covered this year (science class- FAIL!) they look at me blankly

[Delass]

I think one of the biggest problems is education in highschool is we are only taught what, but now how or why. Like pi. We know its 3.14159..., and the symbol that represents it, and its sometimes used in formulas. But we dont know anything about it, like why and how its 3.14159.... (well, all of the math people here do, but as a soon to be highschool graduate not going into a math field, I don't)

Most of my math classes have been memorizing the way to solve a given type of problem, doing it on a test, and then forgetting it, because its meaningless. I don't know why its solved that way, or what it means, its just abstract and meaningless.

This does not encourage thought about the problem, it just teaches memorization. We might as well just be given a list of answers.

[achan1058]

Most of my math classes have been memorizing the way to solve a given type of problem, doing it on a test, and then forgetting it, because its meaningless. I don't know why its solved that way, or what it means, its just abstract and meaningless.

This does not encourage thought about the problem, it just teaches memorization. We might as well just be given a list of answers.

I do agree that the problem lies partly in education and the test based approaches, but it is also partly yours. You can always dig up the info yourself, and see the connections between various types of problems, without the help of the so-called teachers.

[Jorpho]

its just abstract and meaningless.

Well, a lot of math is like that sometimes, and it can be a real stretch to demonstrate practical uses for it. I've never found any practical use for conic sections, despite all the time spent on them in high school. Higher-order derivatives aren't particularly handy either outside of Taylor or Maclaurin series.

I remember back in Grade 5 (or maybe it was 6?) we learned about rotational symmetry. It seemed like the most abstract and useless thing at the time. Eight years later I learned about point groups in inorganic chemistry and for the first time those lessons were useful.

[Delass]

Most of my math classes have been memorizing the way to solve a given type of problem, doing it on a test, and then forgetting it, because its meaningless. I don't know why its solved that way, or what it means, its just abstract and meaningless.

This does not encourage thought about the problem, it just teaches memorization. We might as well just be given a list of answers.

I do agree that the problem lies partly in education and the test based approaches, but it is also partly yours. You can always dig up the info yourself, and see the connections between various types of problems, without the help of the so-called teachers.

Of course, but thats a different argument. I would care more about learning math if I was taught problem solving rather than memorizing, but either way its not very important to me. I'm not going to do anything math related in my life, and can balance a checkbook just fine without algebra or calculus, so quite frankly I don't care. I was just pointing out that my extra math classes did not encourage thought, or make me a better person, or anything else.

I could argue that I actually can't, because I'm busy doing busywork, but thats not quite serious.

I just thought of a fun analogy: its like learning to get from A to B, but not how to read a map or road signs, so if you ever want to go from A to C, it was all useless.

[Ixtellor]

I thought I would just interject:

Sometimes teachers assign "busy work" as you call it, because they want to vary the presentation of subject matter.

I personally would love to lecture every day, but the fact remains that some students learn more through reading or hands on activities. So I throw in some individual assignments where they essentially read and answer questions. (I do use higher order questions not rote memory level questions). Many students call this 'busy work' but it is really just offering material in another format sometimes.


Ixtellor

[ThomasS]

Oh, I agree. But odd as it may sound, I would question whether teaching such a thing in a Physics class is a good use of Physics class time. Physics is a pretty broad subject and if it takes "multiple meetings" to teach each concept you'd be at it for years. I had an utterly amazing critical thinking and epistemology course to hit the true lessons of science home for me.

Regarding New Math, and continuing with the music analogy, both the setup and results sound like the equivalent of handing a class of students a large collection of recorders and having a tone deaf music "instructor" wander around encouraging them to experiment. Of course there has to be a balance. Students in, say, high school bands, play scales and learn to read music, but they know in their bones that the real point is to play music, and they are given significant practice time to do so.

It's great that you had a course that helped you to find what makes science science. However, I think that including that in science courses might make sense, especially since critical thinking and epistemology course are missing outright from a number of high schools. Moreover, as you move away from newtons laws and basic gravitation you get to physics topics which aren't so easy to see experimentally and reading about them becomes essential. However, when I took physics in college, 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.

[Jorpho]

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?

[Rilian]

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.