The Glade 4.0

Your answer is correct for the first form of the question he asked Lex... a square is the orthogonal projection of a cube. However, a Petri projection would be a hexagon.

The object itself is a {4,3}

That said, while the "gotcha" question was amusing, it also doesn't change my point. If the student isn't expected to know that information, so that the question specifically refereed to the component units of a foot, it shows one of 3 problems... 1) the student hasn't yet learned such information, which by the 4th grade should cause concern to everyone here, 2) the student was careless and didn't double check their work and being awarded partial credit doesn't give the student an incentive to fix that problem, or 3) the student has issues with tests.

The first 2 need to be corrected, and not by lowering the standards, or raising the point value of wrong answers to decrease the difficulty in achieving those standards. The last one I don't know, but should not be incorporated into the general grading patterns for all test takers.

Alright. Next question ...

At what value of n-cube does the projection approximate a circle?

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Curious: Are you framing this question with wiggle room to make a point? A pentagon could be argued to approximate a circle.

Sort of.

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Its a non-sense question, as a square (2-cube) "approximates" a circle. The question if of course to what degree does the shape need to approximate the circle to meet the requirements.

For modeling, I use a {32} (projection from a 5-cube) as a good approximation of a circle for visual accuracy during the rendering, but even that depends on the distance of the shape from the camera. The closer it is, and the more refined I need the image to be, the higher the vertices count. I almost never exceed 128 for a full circle component (7-cube).

Obviously, mathematically, the higher the cube count, the more perimeter points to define the edge, and the closer the project will resemble a circle.

It's not a nonsense question at all, actually. We're talking about "learned" knowledge and "facts". I picked something mathematical. [And I corrected my terms to make sure everyone knew exactly what I was thinking. Although, I had to guess you would understand the question.] The second question is much akin to a word problem. It has specific parameters, but it's not exactly "clear". You have to induce or deduce something from it. Generally, we're speaking of the latter.

You correctly deduced that I could point out a square (2-cube) "approximates" a circle, but it doesn't do so very well. And you correctly appended that ...But, honestly, we're talking about things most people never have reason to learn.

In the case of the 24 + 24 = 48, the error is more telling than whatever he did get right. That student got the right answer: twice. What that student didn't do was correctly read the problem; or, as might be likely the case, that student tried way too hard to read the problem correctly.

Corolinth's criticism of the article are not out of place. The examples picked are bad examples. If someone asks me what one-fifth of $400.00 happens to be and I write the figure in the first example, they should be able to determine $80.00 themselves. That's actually worth 1 out of 2 points. Same for the second example.

The problem in the educative process comes in either not showing Student A how to finish the questions; or, in showing Student B how not to confuse himself into thinking he has to add 2 feet + 2 feet in inches.

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"Nonsense" as in there is no definitive answer and subject to the needs of the user or observer, not as in a silly question.

And the "problem" you identified is exactly the point I have been making. However, giving partial credit to reward this lack of educational fortitude of the earlier years does not encourage either the child or the system to correct itself and do what should be the base requirement of the system.

It is social promotion, but less to hurt the feelings of the children and more to hide the inadequacies of the educational system.

So you're still ***** and complaining about those goddamn liberals ruining our schools graar snarl raar gnashing of teeth growl. That's what you're doing. I've pointed out the actual problem, where the information comes out that our educational standards are slipping because we've actually lowered our standards and you just want to ***** about partial credit. What's going on here isn't that you're bothered by our lowered standards, you're just pissed off that your kids are getting partial credit and you didn't. Although you actually did and you just don't realize it. Ever written an answer to an essay question and had points taken off for spelling or grammar? Points taken off, rather than the entire problem being marked wrong outright. Some of you guys don't get that. You've heard that schools are giving out points for "trying" and now you want to ***** about feel-good liberals ruining our schools roar grab the pitchforks growl snarl.

It's exactly like the problem with the oil spill. Greedy corporations don't care about the environment growl snarl raar ban oil drilling everywhere environment environment graar roar snarl. The only difference is in this thread, it's the conservatives *****.

Moving on.

First, we'll take a look at what partial credit accomplishes.

I, when I am teacher, have goals for what my students are supposed to learn. I also require feedback on what they're learning. If I'm teaching math, not only am I trying to teach basic arithmetic, I'm also trying to teach students to understand what those arithmetic operations mean. Does the student understand how to perform them, and what he accomplishes by performing them? Can you read math, and can you do math? Both examples given are examples of students demonstrating that they can read the problem. They understand. The students performed incorrect arithmetic.

So now I have a student taking a test. Let's say he has thirty minutes to do fifty word problems, and we assume the entire test is word problems. That's a little over thirty seconds per problem. I tell them I'm giving them credit for two things: can they set up the problem, and can they solve the problem. If I get a test back from a student who read all of the problems correctly and set them up properly, then I know that one of my teaching goals was met. If he does half the arithmetic properly, then yes he gets a 75 assuming all the problems are word problems. I don't generally make that assumption, because on a proficiency test there's a battery of arithmetic problems, and then a battery of word problems. However, let's go ahead and assume that they all are and the student gets a C. That is still not "try points." It's not feel-good liberal teachers handing out passing grades to boost self-esteem in children. This still isn't a case of, "Well, Timmy showed up to class today. He's really trying, so I'll give him a 20% on the test. Oh, and Jenny wrote her name down, that's another five points for trying." I set out to teach two skills, and the student demonstrated very clearly that he learned one of them. He can come up to me and say, "Mr. Coro! I learned how to read math, and here's proof."

The students don't understand this, and most of the people they talk to after class don't either, but setting up the problem is actually more important than solving it. We've got a lot of fools who can do arithmetic. People drop out of engineering programs left and right because they can't set up the problem. We've told the primary and secondary schools that we want them to teach kids how to **** read, and apparently they're doing that now. Giving partial credit for being able to set up a problem correctly is one of the things they're doing right, not something they're doing wrong. What they're doing wrong is making the entire test word problems so that a kid who is shitty at arithmetic can get a 75%. Another thing they're doing wrong is changing the grading scale so that a 75% isn't a C, it's now a high B.

If you really want to know where are schools are **** up, and why the math skills of incoming college freshmen are going down, here's a video.

[youtube]Tr1qee-bTZI[/youtube]

This is how we want to teach children to do multiplication and division now. Now, some of those methods work, and are the thought process I use. Those "cluster" problems are how I multiply and divide large numbers in my head. They also take way too long on a test. They're useful for demonstrating ideas to a student, such as the idea that multiplication is repeated addition, but they're not going to replace the traditional methods for actually performing the operations. Elementary school teachers latch onto them because they're "new" (they're not - one was Fibonacci's method for multiplication), or more accurately, because they're not the standard algorithms that they were bad at themselves back in elementary and middle school.

Moreover, when your teaching method relies on the fact that students can use a calculator to solve a problem, you have a bad teaching method. Now, students do have calculators available to them, and they should know how to use one. That's why it's important that a school teach children to read math and to understand what a problem is asking them to do. I see evidence that students are being graded on that. That is a good thing. Students will not always have a calculator, and should know how to perform arithmetic. I see evidence that students are being graded on that as well. The fact that there is partial credit being awarded actually allows us to identify the problem so that we can correct it.

Second, yes real life does give partial credit. We have over 60,000 commercial products that came out of the space program. How many of those were actually useful in the space program? How many of them fulfilled their intended function to the astronauts? Some of them certainly did, but you can bet your *** that not all of them did. Here we have a wide variety of products, some of them almost indispensible for 21st-century life, that began as a "wrong answer."

The notion that real life doesn't give partial credit is laughable. Tesla never did get power generators set up that would beam electrical energy through the air and bounce signals off the ionosphere. Every house in America has electricity.

Let's look at some more examples of real life partial credit.

You take your car in for inspection before you renew your license plates. Your car fails the emissions inspection because of the muffler. Does anyone turn to you and say, "You have to buy a new car. Sorry. No partial credit!"

A lightbulb burns out in your living room. Do you hire an electrician to rewire the house and replace the circuit box because there's no partial credit in your home?

Boeing is testing a new airplane. They run it through a series of tests, and they find out the wing snaps when exposed to a certain deflection. Do you think they redesign the entire plane? Do you even think they redesign the whole wing?

If my house is a little bit hot this summer, do you think I should rip out all of the ductwork and have the air conditioner replaced?

Let's talk about the Mars rover. Let's look at all the partial credit given for that wrong answer. It got into outer space. Partial credit. It made it to Mars. Partial credit. It hit Mars. Partial credit. It crashed and broke apart. Now we've found where we went wrong. Time to examine the crash (which probably means more partial credit is coming). Was it oriented properly coming into the planet (if it lands safely, but upside-down, we're still hosed)? Did our positional thrusters come on? Were they pointing in the right direction? We don't completely redesign the rover because Mike didn't land it properly. All that stuff we did right, we're still going to do.

Nagasaki was partial credit. That guy missed. Biggest damn bomb we had, and he missed.

This notion that real life doesn't have partial credit is total bullshit. Being in the military doesn't change that. Being in the military doesn't impress or intimidate me, either. Who do you think builds those shiny jock toys, the Tooth Fairy? You don't think there's partial credit when you're holding one of your fancy toys? You think that if you don't get the right answer, bullets rip through a civilian house? It could blow up in your **** hands!

Here's this list of twenty things I'm teaching this semester. You need to prove you learned at least sixteen of them to pass my class. If you learn something, you get credit for it. This is not hard math. I use tests to determine what you've learned. At the end of the semester, if you've learned the requisite amount of stuff, you'll have test scores that add up to 1600. You've got 1253. Too bad for you. I'm not sitting here saying that kids should get a perfect score for getting the wrong answer. That's Riov. That's also ridiculous. A perfect score is for someone who does it right and gets the right answer. What's being done here is to grade the students for what they actually have done right. Contrary to popular belief, that really is how the world works.

Let's go back to that Boeing example. They test their plane and find out a wing snaps. Well, the landing unit is working properly and the engine is performing to specifications. The electrical systems are all running fine. The tail is solid. They need to look at that wing, but they don't even rebuild the wing from scratch. Nobody approaches that from the notion that the whole wing needs to be redesigned. That would be ridiculous. It might end up being true, but that's not where the analysis starts. They circle where the wing broke, and they start their analysis there. That's the problem area. They run some more simulations to try and figure out which beam broke first, then they look for why it snapped.

Now let's talk about basic stuff that everyone should know. How many yards are in a furlong? How many of you know it? Now how many of you know you can look that **** up on Google? Why should kids know how many inches are in a foot? Because you do? Your grandpa knew how many yards were in a furlong. You're all a bunch of damned disappointments, you stupid bastards.

But okay, we want kids to know how many inches are in a foot. I get it. I had a professor trying to convince everyone that we all should know how many Newtons are in a pound. I'm electrical, so no, I really don't need to know that one off the top of my head, but I can go with that. What I don't quite grasp is how we see an article that cherry-picks two test questions and follow that to the conclusion that kids don't know how many inches are in a foot. (Especially when he was using the right answer as his operands, but that's blown right past some of you more than once, now). This isn't good data. Hell, it's not even bad data. Two problems does not constitute data at all. What's happening here is that several of you have preconceived notions, and someone with no background at all has written a sensationalist article that lets you get up and arms. You were expecting me to back you up, because I've ***** about the level of math proficiency in our kids before, but now you feel betrayed because I've stood up and said, "No, that isn't the problem."

Nevermind the fact that I've bolded the problem for you, and wrote it in huge *** letters. Partial credit is not the liberal devil that's ruining our schools. The fact that 50% might constitute "proficient" rather than "failure" in many districts is.

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Buckle your pants or they might fall down.

Furlongs aren't standard measurement anymore, feet are. How many barrels in a hogshead? (I still had to learn that) but it isn't about the available of information its about the frequency of contact with the information.

Feet are frequent therefore they should be known.

Furlongs are not frequent so they don't need to be.

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"...but there exists also in the human heart a depraved taste for equality, which impels the weak to attempt to lower the powerful to their own level and reduces men to prefer equality in slavery to inequality with freedom." - De Tocqueville

Metric is more prevalent than Imperial, and simpler to work with. Perhaps then metric should be known.

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Metric was always taught as well.

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"...but there exists also in the human heart a depraved taste for equality, which impels the weak to attempt to lower the powerful to their own level and reduces men to prefer equality in slavery to inequality with freedom." - De Tocqueville

I'm not wasting my time with a point-by-point response to your whinefest. However, every one of your above examples is taking a place where real life didn't give partial credit and expanding the problem where no partial credit was given to include 3 or more other problems.

Let's take them one by one:

1. Generators: If you don't have your electrical generating system set up correctly, you don't get power in houses at all, much less power beaming through the atmosphere. By this idiotic argument a kid who gets a problem 100% correct is getting partial credit because mathematicians haven't found the endpoint for pi.

2. Boeing may very well have to redesign the entire plane in that situation. A wing snapping within the expected performance envelope of the airplane is a 100% failure. If they don't have to redesign the entire plane that isn't getting "partial credit", and for the reason I specified: Getting a solution less than 100% is unacceptable.

3. Your house being a little hot is not an example that pertains in any way except to illustrate hyperbole

4. The Mars rover is a series of problems. As the anaolgy goes, launching the rocket and getting it to Mars are not "partial credit", they're earlier questions on the test. As for "examining the crash" being partial credit, that's asinine. That's like saying that a kid who understands what he did wrong if you go over the test with him later is getting partial credit. The **** rover still didn't work and the kid still got the answer wrong. Getting it right on the next test is not partial credit.

5. Nagasaki was not "partial credit" because the mission was accomplished. WWII bombing accuracy was never any great shakes, but the mission still demonstrated to Japan that we could nuke their cities into oblivion and helped prompt the surrender. Laser-guided bomb like accuracy wasn't expected; that was sort of the point of using a **** nuke, you idiot. That's why we still use nuclear warheads on strategic weapons. If you miss an ICBM silo by 100 meters but still knock it out that's not partial credit, that's **** full credit.

As for your snot-nosed ***** about you not being impressed by being in the military, **** off. The examples were to illustrate a point, and I pull examples from what I know. As for "shiny jock toys", yes, they're designed by people who get the designs right, *******. Contrary to what the media likes to think, they actually do work and the ones that can't be made to work right get cancelled. Yes, if things are done wrong, people are in fact likely to die from it. Do you remember that incident with the Canadians that got bombed when a laser-guided bomb locked on to the designator instead of their target? Gee, I guess there's no **** problem with partial credit! After all the bomb locked on to something!

The bottom line here is that you think your math teaching experience gives you some special insight that it really doesn't. You're not the only one here that has taught math, ****. I've taught it to, and to kids with considerable difficulties in getting it, and I've taught it at this basic, one-step problem level. Giving them partial credit before they get to at least pre-algebra is blowing smoke up their ***. The fact of the matter is that all your points pertain just fine to high-school and JR high math but that isn't the level of problem given as an example. All your well-reasoned arguments miss the point because they don't pertain to what's being talked about here.

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"Hysterical children shrieking about right-wing anything need to go sit in the corner and be quiet while the adults are talking."

If those "shiny jock toys" work as designed, they were built by someone who didn't think partial credit was good enough.

"Shiny jock toys"? Really? I didn't think you were still in high school.

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"Dress cops up as soldiers, give them military equipment, train them in military tactics, tell them they’re fighting a ‘war,’ and the consequences are predictable." —Radley Balko

Wow, Coro. That video is terrifying.

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"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades

If everything was gotten right the first time no one would need prototypes. Design calculations DO come up lacking. Simple fact. They're refined and the bugs worked out.

The SAME principle applies to the sciences. No one works their equations, gets an answer and just publishes it. They're worked again. And again. Then they're worked the opposite direction, again, and again. Then they're put through rigorous examination to determine if they work in reality beyond the theory.

Math errors get corrected. If your basic assumptions are wrong however --your basic problem solving is wrong, they're MUCH MUCH harder to catch.

ESPECIALLY Now, when computers, calculators etc do the actual crunching, you STILL have to work the correct equation for the computer to crunch.

Kaffis:

The woman does a very good job of presenting a case for why the standard algorithm is superior. The standard algorithm is standard for a reason, and it's what got us to the moon.

Now as I pointed out, the methods presented in those books do accurately depict how most engineers and physicists perform multiplication and division operations in their head. A few of them should probably be taught to grade school children to introduce them to various factoring concepts. One of the biggest problems facing high school graduates is that they don't know how to think, and that is a concept that could be shored up by practicing those methods of multiplying and dividing numbers by factoring out groups and adding them up at the end. The pitfall is in thinking they're a replacement for the traditional algorithms. When a colleague of mine showed that to me, her opinion was that the schools were shifting not because they thought it taught math better, but because it was incomprehensible to the parents and thereby kept the parents from becoming too involved. I'm rather of the mind that they're doing it because elementary school staff aren't any great shakes at math. They don't understand that there's a reason we haven't made any serious technological breakthroughs regarding the wheel in several thousand years.

I saw another video whereby a gentleman critiqued this woman's spiel, and he raises some salient points.
[youtube]9skRrnN2_HU[/youtube]
[youtube]U1tPHInrEk0[/youtube]
Pay particular attention to around 2:40 in the second video, where he mentions he dug up a letter from 1940 describing how 60% of the university's seniors were testing below the 8th grade level and that the school had been aware of that trend for the past ten years. This is after mentioning the rest of his department talking about how students over the most recent ten years had been declining in math skills. I've seen my great-grandfather's 8th grade math book, and I can guarantee it was just as hard (and most likely harder) than any of the math books anybody on this board used at the same grade level, whether it's Michael and Taskiss or Lenas and Lex. We certainly haven't raised our standards since 1940, nor have we raised our effectiveness at teaching middle school and high school kids. Now, that doesn't mean our standards aren't slipping, but if they are, then they've apparently been slipping for 80 years. That is not good news at all.

His observation that students think math is a series of equations and formulas that you memorize is something I've directly observed myself. Whether it's an elementary algebra student or a calculus student, they're all looking for that magic bullet that will solve the problem, and they all hate word problems, because they don't know how to think. What adults know about math, which is leading to the attitudes we see presented in this thread, is that there's a formula you memorize to get the right answer.

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Buckle your pants or they might fall down.

No kidding. Those are all parts of the entire process of solving the design problem 'test'. The design of any modern piece of equipment is a problem consisting of thousands, maybe even hundreds of thousands or millions of steps.

When your original, prototype design isn't acceptable, you go back and retake the test and if you're lucky, you'll get to only work on the parts that didn't work right.. but if you're not, changing those parts will require changes to other parts which will change others and so forth.

We let people keep working on a design problem until they get an 'A' in real life because we need the end result of their work, and because of the complexity of the design process and the huge number of unknowns in the process. Those factors don't exist with small children doing math problems that are A) not complex B) do not have any unknowns and C) don't produce any result that we need.

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"Hysterical children shrieking about right-wing anything need to go sit in the corner and be quiet while the adults are talking."

How many foundational mathematical operations are there?

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What's that got to do with anything?

Do you have a point? If so, please make it. I'm not going to respond to any Socratic attempts to make it by asking questions.

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"Hysterical children shrieking about right-wing anything need to go sit in the corner and be quiet while the adults are talking."

Diamondeye:

So, I take it you can't answer the question? Because, honestly ...

1. You don't like answering questions when people pose them to you. You seem to think that attempts to establish a) YOUR knowledge and b) a conversational framework are somehow pointless and insulting.

2. You're talking out of your *** in this thread.

So, answer the question.

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My tolerance for other people's stupidity was exceeded after reading this far into your post. But dumbass, since it has obviously escaped your stellar mind, finding bullshit reasons to give partial credit is another form of lowering the standards, and just like directly lowering the standard, its primary goal is to meet some target "success" rate with nothing to substantiate it, masking the problems of the education system.

But by all means, dazzle us more with your brilliance and feed your ego on the boards. We don't get enough of that with your tirades about how you tutor math students from better schools.

Please Excuse My Dear Aunt Sally?

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But it's not a bullshit reason to give partial credit, Ladas. The entire reason you give a word problem instead of presenting an equation (or operation) to solve is to test to see if the student understands what operation/equation a given situation calls for, and how to set it up themselves.

I'm not as firmly behind the 24+24=48 answer being worth partial credit, because it's far more interpretive (and would thus rely on context in the rest of the test, or how much benefit of the doubt you're willing to give the student) as to what the student thought they were doing there.

But there's no possible way you can argue that setting up the 400/5 and flubbing the answer isn't worth partial credit. That's not bullshit.

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"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades

Tests are supposed to identify how well the student understands the material. If you set up a problem, work through most of it correctly, but stumble at the end, you have illustrated some understanding of the material, and should therefore get some credit.

If you are arguing against partial for a problem, then by extension I assume you must have a problem with grades at all? A B on a test is simply partial credit for the tested material. A B in a class is simply partial credit for the class.

Should everything be Pass/Fail? Of course not, so why does each question have to be pass/fail when the rest of the course is not?

I think we all use some form of the alternate techniques in our head. For example do we do long division to figure out 15% of a bill to get the low end of a tip?

Or do we take 10% of the total and add half again to it in our head?

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"...but there exists also in the human heart a depraved taste for equality, which impels the weak to attempt to lower the powerful to their own level and reduces men to prefer equality in slavery to inequality with freedom." - De Tocqueville