I’ll bet that question was one of those really vague ones too, like:
“True or False: The US Civil War was over slavery.”
On the other hand, I went to school with some lazy motherfuckers. They would have just jotted down a T or an F and taken a nap.
I can’t remember exactly. It was something about the Civil War, but it wasn’t that one.
Also, my friend (the only one… “all” was a convenient short-hand in my first post) just jotted down “T” and left to go smoke pot. He got it right and got 100%. I was very jealous, because I also wrote “T” and got 100%, but stuck around to write the damn essay when I could have been off smoking pot with my buddy, which of course is far more entertaining and frequently more edifying than test-taking.
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Under the British system, when I went to school, the “right answer” counted for exactly 1 point out of however many points the question was worth (for Math and Physics, at least). All the other points were for the steps.
So if there was a 5 point question, and you just put down the right answer, you’d get 1/5. If you got all the steps right, but flubbed the right answer at the end (because you messed up on the calculator, say), you’d get 4/5.
This was particularly helpful, because the point value was the same as the number of steps (generally) required. A 5 point question would (ideally) have 5 steps (although if you had a solid way to solve it in 3 steps you’d still generally get full credit).
Not only that, but you could flub any step and continue to get full-credit on any later steps or questions that used that answer, through “error carried forward.” e.g.
1. John went from co-ordinate A (0,1) to co-ordinate B (2,1) in 6 seconds. What was his speed? (2 pts)
distance from A to B: 3 meters | incorrect, -1pt
speed = d/t = 3m/6s = 0.5 m/s | correct (error carried forward).
| total: 1 out of 2 pts
2. How long would it take him to go another 5 meters?
5 m / 0.5 m/s = 10 seconds | correct (error carried forward)
| total: 1 out of 1 pts
My American professors in college all just gave a half-hearted “1 point” or “half points” for getting all the steps correct except for the answer, and no points for error-carried-forward. It drove me mad.
Of course, it requires someone actually reading your work, instead of a TA with an answer sheet.
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Oh, goodness, I like this. It encourages one to care about where one actually went awry, as opposed to thinking, “I’m bad at math.”
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You might be right about the 1pt for the answer. I was talking about the British system too. It was too long ago…
I remember ECF 
…consider the normal mathematics curriculum, which continues relentlessly on its way, each new lesson assuming full knowledge and understanding of all that has passed before. Even though each point may be simple, once you fall behind it is hard to catch up. The result: mathematics phobia. Not because the material is difficult, but because it is taught so that difficulty in one stage hinders further progress. The problem is that once failure starts, it soon generalizes by self-blame to all of mathematics. Similar processes are at work with technology. The vicious cycle starts: if you fail at something, you think it is your fault. Therefore you think you can’t do that task. As a result, next time you have to do the task, you believe you can’t so you don’t even try. The result is that you can’t, just as you thought. You’re trapped in a self-fulfilling prophecy…
–Donald Norman, The Design of Everyday Things
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Well, the thumbs are separated from the rest for a reason.
Having to work out several steps, all neat and organized so someone else can read it, and in the order that someone else would expect, is going to inflict a lot of extra pain, and require people to do every preblem twice.
ECF is great, but labour intensive, especially if something goes awry early on in the problem (such as a sign error on a single term in a large partial fraction expansion). I don’t know how many institutions are willing to pay a fair amount for all the extra work involved (or, in the case of salaried teachers, who would spend all that extra time doing proper marking).
There are dollar coins, which I’m not averse to using, but which require me to go out of my way to obtain. I wish the parking meters in my area took them though. Save me a hassle. Half dollars would also be nice. As a coin collector who takes actually bothers to collect non-US coins, it’s remarkable to me how the US is the only country that seems to dislike using half of their main denomination where the main denomination is of sufficient value to make quarters worth minting.
An aside: I can’t tell you how often people will walk into the coin shop I frequent with Bicentennial quarters, Susan B. Anthonys, and even Sacajawea coins with high hopes. People, those coins are rarely worth more than face value, and the ones with crayon on one side and something resembling jellied sludge eating the face off the other side are worth less than face value from the perspective of someone who would have to touch them at his day job.
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An equation editor, once it’s gotten used to, is much faster than writing. What I’m trying to say is that kids should be used to showing their work so when they’re doing more than just arithmetic they’re used to writing.
You have just made their life difficult. The whole point of the Dilbert comic is that doing that does not help.
Being a cashier is utterly mind-numbing. You learn the routines and algorithms and you do them on autopilot, because no human is capable of being present and inquisitive for eight solid hours of rote busywork. 99.9% of people who hand you cash will either just give you bills, or will count out exact change, so you learn to deal with that mechanically and not screw up too often. When somebody hands you $2.14 on a $1.89 purchase, your first thought is “Uh, this isn’t nearly enough change to cover 89 cents,” and your second thought is “Oh, right, he’s fucking with me. Yeah, mess with the wage slave who has to smile at you, I’m sure it makes you feel like a big man.” And then you dig around in your head for a while and drag your brain out of whatever corner it’s found to hide from the grinding banality of your job, and eventually it tells you to give the jackass a quarter, and then it runs off and hide again while you move on to the next customer.
At no point do you think “Aha, that 10 extra seconds of processing time enabled me to save half a second retrieving coins! Picking up a quarter is so much easier than picking up a dime and a penny! Thanks, Dilbert!”
I didn’t understand what “adversity builds character” meant until I worked at a gas stations for a year and a half after college. I’m much nicer to cashiers now. It’s easy to smirk at the stupid peon who doesn’t understand simple math when your brain is fresh and stimulated and you’ve never actually done his job.
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It’s not about kids not being used to writing.
As an adult, writing still hurts, and typing still hurts, and writing more hurts more, and typing more too.
Respectfully, I disagree. The first method makes sense and (more importantly) teaches you a critical number sense about “place” - tens, hundreds, etc. You can’t understand what, say “234”, actually means if you don’t get that. If you DO get that, then the first method makes complete sense and has the bonus of being both more direct and quicker.
The problem is, Hemant leaps to the assumption that kids can’t understand place. And respectfully, I submit that that is a teacher’s job. Place is the core of number sense (his phrase) that is really, really, really essential.
Point at your kids’ hands and ask them how many fingers (including thumbs) they have. Now relate that to “place”. Each “place” is worth 10 more than the one to the right. We use 10 as the “basis” of our system because we have 10 fingers. It doesn’t hurt to have an abacus around to illustrate how “place” works in a very nice, visual way.
I’ve learned some handy shortcuts for approximation math in my head but what Hemant is doing on the bottom is the worst of both worlds - it’s an approximation approach that takes 4 steps to figure out the answer!
I don’t mind kids being taught some tricks to break a problem down, but that is not a substitute for teaching them the most direct and important method that reinforces what numbers actually mean. that’s number sense!
I can’t hold a sequence of 7 numbers with a total of 16 digits in my head simultaneously, then add them mentally. I don’t have that kind of “RAM”. Is that normal? I’d rather just do the old method of subtraction and at most, only have to hold 3 or 4 numbers simultaneously. I have a hard enough time hanging on to my social security number and phone numbers. And those are just rote memorization tasks, and I don’t have to actually treat them as an “int” but instead a “string”.
Trouble is, when you are making change you aren’t keeping track of the total of the change, which is what the example seems to be doing. When you make change you simply count up you don’t then finish and count the amount of change you pulled out to reach the amount tendered.
If the example shown is a tracking of how making changes works then that’s fine, but it doesn’t appear to be.
I didn’t mean to come off as condescending. I totally realize they’re running on autopilot and I’ve just messed that up. I don’t do it because I think it makes their life easier. I do it because I want quarters for the laundry machine in my building.
I worked the register at a small town hardware store for years. I know what it’s like to give change. But I’m also a professor and utterly saddened by how bad my students’ math skills are, especially considering it’s supposedly a top tier school.
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The metric system is based on multiples of 10 and that’s too complicated for the average American, so this might as well be quantum mechanics.
Any sort of change for a generation of parents who were raised on “Two by Two into the Ark”, and “One Man, One Woman” aren’t exactly going to be open for any sort of change that looks like someone’s trying to pull a fast one.
You’re being awfully unfair…
You want to go to a town in middle earth and a ranger says that’s two leagues away… A leagues is how far again? Well it turns out to be 5.55600 kilometers, so now that you’re visiting middle earth, you have to reckon in a totally different set of base units than you’ve grown up with. You want to buy a sack of potatoes? It’s 10 grains of gold per stone. What’s that in kilograms?
If you’re lucky and went to a good school in America you probably have familiarity with metric units, and might even have a feel for the conversions more or less. But nobody uses metric unless they’re a scientist in the US, because nobody’s forcing us to, and using metric is a bad way to communicate when most people have no feel for the units.
Metric makes a lot more sense objectively compared to the American traditional unit system, but everyone in America grows up reckoning weight in pounds, volume in gallons/ounces, distances in inches, feet and miles, temperature in Fahrenheit, and nobody has an f’ing clue as to what unit to use for barometric pressure, since there’s like half a dozen different ones, and nobody uses them consistently.
Anyway, just because we’re used to a set of base units doesn’t mean we don’t have the ability to multiply/divide by 10.
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