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### Re: 1050: "Forgot Algebra"

Posted: Fri May 04, 2012 2:53 pm UTC
Rotherian wrote:
Fire Brns wrote:7*8?
7*7=49
+7=56
not hard at all.

Or (((7*2)*2)*2)
7*2 = 14
14*2 = 28
28*2 = 56.

/shrug

You are right, my method is for squares.

### Re: 1050: "Forgot Algebra"

Posted: Fri May 04, 2012 2:58 pm UTC
Zamfir wrote:
Yakk wrote:As for 9*9, I don't memorize it, I instead remember the rule -- 9*x is (x-1) in the tens, followed by whatever makes it add to 9 (namely, 10-x) in the ones. Sometimes I'll toss out a guess then verify it. You could call this memorization.

I suspect you (and all of us) have actually memorized quite a large part of the multiplication tables, even if it doesn't always feel that way.

As in, when you don't think about it, you usually know the answer right away. But once you start doubting your memory you have to do a calculation. But the doubt is not really caused by a memory failure, it's an external thing that hinders the more automatic memory.

Like how walking goes more difficult if you're consciously paying attention to it. Oryou recite your phone number flawlessly, then someone asks "are you sure", and suddenly you have think deep and hard. A lot of ingrained memories nearly or entirely bypass conscious thought, and if you try to retrieve them consciously it feels like you have lost the memory.
Good theory. If your theory was correct, I wouldn't make errors when I didn't check. In my experience, when I don't check, I sometimes get the wrong value.

Often I'll end up with 6*7 for 8*7, or 9*6 for 8*7, and the sanity check pass notices the problem and corrects it. When I'm calculating bills without doing a sanity check, the first pass is fast but often error prone. The sanity check pass, which uses an orthogonal method, either agrees with the first pass, or (a non-trivial amount of the time) gives a different answer, at which point I sit down and derive the right answer through a slower method.

You could call this memorization, and all of the sanity checks a bunch of mnemonics. But at some point, you could call everything memorization. As in, I "memorized" the date the war of 1812 ended because I memorized that you can look it up on wikipedia (and that a google crafted like so will get me to the correct page).

### Re: 1050: "Forgot Algebra"

Posted: Fri May 04, 2012 3:16 pm UTC
but does that ever happen for 9*9, or 3*2? for some reason, 7*8 is the hardest to remember for nearly everyone, and the ones near it in the table are next. That would make some sense if we didn't remember them at all but always calculated them from scratch. But timing indicates that we do use pure memorization part of the time, and then 7*8 is still harder than others. We clearly store such facts in very different way than a computer does.

### Re: 1050: "Forgot Algebra"

Posted: Fri May 04, 2012 3:26 pm UTC
Oddly, I remember 7*8 quite well, because, when I was a kid, I could never remember whether 7*8 = 54 or 56, but I knew 6*9 = 54. Eventually, I started remembering 7*8 =/= 6*9, and therefore 7*8 = 56. In short, my brain is a convoluted mess.

### Re: 1050: "Forgot Algebra"

Posted: Fri May 04, 2012 3:58 pm UTC
Zamfir wrote:but does that ever happen for 9*9, or 3*2? for some reason, 7*8 is the hardest to remember for nearly everyone, and the ones near it in the table are next. That would make some sense if we didn't remember them at all but always calculated them from scratch. But timing indicates that we do use pure memorization part of the time, and then 7*8 is still harder than others. We clearly store such facts in very different way than a computer does.
Sure, I have memorized some elements of the times tables.

Ie, from the old song: Two times two is four, four times four is 16, 16 and 16 is 256, 256 and 256 is 65536.

### Re: 1050: "Forgot Algebra"

Posted: Fri May 04, 2012 6:40 pm UTC
I never learned calculus.

I was told in high school that it was an optional course and I probably wouldn't need it in adult life, so being a lazy teenager of course I opted out of that class.

Then, when it came time to do things that needed calculus, I didn't have the time necessary to catch up on it. (Working my way through school, calculus homework load too time consuming on top of almost-full-time job and all my other courses).

Through philosophy I got into logic and from there into set theory and now have passing familiarity with a lot of higher math concepts like categories and transfinite numbers and various extensions of the real numbers, but I still can't calculate an integral. I'm not even sure what an integral is, actually.

If it hadn't been for those "nice" teachers letting me off the hook for math I'd "never need", I would probably be a physicist right now.

### Re: 1050: "Forgot Algebra"

Posted: Fri May 04, 2012 6:55 pm UTC
Pfhorrest wrote:I never learned calculus.
I don't think calculus should be required for high-school students, but it's great to have it as an option. Algebra I certainly think should be required. And basic statistics. (More advanced statistics require calculus).

These seriously are basic life skills that are important for decision making. If you don't have a firm grasp on math when you leave school, than you will forget important things that would help you make wiser decisions later on in life. I liked calculus but I don't put it on the same level of basic life skills.

It does suck that you skipped it when you had a chance. You could always go back and take it but that's probably not very practical. But require something just because a few students might regret opting out would be silly.

The main point of the comic was (and still is) it's silly to be proud that you can't understand or properly use something, and it seems oddly skewed toward math. It isn't a strawman, because it is real behavior that some people have.

### Re: 1050: "Forgot Algebra"

Posted: Fri May 04, 2012 9:45 pm UTC
Pfhorrest wrote:...but I still can't calculate an integral. I'm not even sure what an integral is, actually.

An integral is the area contained within a shape. Whereas earlier classes taught you to find the area of shapes defined by straight lines or perfect shapes (circle), an integral allows you to find the area of any shape, no matter if the lines are straight or curvy.

Calculating an integral by hand involves 4-5 techniques that can be used in various order, along with algebraic manipulation to get it into a form that you can work with. It's rather like opening a combination lock: even if you know the combination, you have to know how to spin the dialer. Calculating an integral on a TI-83 uses something called "fnInt." That will solve any integral as long as it has bounds.

Honestly, all you need to calculate most any integral you will see are 1) reverse Power Rule and 2) how to enter data into "fnInt."

Pfhorrest wrote:I never learned calculus.

Having been brutalized by 8 semesters worth of Calc 1, I can definitively tell you: it's not worth it. Instead of building upon previous concepts, Calc 1 basically crafts all of them into an entirely new field that uses everything before at the same time. Furthermore, the introductory calculus textbook market has been monopolized by one man who used his royalities to custom design a \$25M house in which he lives alone.

Search "The House that Calculus Built" for the article.

Роберт wrote:The main point of the comic was (and still is) it's silly to be proud that you can't understand or properly use something...

Unfortunately, we are all guilty of this in some aspect. No one truly understands the process behind everything they use, be it the production of coffee cups, the path of an oxygen molecule through the body, the manufacture of a motherboard, or the relationship between our constituent subatomic particles. As beings with finite energy, we don't have infinite capacity to learn. Instead, we have built a society that reflects that fact by rewarding people for providing services that others are unwilling or unable to perform. The sooner we all acknowledge our limitations, the sooner we stop coming out as arrogant know-it-alls.

### Re: 1050: "Forgot Algebra"

Posted: Fri May 04, 2012 9:50 pm UTC
goomba25 wrote:
Pfhorrest wrote:I never learned calculus.

Having been brutalized by 8 semesters worth of Calc 1, I can definitively tell you: it's not worth it. Instead of building upon previous concepts, Calc 1 basically crafts all of them into an entirely new field that uses everything before at the same time. Furthermore, the introductory calculus textbook market has been monopolized by one man who used his royalities to custom design a \$25M house in which he lives alone.

Search "The House that Calculus Built" for the article.

Роберт wrote:The main point of the comic was (and still is) it's silly to be proud that you can't understand or properly use something...

Unfortunately, we are all guilty of this in some aspect. No one truly understands the process behind everything they use, be it the production of coffee cups, the path of an oxygen molecule through the body, the manufacture of a motherboard, or the relationship between our constituent subatomic particles. As beings with finite energy, we don't have infinite capacity to learn. Instead, we have built a society that reflects that fact by rewarding people for providing services that others are unwilling or unable to perform. The sooner we all acknowledge our limitations, the sooner we stop coming out as arrogant know-it-alls.

However, if I went through a class that explained thoroughly the process of production of coffee cups, I wouldn't be proud of forgetting everything I learned in that class.

“I basically
wrote the book to use in my own classes,” Stewart says.
“I had no idea it would catch on.”
(From "The House that Calculus Built".)

### Re: 1050: "Forgot Algebra"

Posted: Fri May 04, 2012 10:03 pm UTC
goomba25 wrote:
Роберт wrote:The main point of the comic was (and still is) it's silly to be proud that you can't understand or properly use something...

Unfortunately, we are all guilty of this in some aspect. No one truly understands the process behind everything they use, be it the production of coffee cups, the path of an oxygen molecule through the body, the manufacture of a motherboard, or the relationship between our constituent subatomic particles. As beings with finite energy, we don't have infinite capacity to learn. Instead, we have built a society that reflects that fact by rewarding people for providing services that others are unwilling or unable to perform. The sooner we all acknowledge our limitations, the sooner we stop coming out as arrogant know-it-alls.

I think the point is "proud". There's a big gap between proud and ashamed. You seem to be saying there's no shame in not knowing something; and in many cases that's completely true, nobody can be expected to know everything. But to then be proud of not knowing is perverse. Absolute knowledge is not obligatory, but certainly greater knowledge is at least laudable, not derisibile, is it not?

### Re: 1050: "Forgot Algebra"

Posted: Fri May 04, 2012 11:17 pm UTC
Pfhorrest wrote: There's a big gap between proud and ashamed.

There's also a big gap between a person saying they're ashamed at not knowing something, and actually being ashamed to do something about it. All too often, I encounter people with the attitude that a person can say the words and be immune from further calls to action. I'm not saying that people should learn everything, because that's impossible. But I would like to see people working through learning at least one thing, rather than being proud of only excelling in their comfort zone.

Pfhorrest wrote: But to then be proud of not knowing is perverse. Absolute knowledge is not obligatory, but certainly greater knowledge is at least laudable, not derisibile, is it not?

I am openly disgusted at finding the 89th derivative of a function using Taylor Inequality, because that seems to me (as a non-engineer) to be gross overkill. I'd be the first the point to give another person resources to learn that if they so chose, but I can't conjure a reason of why someone would want to know that. Unless they could show me why that was important beyond the fact that they knew a factoid I didn't, I wouldn't ashamed of not knowing how to use Taylor Inequality.

While greater knowledge is commendable, I would put _much_ more emphasis on conveying an understanding of that knowledge, and what that knowledge means to other people. I think part of the anti-intellectual backlash is due to the fact that the "educated ones" sometimes come off as aloof and arrogant, content to revel in their own accomplishments instead of trying to help others with what they've done (*cough*puremath*cough*). I once asked a math major about what he was studying, and he spoke for a few minutes. Interested, I asked him to define a word I hadn't heard before: toroid. After a minute of hearing coordinates, forms and curves, I was more confused. It wasn't until another math major mentioned "donut" that I instantly got it.

That's what bugs me about Calc 1. I've taken scores of limits, but I still can't tell you the difference between being "infinitely close" to a number and being exactly at that number. I stopped asking "Why?" I took limits, because the people I asked kept robotically repeating "Knowledge is good for knowledge's sake," and sneering at me when I dared to object. So I memorized my toolbox, earned my points and regressed to the point many years ago when I was used rote memorization to learn my times tables.

### Re: 1050: "Forgot Algebra"

Posted: Fri May 04, 2012 11:22 pm UTC
Pfhorrest wrote:I think the point is "proud". There's a big gap between proud and ashamed. You seem to be saying there's no shame in not knowing something; and in many cases that's completely true, nobody can be expected to know everything. But to then be proud of not knowing is perverse. Absolute knowledge is not obligatory, but certainly greater knowledge is at least laudable, not derisibile, is it not?

It was perversely cathartic to in-your-face my forgotten English teacher on the topic of poetry. My rational brain knows that the satisfaction I take in deeming poetry to be pointless is about as stupid as the character claiming never to have solved for X since graduation, but the other parts are still stuck on getting a B in my main source for A's in school based largely on failing The Love Song of J. Alfred Prufrock and partially on a failure to read all the way to the end of The Old Man and The Sea. As a youngster, English was very far from my weakest subject and I took great pride in things like testing out of the lower and upper division comp requirements at UC. (I blame the internet for the subsequent degradation of my language arts skills along with society, the economy and possibly rap music since jazz and rock and roll have already been done.)

For me, remembering the explication incident rendered people priding themselves on certain types of ignorance less perverse than just rude oras evidence of injured pride. I sucked at math from long division through trig, remaining a solid C student until I got a second semester trig instructor who gave out pity grades to graduating seniors. I had no ego invested in algebra and a great deal of respect for my algebra instructor, whom I would never brace in public like the young lady in the strip. The poetry-is-life jackass who failed me on that unit struck at the very heart of my scholastic ego, though, and it would give me great pleasure to have an in-your-face moment with him. My written and oral communications skills have gotten me much further in life than getting a numerical value for X, and he had the temerity to F me on a part of it that has never once come up since that class.

Or, like never-solved-for-X chick, part of me would like a chance to tell that English teacher "life has rendered your negative yet accurate judgment of me irrelevant," which is a much nicer way of saying IN YOUR FACE. The rest of me knows that's juvenile and a waste of time.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 2:43 am UTC
DutchUncle wrote:It's part of general American anti-intellectualism to be proud of inability to think.

Inability to think and irrelevant subjects are two different things. The sum of all human knowledge and creativity is so great that a million people, splitting it amongst themselves, couldn't possibly take it all in. These people aren't celebrating their own stupidity, they're celebrating their freedom from having things that bore them to tears (or otherwise take them in a direction they're not interested in or are simply bad at) shoved down their throats.
If you have television, for example, it'd be like something with authority equal to the school board telling you that you need to tune in to one of the click through stations for an hour each day before you could go to work.
Let people focus on their individual strengths.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 3:47 am UTC
sarysa wrote:
DutchUncle wrote:It's part of general American anti-intellectualism to be proud of inability to think.

Inability to think and irrelevant subjects are two different things. The sum of all human knowledge and creativity is so great that a million people, splitting it amongst themselves, couldn't possibly take it all in. These people aren't celebrating their own stupidity, they're celebrating their freedom from having things that bore them to tears (or otherwise take them in a direction they're not interested in or are simply bad at) shoved down their throats.
If you have television, for example, it'd be like something with authority equal to the school board telling you that you need to tune in to one of the click through stations for an hour each day before you could go to work.
Let people focus on their individual strengths.

It's not a problem not to know something that isn't relevant to you. It is a problem to be proud of your lack of knowledge.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 4:11 am UTC
cjmcjmcjmcjm wrote:
sarysa wrote:
DutchUncle wrote:It's part of general American anti-intellectualism to be proud of inability to think.
Inability to think and irrelevant subjects are two different things...Let people focus on their individual strengths.

It's not a problem not to know something that isn't relevant to you. It is a problem to be proud of your lack of knowledge.

In 2 weeks, after the final for the class I'm taking, these are a few of the things I will be very proud of not knowing:
Epsilon-Delta proofs
The formal definition of a limit
Finding the area of a shape created by rotation (disc/washer)
Integrating by partial fractions
Conics
Taylor Inequality
This list has caused me no shortage of grief over the span of 8 semesters. Lacking the ability to retaliate against ephemeral concepts, my only recourse is to discard them as soon as possible.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 5:17 am UTC
goomba25 wrote:This list has caused me no shortage of grief over the span of 8 semesters. Lacking the ability to retaliate against ephemeral concepts, my only recourse is to discard them as soon as possible.

I feel like there is some unwarranted conflation here between anger at being forced to do something unnecessary (no comment from my part on how forced or unnecessary anything is, but that's clearly your experience), and pride in losing anything that may have been gained from the experience.

Pride, to me, implies that you consider it an accomplishment to have resisted learning something (despite not successfully resisting going through the forces motions of pretending to learn it); like you have a leg somehow up on those who did learn something from it.

For an analogy, consider a group of people forced through military boot camp; and for the sake of argument lets say it's really forced, like at gunpoint, and really is unnecessary, for no purpose other than to break their spirits or something.

Most people who go through boot camp come out of it in much better shape than they went it. I am not in great shape, and I certainly as hell would not appreciate being put through boot camp against my will; I would be angry as all fuck the whole time through. When it was finally over, I would just be satisfied that it was over. If I came out of it fit for the experience, I probably wouldn't feel especially proud of that; the forced tribulations would be much more salient in my mind.

But, if somehow I managed to make it through without getting in any better shape, or quickly reverted back to my current shape, I wouldn't feel any pride in that either. I wouldn't feel any urge to say "Fuck you Drill Sergeant, I'm still fat!" I would probably want to say "Fuck you Drill Sergeant, you fascist piece of shit", but my being fat wouldn't be something to throw back at him. That's the part I don't understand.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 5:50 am UTC
Zamfir wrote:but does that ever happen for 9*9, or 3*2? for some reason, 7*8 is the hardest to remember for nearly everyone, and the ones near it in the table are next. That would make some sense if we didn't remember them at all but always calculated them from scratch. But timing indicates that we do use pure memorization part of the time, and then 7*8 is still harder than others. We clearly store such facts in very different way than a computer does.

In my elementary math ed class, we were told that the reason for this is because when most teachers start teaching multiplication, they usually start with 0 and build up to 10, which means students are still working on committing the 7s, 8s, and 9s to memory as the unit is wrapped up. We were taught to teach multiplication tables starting with 7. This way, by the time the unit is wrapped up, they've practiced all the harder ones so much that they're memorized and the easier ones are, well, easy. Doing it this way also builds self-confidence, as the 7s table is the only one without any easy pattern to remember. As you progress through the unit, students start jumping at patterns that they notice and learn them that much more quickly.

All theory, of course.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 6:28 am UTC
ccaccus wrote:Doing it this way also builds self-confidence, as the 7s table is the only one without any easy pattern to remember. As you progress through the unit, students start jumping at patterns that they notice and learn them that much more quickly.

How exactly does the 7s table have any less pattern than any other number? They all have the pattern of "add N again at each step", and 'shortcuts' like "increase the tens by 1 and decrease the ones by 10-N".

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 7:21 am UTC
Comic 519 is a good example of being proud of not having learned anything at school. Perhaps it's more common than I thought.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 7:32 am UTC
babble wrote:Comic 519 is a good example of being proud of not having learned anything at school.

I think in that case it's less a commentary on the value of knowledge, and more a comment on the comparative quantities of knowledge delivered by traditional education vs hands-on self-education. He's not proud to have not learned what was being taught, he's disappointed that what was being taught was so paltry compared to what he could teach himself.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 7:44 am UTC
Well, the person who says they haven't used algebra in their life isn't inconsistent with that interpretation either. Comic 519 is saying 'in your face' to 11th-grade teachers. The person in this new comic might well follow theirs up with 'my self-taught expertise in art history has been so much more useful'.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 7:45 am UTC
Pfhorrest wrote:
goomba25 wrote:This list has caused me no shortage of grief over the span of 8 semesters. Lacking the ability to retaliate against ephemeral concepts, my only recourse is to discard them as soon as possible.

I feel like there is some unwarranted conflation here between anger at being forced to do something unnecessary (no comment from my part on how forced or unnecessary anything is, but that's clearly your experience), and pride in losing anything that may have been gained from the experience.

Pride, to me, implies that you consider it an accomplishment to have resisted learning something (despite not successfully resisting going through the forces motions of pretending to learn it); like you have a leg somehow up on those who did learn something from it.

I am proud because I resisted learning - not because I feel superior to those who learned it, but because I feel superior to those who assigned it. Every additional day that passes without approaching the point where I might consider a tinge of regret at forgetting what I learned in Calc is more vindication that I was right and they were sadistic. I was a biology major that was forced to take engineer-level Calc, even as every other biology-related department thought that level of understanding was overkill. After I graduated, my department came to its senses, scrapped the requirement, and created a custom course, tailored to biology majors*, which deemphasizes theory and focuses on application problems and Statistics.

*In Calc 1, you learn to use differential equations to estimate the amount of bacteria that will inhabit a dish after a certain period of time, given a constant growth rate. From personal lab experience, I never saw anyone using such an imprecise estimate. Knowing that various factors would change the growth rate from minute to minute, we sectioned off a bit of the dish and counted individual dots with a tally machine, then extrapolated.
Pfhorrest wrote:But, if somehow I managed to make it through without getting in any better shape, or quickly reverted back to my current shape, I wouldn't feel any pride in that either. I wouldn't feel any urge to say "Fuck you Drill Sergeant, I'm still fat!" I would probably want to say "Fuck you Drill Sergeant, you fascist piece of shit", but my being fat wouldn't be something to throw back at him. That's the part I don't understand.

The underlying reason is not that I stayed fat after boot camp, it's that I was never shown why being fit would be useful outside of boot camp. Not only was Calc hard, it broke the truce I had with math. After years of being lost, I stopped deriding math when I took Statistics**, because for once my calculations meant something other than another arbitrary value. Right after that class, I entered college and had a Fields Medalist as my first math professor who ground my spirits to dust through 17 weeks of abstract theory. I've taken calculus 8 times, and 99% of my assignments focused on practicing a tool (u-sub, ddy) instead of putting forth situations where a person could use the tool. Even if the situation was contrived, it would have preferable to the silent vacuum of an endless score of problems asking me to "evaluate" another meaningless string of symbols and numbers. Because Calc didn't even try to prove itself useful and instead kept insisting on its importance in and of itself, I responded in kind and determined that beyond the high school level and Statistics, the math was worthless to all but a select few.

I suffered greatly at the cold hand of Calc, and I will not support any idea that leads to people being forced to go through what I did. It wasn't until college that I became smug at my mathematical deficiencies, and had I been allowed to choose the non-engineer Calc series that already existed and was "intended for majors in the life and social sciences", I would have happily endorsed a "I have my cake and you can have yours" attitude. Instead, I am convinced that Calc, with its current fixation on abstract topics and esoteric theory, should not be taught to anyone but those in the most quantitative of disciplines. The rest can easily subsist on a highly-sanitized version.

**Please don't point out that I need Calculus to really understand Statistics, because 1) coffee cups and 2) no person I know who works in an actual biology lab and conducts experiments with living organisms (i.e. everyone but biostaticians) is even aware that Calculus underlies Statistics, much less is actually able to use Calculus in any work-related situation.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 11:06 am UTC
Pfhorrest wrote:
ccaccus wrote:Doing it this way also builds self-confidence, as the 7s table is the only one without any easy pattern to remember. As you progress through the unit, students start jumping at patterns that they notice and learn them that much more quickly.

How exactly does the 7s table have any less pattern than any other number? They all have the pattern of "add N again at each step", and 'shortcuts' like "increase the tens by 1 and decrease the ones by 10-N".

The patterns are in the shortcuts.
9 times table - add one to the first digit, and take one from the second digit (only works up til 90 though).
5 times table - number ends in 5 or 0 (bonus for getting 5 for 5 times odd numbers and 0 for even)
3 times table - digits add up to number divisible by 3
6 times table - digits add up to number divisible by 3 + last digit is even number
2 - all the even numbers
4 and 8 are a bit more difficult off the top of my head, but they always end in even numbers.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 12:32 pm UTC
5s: half the number. That's the tens. If you rounded down, stick a 5 in the ones.
9: Subtract 1 from the number. That's the tens. The ones is 10 minus the number.
2: Add the number to itself.
4: Run 2 twice.
8: Run 2 three times.
3: Somewhat tricky. (there is the add the digits trick, but that just makes sure you didn't get it wrong).
6: Run 3, then double it.
7: Also tricky, but a higher value.

Note that being able to do 2/4/5/8/9 means only (3*3, 3*6, 3*7, 6*6, 6*7 and 7*7) are out of reach -- for others, you can use the other half of the pair to find the answer. Of 2/4/5/8/9, 8 requires 3 steps, so the next hardest will be 3*8, 6*8 and 7*8.

Squares can be found from adjacent squares if you really need to. If you know x^2, you can add 2x+1 to it and get (x+1)^2 -- or subtract 2x and then add one to get (x-1)^2. So if you know 5^2, you +11 for 6^2, or -9 for 4^2. If you aren't sure of the rule, you can derive it (x+1)^2 = (x+1)(x+1) = (x+1)x + (x+1)1 = x^2+2x+1 for a sanity check.

Plausibility testing is also important to keep your errors down. For 3, the "sum up digits and get a number divisible by 3", for 9 "add up digits and get 9", for 6 "halve it, and do the 3 test", for 2 "does it end in an even digit?", for 4 "halve it, do 2 test", for 8 "halve it, do 4 test", for 5 "does it end in a 0 or a 5?". That leaves 7, whose equivalent test is seriously messy. So when you guess that something is the result of a number multiplied by 7, there isn't a quick sanity check you can do.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 12:47 pm UTC
Pfhorrest wrote:For an analogy, consider a group of people forced through military boot camp; and for the sake of argument lets say it's really forced, like at gunpoint, and really is unnecessary, for no purpose other than to break their spirits or something.

Most people who go through boot camp come out of it in much better shape than they went it. I am not in great shape, and I certainly as hell would not appreciate being put through boot camp against my will; I would be angry as all fuck the whole time through. When it was finally over, I would just be satisfied that it was over. If I came out of it fit for the experience, I probably wouldn't feel especially proud of that; the forced tribulations would be much more salient in my mind.

But, if somehow I managed to make it through without getting in any better shape, or quickly reverted back to my current shape, I wouldn't feel any pride in that either. I wouldn't feel any urge to say "Fuck you Drill Sergeant, I'm still fat!" I would probably want to say "Fuck you Drill Sergeant, you fascist piece of shit", but my being fat wouldn't be something to throw back at him. That's the part I don't understand.

A military boot camp tries to teach quite a lot of things. Would you understand someone saying "Fuck you Drill Sergeant, I let my hair grow long" or "I still don't mindlessly do what I am ordered"? The reason there is pride possible in those (and in the algebra example), is that the Drill Sergeant/maths teacher places an unwarranted moral value on obedience/algebra. The pride isn't in the absence of knowledge, it is in the validation of the earlier rejection.

The pride in the comic is that the student knew at school that algebra would be useless for them, the teacher berated them for that view, and they subsequently found out that they had been right, and the person in authority had been wrong. Why wouldn't you have pride in showing that you were more insightful about the utility of maths than a maths teacher?

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 6:02 pm UTC
cjmcjmcjmcjm wrote:
sarysa wrote:
DutchUncle wrote:It's part of general American anti-intellectualism to be proud of inability to think.

Inability to think and irrelevant subjects are two different things. The sum of all human knowledge and creativity is so great that a million people, splitting it amongst themselves, couldn't possibly take it all in. These people aren't celebrating their own stupidity, they're celebrating their freedom from having things that bore them to tears (or otherwise take them in a direction they're not interested in or are simply bad at) shoved down their throats.
If you have television, for example, it'd be like something with authority equal to the school board telling you that you need to tune in to one of the click through stations for an hour each day before you could go to work.
Let people focus on their individual strengths.

It's not a problem not to know something that isn't relevant to you. It is a problem to be proud of your lack of knowledge.

You kind of blew off my point. People are really proud of their freedom to choose what to take in, not to have it chosen for them. I've had moments where I was like the woman in the comic or Jimmy Kimmel during the White House Correspondents' Dinner...but deep down inside it was just an irrational way to celebrate my freedom.

Human behavior is more than skin deep.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 6:11 pm UTC
Sometimes I wonder how people can function in this world without understanding basic information theory, logic, math, science. Then I wonder what I must be missing in life because of all the subjects which I never studied.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 6:39 pm UTC
Pfhorrest wrote:I think the point is "proud". There's a big gap between proud and ashamed. You seem to be saying there's no shame in not knowing something; and in many cases that's completely true, nobody can be expected to know everything. But to then be proud of not knowing is perverse. Absolute knowledge is not obligatory, but certainly greater knowledge is at least laudable, not derisibile, is it not?

Point from the flip side:
The object for our players is to get three stars in a row: across, up and down, or diagonally. It is up to them to figure out if a star is giving a correct answer or making one up. That's how they get the square. Each game is worth two hundred dollars. We play a two-out-of-three match. Our players play for four hundred dollars, and once a day we play the Secret Square game. We'll play that game as soon as we complete the one in progress.

From memory. Placed there before there was such a thing as Wikipedia to look up stuff that you hadn't safeguarded in your own wetware. I'm not proud of that being saved in long-term storage and taking up space that could have otherwise gone for something useful. And if I had once known it once and then forgotten it, I could honestly say that I was proud of having let it go.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 8:56 pm UTC
goomba25 wrote:**Please don't point out that I need Calculus to really understand Statistics, because 1) coffee cups and 2) no person I know who works in an actual biology lab and conducts experiments with living organisms (i.e. everyone but biostaticians) is even aware that Calculus underlies Statistics, much less is actually able to use Calculus in any work-related situation.

…and that's why I laugh every time one of my psychology major friends drops to communication because they failed stats. (Although I do understand that no where near a significant population of the total psychology students are interested in doing research; most of them want to do clinical work or something involving criminal justice, but that's another rant about my school.) (It also doesn't help that apparently the psych/social science stats is almost as hard as real stats, but without the 5 semesters of maths prereqs, and taught as a language, not maths.)

Personally, I like math because it is esoteric. Art doesn't have any logical purpose, yet people still make it and it definitely does bring joy to many people's lives. As someone else said, all you have to do is take your first breath and take your last breath, and sometimes they're one and the same. Look at what else we do.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 9:45 pm UTC
Роберт wrote:But to then be proud of not knowing is perverse. Absolute knowledge is not obligatory, but certainly greater knowledge is at least laudable, not derisibile, is it not?

Everyone here who has ever proudly stated that you know nothing about baseball (or insert any other sport) and don't care, raise your hand. Bet your old PE teacher used to say it was important too.

Never in my life have I met anyone that doesn't show pride at ignorance of at least one subject. It's all relative.

### Re: 1050: "Forgot Algebra"

Posted: Sat May 05, 2012 10:16 pm UTC
cjmcjmcjmcjm wrote:
goomba25 wrote:**Please don't point out that I need Calculus to really understand Statistics, because 1) coffee cups and 2) no person I know who works in an actual biology lab and conducts experiments with living organisms (i.e. everyone but biostaticians) is even aware that Calculus underlies Statistics, much less is actually able to use Calculus in any work-related situation.

…and that's why I laugh every time one of my psychology major friends drops to communication because they failed stats. (Although I do understand that no where near a significant population of the total psychology students are interested in doing research; most of them want to do clinical work or something involving criminal justice, but that's another rant about my school.) (It also doesn't help that apparently the psych/social science stats is almost as hard as real stats, but without the 5 semesters of maths prereqs, and taught as a language, not maths.)

Statistics education has been a travesty since the 1930's. Now that we have so much computing power available, they really ought to start out with visual stuff explaining about how random stuff and unknown causes can jumble things up, and then jump right to doing a jack-knife etc to test with, and toward the end explain about traditional methods that are needed to publish in traditionalist journals.

Usually statistics classes don't even try to make it make sense. It's no wonder the students hate it.

### Re: 1050: "Forgot Algebra"

Posted: Sun May 06, 2012 4:58 am UTC
Pfhorrest wrote:
ccaccus wrote:Doing it this way also builds self-confidence, as the 7s table is the only one without any easy pattern to remember. As you progress through the unit, students start jumping at patterns that they notice and learn them that much more quickly.

How exactly does the 7s table have any less pattern than any other number? They all have the pattern of "add N again at each step", and 'shortcuts' like "increase the tens by 1 and decrease the ones by 10-N".

As others have said, the patterns are in the shortcuts. A lot of times, they don't realize the shortcuts are math or find their own methods that work for them until they memorize the routine. It's easy to do for smaller numbers, but once you hit 6, 7, and 8, the patterns get harder. And yes, the base pattern is "add N at each step." But which is easier to add for a young student? 2, 3, 5, and 10 or 6, 7, and 8? You have to remember, many of these students may not have fully mastered addition when multiplication is being introduced.

Finger tricks are also good to introduce at that age. Many students for the twos table, for example, will count by twos as they count on their fingers. (Hold up 10 fingers and put one down for each that you're multiplying by and count by twos as you do it. So 2x3 (2,4,6) is 6.) 3s, 5s, and 10s are just as easy.

To multiply by 9, hold up 10 fingers and put down the one you're multiplying by. The number of fingers on the left is the 10s place, and the numbers on the right is the ones place. So for 9x4, put down the fourth finger counting from the left. You should be holding up 3 fingers on the left side and 6 fingers on the right. 36.

The methods they find can also be interesting.

I once had a student who noticed that the 4's table repeated in the ones place: 4,8,2,6,0. Whenever he had to multiply by 4, he held up 2 fingers on each hand and start counting. When he changed to the right hand or hit zero, he knew the 10s went up by 1. Complicated? Probably, but it worked, and he came up with it himself. Eventually, he stopped using the method and had the 4s memorized. I asked him why he'd stopped using it and he'd forgotten he'd even done it at all.

I shouldn't have picked specifically on 7, as 6, 7, and 8 are all difficult for young students. But 6 and 8 have a repeating sequence of numbers: 6,2,8,4,0 and 8,6,4,2,0, which some students pick up on, others don't. 7, on the other hand, doesn't have that. For a standard 1-10 7s table, the ones' place runs through each number once seemingly randomly before repeating in the next 10. (7,4,1,8,5,2,9,6,3,0)

Sorry for the long post.

### Re: 1050: "Forgot Algebra"

Posted: Mon May 07, 2012 12:17 pm UTC
FruitbatNT wrote:The way I read it, he's saying that being force-fed difficult concepts through pointless repetition

If you don't learn difficult concepts in school, will you be prepared to attack difficult concepts out of school? You want someone to do hard things, you need to push them through the hard part at least once; you need to deny them the option of saying "I can't" so that they learn they can.

And if they're difficult concepts, the repetition isn't pointless at all.

learning how to ... communicate with people who happen to be born in another country?

That's hilarious. I had a year of German in kindergarten, two in high school and one in college. I remember probably less than 20 words of vocabulary. (Perhaps my college years were problematic, but I was an above average high school student.) Far and few between are Americans who took a foreign language in high school and walked away with anything at all useful, who could communicate even the most bare necessities to a foreign speaker.

### Re: 1050: "Forgot Algebra"

Posted: Mon May 07, 2012 12:50 pm UTC
aerogen42 wrote:This comic is wrong because:

1-Algebra is not fun.

That's certainly not a universal truth.

2-Music, Cooking and Language are actually quite interesting and not boring at all.
3-I can use music to make something beautiful, cooking to make something tasty and foreing language to argue with foreing people on the internet (as I just happen to be doing right now).

Music classes have taught me that I shouldn't sing even in private, for fear someone might hear me. Maybe I should take some cooking classes, but all my practice in cooking has taught me is that it's way too likely to involve a lot of clean up and inedible results (frequently connected to the first). In any case, unlike music and algebra, cooking has never struck me as more than a practical skill. Languages, like music, are interesting in theory but not in the least worth the time expended on them for me. Learning thousands of vocabulary words is not interesting.

### Re: 1050: "Forgot Algebra"

Posted: Mon May 07, 2012 3:01 pm UTC
*Kat* wrote:Math is the reason why I did not pursue a degree in computer science. I have a life long love of computers but was told that I had to be good at math in order to be good in computer science. So I studied history instead. Through luck and chance though I was presented with the opportunity to learn a database language and I took to it like a duck to water. One thing led to another and I got a similar chance to learn how to write JSP. Which I also did...and LOVED. So far I have been good at every computer related activity that has come my way. But to even try for a degree in computer science would be worthless and stupid because, again, I can't do higher math worth a damn.

You may not need much math to be a useful programmer, as you found out. You'd still need the math to learn computer science though. Computer science science is not so much programming, but figuring out how much time some program will need for various inputs. And prove it, using math. so without math, you won't do well in computer science.

A programmer can do some nifty things, but a computer scientist can tell why some programs are slow. The programmer can then try a different approach experimentally, a computer scientist can sometimes know that no approach will be fast for just this class of problem.

### Re: 1050: "Forgot Algebra"

Posted: Mon May 07, 2012 3:20 pm UTC
Dr_Revels wrote:I accompanied my fiance to a meet up with some high school friends she hadn't seen in 17 years, and this exact sentiment arose in the course of their reminiscing. She turned to me and said, "can you think of any time you have had to use algebra since high school?", but wasn't amused when I answered back, "yes, daily"..

Some people love to say "I haven't had any use for the math I learned in school." And they expect others to agree too. I met an annoying woman like this at a party once. Annoying, because I happen to be good at math, and nobody like being belittled. So I turned it around: "That applies to so many other things from school too. All that litterature, and the great writers they told us about. It was actually kind of cool, but I haven't had any use for that at all." She got so angry, it was fun to see.

### Re: 1050: "Forgot Algebra"

Posted: Mon May 07, 2012 4:04 pm UTC
Роберт wrote:But to then be proud of not knowing is perverse. Absolute knowledge is not obligatory, but certainly greater knowledge is at least laudable, not derisibile, is it not?

Everyone here has proudly stated that they know nothing about baseball.

Don't put words in my mouth.

### Re: 1050: "Forgot Algebra"

Posted: Mon May 07, 2012 4:41 pm UTC
Роберт wrote:
Роберт wrote:But to then be proud of not knowing is perverse. Absolute knowledge is not obligatory, but certainly greater knowledge is at least laudable, not derisibile, is it not?

Everyone here has proudly stated that they know nothing about baseball.

Don't put words in my mouth.

Directed by M. Night Shyamalan

### Re: 1050: "Forgot Algebra"

Posted: Mon May 07, 2012 5:29 pm UTC
Роберт wrote:
Роберт wrote:But to then be proud of not knowing is perverse. Absolute knowledge is not obligatory, but certainly greater knowledge is at least laudable, not derisibile, is it not?

Everyone here has proudly stated that they know nothing about baseball.

Don't put words in my mouth.

You misread it, and misquoted it. He didn't say that.

Edit: Oops! As Роберт pointed out, he didn't say it.

### Re: 1050: "Forgot Algebra"

Posted: Mon May 07, 2012 5:44 pm UTC
J Thomas wrote:
Роберт wrote: