## Stupid Math Teachers?

For the discussion of math. Duh.

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Twasbrillig
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### Stupid Math Teachers?

In my grade 10 Math class today, we were learning about finding the size of angles on a Cartesian Plane in excess of 360 degrees. Pretty basic stuff, as most grade 10 Math is. Our math teacher decided to go off on a tangent (pun definitely intended) about how you should always make sure your calculator is set to degrees, and not radians or gradients.

He then stated quite bluntly, after explaining what radians were, that neither he, nor ANY MATH TEACHER IN OUR SCHOOL OF 1500+ STUDENTS knew what a gradient was. Whatsoever.

Is it just me, or does it seem a bit strange that an entire school, one that prides itself on being one of the top in the province, is full of math teachers that have never taken vector calculus? Or even dabbled into vector calculus?

They didn't just not understand gradients, they had no idea what they were for!

Bah!

[/rant]

And no, I didn't have to wiki gradients. I am the dorkiest dork who ever dorked.
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SpitValve
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360 degrees = 400 gradients. It's a weird unit, and I've never seen it outside of my calculator in my 5 years of uni. Not wholely surprised most people haven't heard of it. I don't really know what they're for either, other than some failed attempt to make angles have slightly nicer numbers...

The vector calculus gradient (represented by the nabla/upside down triangle/"grad") is different... check whether they have done curl and gradient and stuff as opposed to the gradient unit.

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SpitValve wrote:360 degrees = 400 gradients. It's a weird unit, and I've never seen it outside of my calculator in my 5 years of uni.

Seconded. I was a double math/comp sci major as an undergrad, and I have never used them.

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BAMs are more useful, but you won't find that on your calculator for some reason.

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Twasbrillig wrote:n my grade 10 Math class today, we were learning about finding the size of angles on a Cartesian Plane in excess of 360 degrees.

This sentence made no sense to me. What kind of crazy grade 10 math does BC have?
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Oort
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My math teacher isn't stupid so much as annoying. Recently, a couple students were talking while he was teaching, and he assigned all his classes a test, because "obviously we already uinderstand this if we don't need to pay attention." I hate it when lots of people are punished for no reason. Sometimes he can be stupid, though. Two days ago he assigned us homework, and he didn't understand how to do problem 1. [/rant][/b]

Twasbrillig
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Vandole wrote:
Twasbrillig wrote:n my grade 10 Math class today, we were learning about finding the size of angles on a Cartesian Plane in excess of 360 degrees.

This sentence made no sense to me. What kind of crazy grade 10 math does BC have?

Um... normal math?

What with the Syrcxrtyx.

Today in math, our teacher was explaining how to find lengths of hypotenuses and side lengths of right triangles on a Cartesian plane, and gave us the equations:

Sin = y/r (r being radius of a circle, the hypotenuse of a right triangle created in a circle on the plane being the length of the radius of said circle)

Cosine = x/r

and

Tangent = y/x.

I looked up to this equation and immediately stated that it's easy to remember, "because the mnemonic is syrcxrtyx. Sir-kuhsir-ticks."

To which uproarious laughter ensued.
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The LuigiManiac
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Ah, Trigonometry. Exactly what I was doing today. That, and posting in between questions. Internet schooling, you have to love it.

(apart from the ludicrous amount of work, of course)

EDIT: We were taught the mnemonic SOHCAHTOA, meaning:

Sine of an angle = Opposite side/Hypotenuse

Cosine of an angle = Adjacent side/Hypotenuse

Tangent of an angle = Opposite side/Adjacent side
Spoiler:
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hyperion
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The LuigiManiac wrote:We were taught the mnemonic SOHCAHTOA

Same here.

My current teacher is just painful. She'll try to explain something and make it even more confusing. Yesterday she was trying to explain uses for differentiation. I ended up with 2 pages of gibberish that didn't actually tell me anything.

Also, on the first day (year 11 mind you), she asked the class if we'd ever seen the graph of a cubic equation before. *facepalm*
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Sin, Cos, Tan

A Heap
Of Apples

Granted, that method doesn't have letters for sine, cosine, and tangent, but since that's the natural order in which they're said, it doesn't matter.

If you're weird and say tangent, sine, cosine for some reason, you deserve to get it wrong. :p
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Silly Old Harry
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Trawling Off America

Pfft. This is what happens when you ask a highschoolkid to come up with one:
Suck Off Horny

Cows And Hit

The Other Arses

Incidentally, I have had to teach one maths teacher how to pronounce "Su Do ku" ("Sudu ko" she said. . . .) and that eleven plus five is not seventeen.
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el sjaako
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According to wikipedia they're part of the metric system, and they are sometimes used for surveying and in Scandinavia, or possibly just used for surveying in Scandinevia.

I think a unit where 1 unit = 360 degrees would be useful. At least, more useful than this.

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el sjaako wrote:I think a unit where 1 unit = 360 degrees would be useful. At least, more useful than this.

Found one!
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el sjaako
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1/4 of a circle is not equivalent to 90 degrees. For one thing, it has a radius, whereas a 90 degree angle doesn't. It could even simply be the top 1/4 of a circle.
Maybe this is a usage of the word "circle" that I'm not aware of, and that I missed in the article, but I dont think you found one. Maybe you defined one?

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el sjaako wrote:1/4 of a circle is not equivalent to 90 degrees. For one thing, it has a radius, whereas a 90 degree angle doesn't. It could even simply be the top 1/4 of a circle.
Maybe this is a usage of the word "circle" that I'm not aware of, and that I missed in the article, but I dont think you found one. Maybe you defined one?

Depend on which 1/4th of the circle you're looking at. If you look at half of a semi-circle, it is most certainly 90 degrees.

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el sjaako wrote:Maybe this is a usage of the word "circle" that I'm not aware of, and that I missed in the article, but I dont think you found one. Maybe you defined one?

I think it was a joke.

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el sjaako wrote:According to wikipedia they're part of the metric system, and they are sometimes used for surveying and in Scandinavia, or possibly just used for surveying in Scandinevia.
I'm from Sweden and I've never seen it (except for on calculators).

Solt
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Soh Cah Toa.

I still use that exact mnemonic fairly often, in the second year of an engineering degree. Very useful, though I'm finding that I'm so used to doing it that a lot of times I have already "seen" the correct relation and am writing it down before I have time to say it in my head.

And I've never heard of gradiens. Gradients, yes, which is basically just a slope in calculus. But not for units. My calculator only has degrees and radians.
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Twasbrillig
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Oooh, so the button is for gradians and not gradients? That makes him seem a whole lot less stupid.

Well, that isn't nearly as complicated as I thought it would be.
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Tchebu
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My grade 8 teacher was genuinely confused when i presented her with the following:

28-36+8 = 35-45+10
4(7-9+2) = 5(7-9+2)
4=5
2*2=5

Solt
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Tchebu wrote:My grade 8 teacher was genuinely confused when i presented her with the following:

28-36+8 = 35-45+10
4(7-9+2) = 5(7-9+2)
4=5
2*2=5

Good job dividing by 0 there. Apparently she was confused because you didn't learn anything.
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produced a more reliable product. But sailors do

not float on theory, and the welded tankers had a

most annoying habit of splitting in two."

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2+2=5, yo

2.4 = 2 (round down)

2.4 + 2.4 is 4.8 = 5 (round up)
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Meh, I'm not particularly impressed by most of the stories in this thread. It's just a matter of terminology. I don't judge teachers based on individual anecdotes - everyone makes mistakes. It's when they consistently repeat their mistakes that you need to worry.

I had a 10th grade teacher who deducted points for simplifying an expression, because the question asked us to distribute and the original question could be simplified. Her reasoning was that factoring it out again didn't yield the original expression.

There were also several instances where she absolutely fought me on operator precedence, or rather, syntax: she believed that parenthesis were necessary around a fraction if you negated it, or else the negative sign applied only to the first term of the numerator. And that you needed parenthesis around a radical raised to a power, likewise to prevent the power from applying only to the last term inside.

I did however enjoy correcting her in front of the class when she got confused about a transformation on a graph of an absolute value function. She told us to pull out the TIs, and we did. Perhaps I was a bastard about it, but it was gratifying nonetheless.

I did legitimately screw up though: When we were doing trig proofs using identities, I applied an operation to both sides of the equation. This is of course not allowed because showing that the result of an operation applied to two arguments does not imply that the original operands were equal - for instance multiplication by zero. She told us numerous times in class not to do this, but each time she qualified it with "because it will make your life more difficult", so I assumed she was simplifying the process down to a simple non-creative computation.

I believe that was her first year teaching, and after that she never taught an honors classroom again.

aldimond
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I don't really mind when people don't know things. Some people don't. Or even if they're not quick about things. Some people aren't. It's life. It bothers me when people don't admit they're wrong. That should be possible for everyone.

What really bothers me is that nobody realized what was going on. That I never said, "Let's go back to the statement of the problem," which would have made the whole misunderstanding clear. The experience is something I've taken with me, even though it wasn't intentional (it would be a pretty malicious way to teach that lesson, on a few different levels).

Anyhoo, the next year my brother had the same teacher. He wrote some nifty program for his graphing calculator and showed it to her. He also showed it to some of his younger friends. The next year, those friends told him that she'd taken the program, replaced his name with hers, and presented it as her own. My brother checked back and found this indeed to be the case.
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About trigonometry mnemonics - the way I learned it:
The coordinates of a point on a unit circle are (cos t ; sin t), where t is the angle compared to the x axis. I always found that way easier than trying to remember poems... Just need to remember that cos is horizontal and sin is vertical.
And tan t - well, make a line *tangent* to the circle (x=1), and see where it intersects the line of angle t...

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I learned sohcahtoa, which isn't hard to remember and is best when given a triangle, and also the unit circle definitions, which are more useful for applications other than just looking at a right triangle.

Also, did you guys have to learn a bajillion trig identities? I could never remember the double angle formulas, so I just remember cos^2+sin^2=1, and the rotation matrix (you know, this one), since you can easily derive all the other formulas from those two using only matrix multiplication.
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When I first saw one on a calculator, my dad told me the grad is a French unit for angles and 360 degrees equal 400 grads. Wikipedia confirms this.

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skeptical scientist wrote:I learned sohcahtoa, which isn't hard to remember and is best when given a triangle, and also the unit circle definitions, which are more useful for applications other than just looking at a right triangle.

Also, did you guys have to learn a bajillion trig identities? I could never remember the double angle formulas, so I just remember cos^2+sin^2=1, and the rotation matrix (you know, this one), since you can easily derive all the other formulas from those two using only matrix multiplication.

I only know cos^2+sin^2=1 and euler's identity e^(ix)=cos x+i sin x, which are easy to derive those equations from.

I never learned any sohcahtoa rule, I just memorized that cos has to do with the "x-value" and sin with the "y-value" and tan=sin/cos. Further, I haven't memorized any values of cos or sin. I just know they look wavey, and that sin starts at 0, going up, while cos starts at 1, and that they have a period of 2pi, so I always have to draw them if I want, say, sin(pi). If I want sin(pi/3) I have to draw a circle.

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Torn Apart By Dingos wrote:Further, I haven't memorized any values of cos or sin. I just know they look wavey, and that sin starts at 0, going up, while cos starts at 1, and that they have a period of 2pi, so I always have to draw them if I want, say, sin(pi). If I want sin(pi/3) I have to draw a circle.

I do that, too. The number of undergrad exam scripts I handed in with little wavy lines drawn so I could work out what trig derivatives were... Must be almost as high as the number of little triangles I drew thereafter to work out other things.

I don't memorise. I understand. Then I can work out the things other people memorise, and it takes me a little monger but I can apply them better.

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skeptical scientist wrote:I learned sohcahtoa, which isn't hard to remember and is best when given a triangle, and also the unit circle definitions, which are more useful for applications other than just looking at a right triangle.

Also, did you guys have to learn a bajillion trig identities? I could never remember the double angle formulas, so I just remember cos^2+sin^2=1, and the rotation matrix (you know, this one), since you can easily derive all the other formulas from those two using only matrix multiplication.

For me the easiest is to get them with complex numbers (by working with e^(tÂ·i)=cos t+i sin t instead of t)
For instance, for the double angles, writing c for cos t and s for sin t:
(c+is)Â²=cÂ²+2ics-sÂ²=cÂ²-sÂ² + iÂ·(2cs), which is equal to cos(2t)+i sin(2t). So cos 2t=(cos t)Â²-(sin t)Â² and sin 2t=2 cos t sin t.

(I'm squaring because e^((2tÂ·i))=(e^(tÂ·i))Â² )

Works similarly for cos(t+u) and friends.

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el sjaako wrote:According to wikipedia they're part of the metric system, and they are sometimes used for surveying and in Scandinavia, or possibly just used for surveying in Scandinevia.

I think a unit where 1 unit = 360 degrees would be useful. At least, more useful than this.

http://en.wikipedia.org/wiki/Turn_%28geometry%29

Alternately, 'revolution' or 'rotation'

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Our high school math teacher was always cool about mistakes. Whenever somebody pointed one out, he'd thank for the correction and continue with the proper version. And if somebody didn't pay attention but mindlessly transferred what he wrote on the blackboard, well that should prompt him to reconsider. But he's a great teacher and didn't really screw up in a royal way as far as I remember. Well, maybe once, when he thought he thought up some cool calculus question, only to find it was really ungodly time-consuming. And there was this legend that after like an hour and a half of vigorous assaults on some exercise, he just wrote "This is a wrong path to take" on the blackboard and started a totally different, effective and fast approach. That must have been rather funny.

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### Re: Stupid Math Teachers?

Twasbrillig wrote:He then stated quite bluntly, after explaining what radians were, that neither he, nor ANY MATH TEACHER IN OUR SCHOOL OF 1500+ STUDENTS knew what a gradient was. Whatsoever.

Is it just me, or does it seem a bit strange that an entire school, one that prides itself on being one of the top in the province, is full of math teachers that have never taken vector calculus?

Since we're in the same province, I have to say... it doesn't surprise me in the least, given that out of the three math teachers that I've had, not a single one believed that I could do many of the questions in my head. One teacher threatened to fail me for cheating because I never showed my work on assignments, and when we had the parent-teacher conference, he wrote a big equation on the board and told me I couldn't possibly solve it without the use of a calculator. So when I solved it without the use of a calculator, in front of him and my parents, he grudgingly agreed not to fail me, but said he would only mark me at 50% if I didn't show my work.

....

It wasn't even that hard, either.

Math teachers, largely, are just math teachers because they took teaching courses in college, and somehow ended up unlucky enough to be teaching math. Most of them would rather teach English, or Art, or shop, or something...

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Showing working is important though... communication is more important than showing off.

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SpitValve wrote:Showing working is important though... communication is more important than showing off.

I wasn't showing off.... I was doing the question faster and more efficiently, mostly because I couldn't understand the way the teacher expected us to do it. Showing work is important for other applications (in college, showing work was 90% of the mark), but for high school math, the fact I got the correct answer at all should be enough (given that most other people did show their work, and got lower scores than me).

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aldimond wrote:I don't really mind when people don't know things. Some people don't. Or even if they're not quick about things. Some people aren't. It's life. It bothers me when people don't admit they're wrong. That should be possible for everyone.

What really bothers me is that nobody realized what was going on. That I never said, "Let's go back to the statement of the problem," which would have made the whole misunderstanding clear. The experience is something I've taken with me, even though it wasn't intentional (it would be a pretty malicious way to teach that lesson, on a few different levels).

Anyhoo, the next year my brother had the same teacher. He wrote some nifty program for his graphing calculator and showed it to her. He also showed it to some of his younger friends. The next year, those friends told him that she'd taken the program, replaced his name with hers, and presented it as her own. My brother checked back and found this indeed to be the case.

That's gross. I would have wanted to complain to a counselor or something. It's not just rude, it's stealing his program.

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Mighty Jalapeno wrote:
SpitValve wrote:Showing working is important though... communication is more important than showing off.

I wasn't showing off.... I was doing the question faster and more efficiently, mostly because I couldn't understand the way the teacher expected us to do it. Showing work is important for other applications (in college, showing work was 90% of the mark), but for high school math, the fact I got the correct answer at all should be enough (given that most other people did show their work, and got lower scores than me).

Donno what High School you goto but when I went to high showing working was 3/4 of the marks for a 4 mark question. The only time you got full marks just for the answer was if it was a 1mark question.

Communication is VERY VERY important, whether you want to be a teacher or scientist or what ever.

Sure the end result is important, but guess what? Some people CAN'T do calculations perfectly in their head like you! And if they can't, how do they know the answer you've given is correct? Especially if they don't know the method?

In High school I got a b+ in mid year chem exam? Why so low? Because I didn't do ANY homework what so ever and I slept in class. But guess what? I still topped the class, but that doesn't mean anything. I could've got an A if I actually did the work.

If you didn't understand the way the teacher expected you to do it, then you SHOULD get a lower mark. Regardless of whether you can do it some cool and special way in your head the whole idea of exams/tests and school work is to show you've learned what's being TAUGHT. Just blindly writing down answers, whether they're right or not, won't tell the teachers that.

The whole idea of assessment is to see if you've learned what they've taught, not whether you can get the right answer.
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The whole idea of assessment is to see if you've learned what they've taught, not whether you can get the right answer.
However, seeing whether or not you learned their method should not take the place of seeing whether or not you learned skills that will allow you to answer the question.

Communication is largely important for proofs and related things; it's silly for someone to expect "oh, I proved it in my head" to work. But, to add and multiply in your head, or similar things? It's not something that should be punished.
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