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Misleading graphs

caveman1917 said:
Definition of a Cartesian coordinate system. Depending on how you define it, the x-axis is either the set of points with y coordinate equal to zero (and likewise for the y-axis), or coordinates get defined as signed distances from the x-axis and y-axis. In both cases the x-axis and y-axis intersect at coordinates (0,0).

That doesn't mean anything about how you draw a graph, of course, you can start your graph at, say, y = 500 if you want. But that horizontal line you draw at y = 500 is not the x-axis, strictly speaking.
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From your wiki link:

" Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0, 0). "

Suggesting that the axes are not axes unless they start at 0 strikes me as Olympic standard nitpicking.
 
GlennB said:
From your wiki link:

" Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0, 0). "

Suggesting that the axes are not axes unless they start at 0 strikes me as Olympic standard nitpicking.
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I don't care how it "strikes you as" - a definition is a definition.
 
caveman1917 said:
No it doesn't, the article has the word "usually" in it (for FSM knows why).
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Amazing. The article was put forward by you, accompanied by your word 'definition'. The word usually is in the second sentence of the article. If the definition ended at the first sentence then it contains no mention of 0,0. If not, it includes the word usually. Which way do you want it?

Perhaps you could suggest a different definition, as the one you've provided doesn't support your claim.
 
GlennB said:
Amazing. The article was put forward by you, accompanied by your word 'definition'. The word usually is in the second sentence of the article. If the definition ended at the first sentence then it contains no mention of 0,0. If not, it includes the word usually. Which way do you want it?

Perhaps you could suggest a different definition, as the one you've provided doesn't support your claim.
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:rolleyes:

I'm done, believe whatever you want.
 
GlennB said:
Amazing. The article was put forward by you, accompanied by your word 'definition'. The word usually is in the second sentence of the article. If the definition ended at the first sentence then it contains no mention of 0,0. If not, it includes the word usually. Which way do you want it?
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There, fixed it. Happy now?
 
sphenisc said:
"Usually" was correct.
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No it wasn't. Read my edit comment carefully: "by the definitions given". The definitions given in the rest of that paragraph specify two dimensions. If you want to rewrite the whole paragraph so as to account for different dimensionality, feel free to do so. I did exactly as much as I had to do to stop a particular nuisance, and my edit is exactly correct.

Axes may meet at an ordered triplet (0,0,0), and this can be extended to higher dimensions.
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Obviously. The origin (ie intersection point of coordinate axes) must still have 0 as all coordinates though, so I'm not even sure how it's relevant.
 
The horizontal and vertical scales on a graph are not necessarily the x-axis or y-axis. There is not necessarily a requirement to draw them linearly either.
 
If a person put together a graph tracking (say) global population since the year 2000 (horizontal), with the vertical scale starting at 5 billion, and then discussed the scales using the terms "x-axis" and "y-axis" is there a soul in this forum that would criticise them for using those terms?

Graphs are intended to convey information, and not be treated as a minefield for nitpicking terminology obsessives. If the axes are faulty in some way then knock yourself out, by all means.
 
GlennB said:
This is a new one on me. You got around this difficulty by editing your own source :confused::D
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I agree with his edit. The definition said that the coordinates are signed distances from the axes. That implies that the axes must intersect at (0,0,...).
 
jt512 said:
I agree with his edit. The definition said that the coordinates are signed distances from the axes. That implies that the axes must intersect at (0,0,...).
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Why? They are a signed distance from anywhere else on the grid, too. Where someone chooses to locate the axes is nothing but a matter of convenience. The only important consideration is that the choice be clearly labeled and defined.

One of the most fundamental manipulations that surveyors perform is to translate (and/or rotate) coordinates through different relative frameworks. Nothing is fixed except each points relative distance to any other, and the frame of reference you happen to be applying at the time is whatever one is most appropriate for the task at hand.

As someone has already pointed out in this thread, a common convention for a data set for surveyors is to have the axes intersect at (y=10,000, x=10,000), just to avoid having to use negative numbers.
 
jt512 said:
I agree with his edit. The definition said that the coordinates are signed distances from the axes. That implies that the axes must intersect at (0,0,...).
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quadraginta said:
Why?
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Because:

Let (v,w) be a point in R² with x-axis y=c and y-axis x=d. If v is the signed distance from the x-axis, then v–c=v. Therefore c=0. And if w is the signed distance from the y-axis, then w–d=w. Therefore, d=0. Thus the axes are the lines y=0 and x=0.
 
Yeggster said:
I'm really surprised (not being facetious) ... from what little I've seen on line I thought there was a set curriculum, with all the lessons planned out ... so you just taught them to pass the standardized tests they got at the end of the year.

How much leeway do you have in the curriculum?
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I have more leeway than I want. Ordinarily a substitute executes lesson plans put in place by the regular classroom teacher. In this case there is no regular classroom teacher; that person quit. Also, this school is on a quarter system - students get .5 credit for each class per quarter, and class periods are 85 minutes long. In theory that means Algebra 2 is done after 2 quarters. So all the stuff that would be paced at 1 year for what I think of as a traditional schedule must be done in one semester.

This is a charter school that serves a lot of former dropouts, teenage parents etc. and they are all over the place in terms of what they remember from Algebra 1. The absentee rate is extremely high. There is no actual exit exam. There is no textbook. There is no class set of laptops that would enable students to each do their own work at their own computer.

I have a few different textbooks to draw from but they each sequence things differently. There are great online resources but I overthink things and feel like every student must understand basics about lines before we go into other functions. But that's not reality. It worries me, actually.
 
Chanakya said:
But of course you’re teaching children. I wouldn’t presume to guess at what might be the best way to deal with this sort of thing with kids. But then, do you necessarily have to treat them differently, in this respect, just because they’re children? Do children behave so very differently from how adults do? (I don’t know the answer, no clue at all! Just thinking aloud. If you don’t know the answer either, perhaps you could just try it once and see if it works, taking a more open approach I mean? You can always stop doing it if doesn’t seem to be working.)
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In trying to teach them all at the same level I feel like I'm losing brighter students *and* losing the ones who struggle most. It's almost like there is no middle ground. Some could be in college algebra and others would do well to repeat sixth grade. Some are stimulating company who are able to make good arguments about presenting data a certain way, while others as of a quiz yesterday did not know how to graph a line going through (0, 0) with a slope of 1/3.

With a class full of adults, either in college or workplace training, the default assumption is that students are adults and choose to be in the class and are responsible for keeping up as long as the teacher clearly presents several examples of related problems. Students have to test into classes or to have the appropriate prerequisites. I would probably do better to act as if this were the case in high school, but it's really not. It's a different level of responsibility. Even if students have forgotten everything about freshman algebra, it's still my responsibility to get them through Algebra 2. Or I feel like it is, at any rate.
 
Minoosh said:
In trying to teach them all at the same level I feel like I'm losing brighter students *and* losing the ones who struggle most.
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Ignore the brighter students, if they're bright and interested enough then they'll push each other and themselves forward. Focus your energy on those who actually need your help, ie the ones who struggle with it.

In my 3rd and 4th year (in Belgium high school is 6 years, 1st to 6th, and for every pair of years you get to choose increasing specialization) I had a math teacher who had this "everyone must go at the speed of the slowest" thing. It felt like being forced to solve mind-numbing things like "1 + 1" and "1 + 2" over and over and over again, it almost destroyed my interest in math altogether.

Then in 5th and 6th year I had a different math teacher (who was also more mathematically inclined, probably given that she taught the math specialization class). After about two weeks into the 5th year I had read the full textbooks for that year so I was getting bored again. So I started immediately shouting the right answer to every question she asked (someone in) the class. By that time she was annoying me by forcing me to participate so I started annoying her. After a bit of this she put me in her 6th year class instead.

Somewhat later she gave in to my refusal to make my homework as well. I had explained that it was a mindnumbing waste of time (it was always of the sort of "solve these integrals" or "solve these equations" etc, something a computer could do just as well) but she didn't go along with that at first, but at least she wasn't putting me in detention all the time for refusing, like that previous teacher did.

One time homework consisted of solving a bunch of integrals, which I of course didn't do, and which she had noticed I didn't do. So she wrote the most difficult one on the blackboard and then called me to show my solution. Normally in those situations the guy who sat next to me would just give me his homework and the teacher wouldn't know, but he had been unable to solve that particular one. So I was in a bit of a problematic situation, so I got up from my chair and started walking towards the blackboard, trying to solve that integral in my head. After a couple of steps the teacher said "well you obviously didn't make your homework again, did you?" to which I replied "wait, I didn't get to the blackboard yet." A couple of steps further I saw the solution, so I smiled, increased my pace, and wrote the solution on the blackboard. After which she said "fine, you win, you don't have to make your homework."

After a couple of weeks in the 6th year class I had fully read the textbooks for that year as well, after which I didn't have to participate at all anymore (this actually took another round of annoying her by immediately shouting the answer to every question she asked the class). In the end I spent the last 3 years of highschool (I had to do the 6th year twice) being 8 hours per week out of 32 (I picked maximum math specialization, hence 8/32 hours) completely free to do whatever I wanted (just as long as I didn't bother her teaching the rest of the class). She even put a computer with Mathematica on it in class just for me to experiment with.

My point is, trying to teach everyone at the same level is a fool's errand. See who it is you're actually helping and who it is you're actually holding back, and put your energy into those who actually need your help and just ignore the ones who you're holding back.
 
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