• Quick note - the problem with Youtube videos not embedding on the forum appears to have been fixed, thanks to ZiprHead. If you do still see problems let me know.

Misleading graphs

Chanakya said:
Unless I’m misunderstanding what you’ve said, I think your students have displayed excellent creative thinking!
Click to expand...
I don't disagree. The students at this particular table were smart/advanced enough to challenge me. Others really do just want to do whatever the teacher is looking for. I'm not saying that's a good thing, but within the context of this not-very-exciting lesson, there was plenty of room to include the origin in the graph.

What I need to do is get better at challenging students who welcome it, while keeping the material manageable for others who just want to check their answer against my key (the key I make myself - it's not provided).

Chanakya said:
I don’t know how old your students are, but if these “kids” have by themselves hit upon the understanding that this is merely a convention, and that the convention can legitimately be fiddled around with if the situation so warrants, then surely that’s a good thing?
Click to expand...
This is the part I'm slightly conflicted about. Some students thrive on ambiguity, but for others these discussions might amount to cognitive overload.

They aren't all at the same level, and virtually none of them is really at what I would consider an Algebra 2 level. Many think a negative plus a negative equals a positive. Their "real" teacher (just hired) quit right before school started. I was given no set pacing chart despite virtually begging for it. Two textbooks from two different publishers start off at completely different places. There are also several large binders labeled Algebra 2-1, Algebra 2-2, etc. with yet a third sequencing scheme.

This one kid absolutely would not believe the slope formula. He said it seemed too complicated. I might have agreed, except that whatever mojo he was using was yielding wildly inaccurate results. Rise over run, I reminded him. He was clinging to a graphing calculator (zoomed out enough so that no numerals were showing) and was refusing to hand-graph a line that would maybe make it clearer. (I think he may have a thing for neatness, and was offended by my wobbly whiteboard concoctions). I apparently need to run off some graph paper. I thought I had found some in an old armoire, but on closer inspection it turns out the x axis is labeled for trigonometric functions.
 
bytewizard said:
More importantly, where can I get a pepperoni, olive and cheese pizza for $7.00?
Click to expand...

The party store* down the street from us sells a large pizza with one topping for 5.00, with each topping $1.75. Cheese doesn't count as a topping. Your pizza would be $6.75.

It's pretty decent pizza, too.

But that makes the pizza cost non-linear, since 0 or 1 topping both cost $5.00.

*Here in the Detroit area, we call convenience stores "party stores", unless they are chains. i.e. 7-11 is not a party store, but a privately owned store that sells the same stuff, plus liquor, is a party store. Some of them, including the one down the street, sell pizza.
 
Trebuchet said:
Wait..what? Are you telling me you can't just go and BUY graph paper?
That makes me feel old. And sad.
Click to expand...
Yes, you can buy it. But if I call up a sheet of free online graph paper on a school computer, I can print it out on a school printer. Depending on students to supply it probably won't work.
 
Chanakya said:
ok, thanks. yes, I figured out the "upload" thing, but one may not always want to do that.
Click to expand...


You can put the url of the image between bbcode tags:

Code: 
[img]http​://jt512.dyndns.org/images/randomcat2.png[/img]
however, there is a rule that you can only post such a "hot link" if the hosting website allows it.

[imgw=400]http://jt512.dyndns.org/images/randomcat2.png[/imgw]​
 
John Jones said:
I'm sure that approach is helpful. Give a teacher a break FFS.
Click to expand...
What a silly comment.

This is just fundamental teacher training. One of the first things a student teacher is taught is that students (especially in primary school) handle verbal instructions poorly. That is why there are literally hundreds of different models of teaching available.

As far as the OP goes, if the kids haven't been clearly taught what is expected in a graph then any interpretation of the question is valid.
 
jt512 said:
You can put the url of the image between bbcode tags:
[img]http://jt512.dyndns.org/images/randomcat2.png[/img]
Click to expand...
Better if you specify the size of the image so that it doesn't violate rule 6.

[imgw=100]http://jt512.dyndns.org/images/randomcat2.png[/imgw]

[imgw=100]http://jt512.dyndns.org/images/randomcat2.png[/imgw]
 
The usual way to present a graph which doesn't start at 0 is to use a couple of wiggles or otherwise prominent marks to skip to the number you want:
G3ea.jpg
 
Minoosh said:
I'm working as a long-term substitute for 3 math classes.
...
I told them we were using the graph to communicate and that this was too misleading. ...
Click to expand...

It is only "mis"leading if the assignment made it clear where the commincation is supposed to lead.

As a mere math assignment, understanding that the x-axis doesn't have to intersect the y-axis at [0,0] if correctly labeled is a concept that's valuable to master (I am supposing this was done on some purpose and not a misunderstanding of how coordinate systems are constructed :p). From a mathematics point of view, the message in the graph is identical.

The misleading occurs when a mathematician tries to communicate a concept to a non-mathematicion by breaking a complicated algebraic or statistical connection down to a more easily comprehensible graphic representation. Then, depending on what the intended message is, bad choice of origin indeed frequently is a problem - but did you anticipate and indeed expect your students would fully reflect on this situation without being prompted?

Perhaps you can make the best of this and present in class graphs that look different despite plotting the same facts, and then graphs that look very similar despite depicting very different facts. Cherry-picking origins is one pitfall, adjusting scales another.
 
psionl0 said:
Better if you specify the size of the image so that it doesn't violate rule 6.

[imgw=100]http://jt512.dyndns.org/images/randomcat2.png[/imgw]

[imgw=100]http://jt512.dyndns.org/images/randomcat2.png[/imgw]
Click to expand...

1. I did use the imgw tags. 2. I didn't violate rule 6. 3. You can actually see the content of the imgae in my post.
 
psionl0 said:
What a silly comment.

This is just fundamental teacher training. One of the first things a student teacher is taught is that students (especially in primary school) handle verbal instructions poorly. That is why there are literally hundreds of different models of teaching available.

As far as the OP goes, if the kids haven't been clearly taught what is expected in a graph then any interpretation of the question is valid.
Click to expand...

And I respect their interpretations. But I'm not sure you appreciate how complicated it can be to instruct a group of 30 students of varying levels. These are not primary school students; some of them are 18.

Instructions are almost never solely verbal (or oral, if that's what you meant). They are in writing, which is verbal but also visual; they see it modeled on a whiteboard; they may watch videos that contain animations of, for example, slope being taken from two points. I can use different colored markers to make a point. I can make sure one person at a table understands the instructions and communicates them to his/her peers. You are right: There are all sorts of strategies. Knowing which ones to pick among "hundreds" may depend on trial and error. If you go too fast, you lose some students. If you go too slow you lose some students. Try it sometime if you haven't already.

I can tell them to start their graph at zero, draw a picture on the board, give them examples of what I'm looking for. For the task at hand giving them 2 points to plot wasn't useful. They were learning to turn words into graphs and algebraic expressions. It's hard to avoid using words when presenting a word problem.
 
Last edited:
C_Felix said:
And this is what I came to post.
Click to expand...
Thanks to both of you for the wiggling notation.

Using it depends on having some clearance on the vertical axis to insert the wiggles. I had students starting the vertical axis at $5 - no room underneath it at all.

Oystein said:
Perhaps you can make the best of this and present in class graphs that look different despite plotting the same facts, and then graphs that look very similar despite depicting very different facts. Cherry-picking origins is one pitfall, adjusting scales another.
Click to expand...
Absolutely.
 
Last edited:
bytewizard said:
More importantly, where can I get a pepperoni, olive and cheese pizza for $7.00?
Click to expand...


If you live near a Harris Teeter with in-store pizza making you can get a Deluxe (or any other combo) for $8.00.

On Mondays. The rest of the week they are $12.00

They actually do a pretty good pie.

Like anywhere else it depends on who's making them, but at the one I go to now the guy who's in charge of the pizza kiosk is from a family of NYC refugees who moved down here decades ago and started a local pizza chain.

And like anywhere else, since the same people work the kiosk most of the time you can generally (if you treat them well) develop a good relationship and get your pizza the way you want it.

Mrs. qg always gets a deluxe, modified for vegetarians. On wheat crust.

They've been known to hold back a couple of wheat crust doughs on Mondays just in case we come in to order.
 
Minoosh said:
How many toppings?

Screw math, now I am hungry for pizza.
Click to expand...


Their (16") Deluxe comes with pepperoni, onions, mushrooms, sausage, olives, and peppers. They're fine with substitutions. I've never been charged for extra toppings. They're very good about doing custom combinations, and usually get them right. Extra sauce, less cheese, crispier crust, etc. are all no problem.

I've bought pizzas from three different branches of their stores in the area and the quality seems consistent. (Although, as I mentioned earlier, befriending the staff for your preferences always makes a difference.)

Here's a link to a photo of their menu for their standard combos.

I may sound like I'm boosting them, because I guess I am. It's a brilliant come-on to get people in the store on a slow day. Best price in town for a damn good pie. Even the not-Monday price of $12.00 is a pretty good deal.

I restrict my shopping there because their grocery prices overall tend to be noticeably higher than places like the Food Lion right across the street, but I'll end up leaving the store with more than just pizza on Mondays, so I guess it works.
 
jt512 said:
1. I did use the imgw tags. 2. I didn't violate rule 6. 3. You can actually see the content of the imgae in my post.
Click to expand...
1. You used imgw tags but your instruction was for img tags only. 2. Somebody using img tags instead of imgw tags could easily end up posting an image that is disruptively large. 3. Size matters. :p
 
psionl0 said:
1. You used imgw tags but your instruction was for img tags only. 2. Somebody using img tags instead of imgw tags could easily end up posting an image that is disruptively large. 3. Size matters. :p
Click to expand...

Good points. All three.
 
psionl0 said:
1. You used imgw tags but your instruction was for img tags only. 2. Somebody using img tags instead of imgw tags could easily end up posting an image that is disruptively large. 3. Size matters. :p
Click to expand...


But his wasn't

Just taking an opportunity for a teaching moment?

That usually makes more sense when someone has made a mistake. Correcting someone who didn't doesn't have the same sort of effect.
 
You must log in or register to reply here.

Back
Top Bottom