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[polly_mer]

The biggest problem, Luvstowrite, is that students don't grok the graph.  They will make a graph because we told them to do so.  They will stick a line through the data because that's what you do with data on a graph.  But they often are seriously missing the point.  Even after I explained about how to construct a line of best fit by moving your ruler so that it touches as many points as possible before drawing your line, I still had several connect-the-dots pictures submitted instead of lines of best fit.  In spite of my demonstration with how to make Y versus X plot (X goes along the bottom, Y goes along the side, everything is labeled including units), I get random stuff where students apparently arbitrarily decide each point whether X or Y is listed first in the (x,y) pair even though the sheet has two columns of five blanks with each blank labeled in order something useful like x1 (first column, first row) or y5 (second column, fifth row) and I demonstrated how to go over x spaces and up y spaces before putting a point.

Another problem I see: inconsistent spacing.  Not just poor a poor choice (7 boxes for 5 meters?)  because they stretch the axes out to fill the paper in completely (and there are those that use very little of the paper, as well) regardless of whether the math comes out evenly, but sometimes there are weird jumps: 7 boxes, then 6, then 4...

Yep.  I see this far less than the other problems,  particularly the poor choice of spacing like three boxes for five meters on the first graph until they realize that they can't read their points back off using that method and they really don't like it when I show them how to do the math so that they can read their points back off without redoing their plot.  However, I have seen those oddities of uneven skips and this week's redo lesson included the admonishment to make the labeling even so that drawing a line and calculating a slope makes sense.

[cc_alan]

Even when I have the students plot using Excel and show them how to check the display equation box, they often cannot tell me what the slope of the line is.  Every class, I have at least one conversation about how the slope of the line is positive for this graph just like they vaguely remember from math class; the negative number in the equation is the intercept.

And even when they manage to do all that, they don't tell you what the graphs mean. No interpretation at all. I even see this in grad classes. It's like, "Here's the damn graph you wanted. Happy now?"

I usually ask something about the best-fit line, whether it goes through (0,0), and whether they expect it to go through the origin.

Even after discussing it more than once, I still have students telling me-

1. No, the best-fit line doesn't appear to go through the origin.

(ok, the data may not be perfext "textbook" data)

and

2. No, I wouldn't expect it to go through the origin since the best-fit line doesn't go through the origin.

<sound of head-desk>

On a plot of mass versus volume of a solution (the flask/beaker/graduated cylinder/etc. factored out), one would expect the line to go through the origin since 0 volume implies 0 solution and thus 0 mass. I have made a big effort to work on this concept of "what the heck does a graph mean?" and I think I'm making headway but it can be frustrating.

And even though we use graphing calculators to quickly look at the data, I still require a lot of graphing by hand using lots of graph paper. I don't believe a student can really learn to graph until they get down-and-dirty and put it all down on paper.

Alan

[polly_mer]

Even when I have the students plot using Excel and show them how to check the display equation box, they often cannot tell me what the slope of the line is.  Every class, I have at least one conversation about how the slope of the line is positive for this graph just like they vaguely remember from math class; the negative number in the equation is the intercept.

And even when they manage to do all that, they don't tell you what the graphs mean. No interpretation at all. I even see this in grad classes. It's like, "Here's the damn graph you wanted. Happy now?"

I usually ask something about the best-fit line, whether it goes through (0,0), and whether they expect it to go through the origin.

Even after discussing it more than once, I still have students telling me-

1. No, the best-fit line doesn't appear to go through the origin.

(ok, the data may not be perfext "textbook" data)

and

2. No, I wouldn't expect it to go through the origin since the best-fit line doesn't go through the origin.

<sound of head-desk>

On a plot of mass versus volume of a solution (the flask/beaker/graduated cylinder/etc. factored out), one would expect the line to go through the origin since 0 volume implies 0 solution and thus 0 mass. I have made a big effort to work on this concept of "what the heck does a graph mean?" and I think I'm making headway but it can be frustrating.

And even though we use graphing calculators to quickly look at the data, I still require a lot of graphing by hand using lots of graph paper. I don't believe a student can really learn to graph until they get down-and-dirty and put it all down on paper.

We definitely share the brain.  I hope your newest students catch on faster than my newest students appear to be. Right now, I'm just hoping that Monday's resubmission of their first graphing exercises mean that I only have to give the how-to-read-a-graph-spiel twice more next week.

[cc_alan]

We definitely share the brain.  I hope your newest students catch on faster than my newest students appear to be. Right now, I'm just hoping that Monday's resubmission of their first graphing exercises mean that I only have to give the how-to-read-a-graph-spiel twice more next week.

Last term I was fairly successful at getting most of them to tell me what is meant by the best-fit line running through (or near) the origin. It did take much of the term and by the end I had the wonderful sense that they were sighing and rolling their eyes when they answered that type of question. Something like-

"OMG. We frikkin' get it Mr. GrillUsaboutGraphsUntilWeWantToPuke. PLEASE STOP."

Ok. But only because the term is over...

Alan

[polly_mer]

We definitely share the brain.  I hope your newest students catch on faster than my newest students appear to be. Right now, I'm just hoping that Monday's resubmission of their first graphing exercises mean that I only have to give the how-to-read-a-graph-spiel twice more next week.

Last term I was fairly successful at getting most of them to tell me what is meant by the best-fit line running through (or near) the origin. It did take much of the term and by the end I had the wonderful sense that they were sighing and rolling their eyes when they answered that type of question. Something like-

"OMG. We frikkin' get it Mr. GrillUsaboutGraphsUntilWeWantToPuke. PLEASE STOP."

Ok. But only because the term is over...

I had a Classroom Victories moment regarding the term being over the other day.  One student was sick on Wednesday and missed my science for teachers class.  She sent her homework with a friend (who happens to be in my engineering class) and came by my office hours on Thursday to pick up hand-outs from the class she met.  She brought along a friend who was in my science for teachers class last semester.  One of the hand-outs was the "just follow the frickin' instructions" quiz that I mentioned on the Favorite Student Conversations thread.  Her friend said, "Quiz on motion, huh.  Did you ask the question about the acceleration of the ball at the top of the arc?"  Of course, that was question number 1.  "Yeah, I can still hear you saying that it's always 10 m/s/s on Earth because gravity always acts even if the velocity is zero.  [Friend], be sure you make note of that answer because you really, really need to know that answer because she'll ask the question all semester on every quiz and test if the class doesn't get it right on the first test."

I may be a broken record, but at least one student got it.

[luvstowrite]

To take a turn in direction, if anyone has any ideas about how to get my seriously math-phobic students to really get the hang of graphs in short order, I'm all ears.  My students are slightly more on track with that than G_H's.  I told them to slap a line of best fit through the data and they did.  Then, in the slots for the recording of two points on that line, they promptly recorded two random data points from the original data set with no regard for whether those points were on the line, in spite of my explicit instructions about how to select points that lay on the line and were at the intersection of the grid so that one could easily read them off the plot.

I have the *same* problem with my chem students. I don't think they really understand what a line of best-fit represents. They look at it as a line on the paper with no connection to the data.

Alan

Can you discuss regression and how that helps us make better decisions with new points of interest?

I'm not sure if our experiences correlate well.

Polly, you're right. These students have had a semester of stats and a semester of experimental design so their cart and horse are at least in the same corral.

Don't be lazy.  Plot it up and look.  Sheesh.

<serious hat on>
The biggest problem, Luvstowrite, is that students don't grok the graph.  They will make a graph because we told them to do so.  They will stick a line through the data because that's what you do with data on a graph.  But they often are seriously missing the point.  Even after I explained about how to construct a line of best fit by moving your ruler so that it touches as many points as possible before drawing your line, I still had several connect-the-dots pictures submitted instead of lines of best fit.  In spite of my demonstration with how to make Y versus X plot (X goes along the bottom, Y goes along the side, everything is labeled including units), I get random stuff where students apparently arbitrarily decide each point whether X or Y is listed first in the (x,y) pair even though the sheet has two columns of five blanks with each blank labeled in order something useful like x1 (first column, first row) or y5 (second column, fifth row) and I demonstrated how to go over x spaces and up y spaces before putting a point.

Even when I have the students plot using Excel and show them how to check the display equation box, they often cannot tell me what the slope of the line is.  Every class, I have at least one conversation about how the slope of the line is positive for this graph just like they vaguely remember from math class; the negative number in the equation is the intercept.

Talking about regression and correlation before I can get them to reliably put points on a graph and read points off of a graph is putting the cart way before the horse.

[polly_mer]

To take a turn in direction, if anyone has any ideas about how to get my seriously math-phobic students to really get the hang of graphs in short order, I'm all ears.  My students are slightly more on track with that than G_H's.  I told them to slap a line of best fit through the data and they did.  Then, in the slots for the recording of two points on that line, they promptly recorded two random data points from the original data set with no regard for whether those points were on the line, in spite of my explicit instructions about how to select points that lay on the line and were at the intersection of the grid so that one could easily read them off the plot.

I have the *same* problem with my chem students. I don't think they really understand what a line of best-fit represents. They look at it as a line on the paper with no connection to the data.

Alan

Can you discuss regression and how that helps us make better decisions with new points of interest?

I'm not sure if our experiences correlate well.

Don't be lazy.  Plot it up and look.  Sheesh.

<serious hat on>
The biggest problem, Luvstowrite, is that students don't grok the graph.  They will make a graph because we told them to do so.  They will stick a line through the data because that's what you do with data on a graph.  But they often are seriously missing the point.  Even after I explained about how to construct a line of best fit by moving your ruler so that it touches as many points as possible before drawing your line, I still had several connect-the-dots pictures submitted instead of lines of best fit.  In spite of my demonstration with how to make Y versus X plot (X goes along the bottom, Y goes along the side, everything is labeled including units), I get random stuff where students apparently arbitrarily decide each point whether X or Y is listed first in the (x,y) pair even though the sheet has two columns of five blanks with each blank labeled in order something useful like x1 (first column, first row) or y5 (second column, fifth row) and I demonstrated how to go over x spaces and up y spaces before putting a point.

Even when I have the students plot using Excel and show them how to check the display equation box, they often cannot tell me what the slope of the line is.  Every class, I have at least one conversation about how the slope of the line is positive for this graph just like they vaguely remember from math class; the negative number in the equation is the intercept.

Talking about regression and correlation before I can get them to reliably put points on a graph and read points off of a graph is putting the cart way before the horse.

Polly, you're right. These students have had a semester of stats and a semester of experimental design so their cart and horse are at least in the same corral.

[fixed your post to make sense]

Sadly, many of my students had AP stats in high school (as they indignantly inform me when I ask why their previous math classes didn't uncover some of these severe deficiencies) and plenty of good math right here at our college, but they have no carts at all and I'm pretty sure that some of those corrals are empty because the gate was left open last year.

[anakin]

I'm grading the first bunch of quizzes (basic anatomy and function of a particular plant). While I'm quite a bit disappointed, I have unwittingly stumbled on a very useful, helpful quiz technique: "Draw a picture of _______." I'm finding it useful because I'm seeing all sorts of misconceptions, like:

Seeds grow at the tip of stems on flowering plants (e.g. not encased in fruits or pods).
A dicot seed stays in the ground as it grows.
Anthers just bend over and drop their pollen on stigmata.

And others. This I can fix. If I had just asked them to define or fill in the blank or whatever, I never would have known.

[luvstowrite]

I'm grading the first bunch of quizzes (basic anatomy and function of a particular plant). While I'm quite a bit disappointed, I have unwittingly stumbled on a very useful, helpful quiz technique: "Draw a picture of _______." I'm finding it useful because I'm seeing all sorts of misconceptions, like:

Seeds grow at the tip of stems on flowering plants (e.g. not encased in fruits or pods).
A dicot seed stays in the ground as it grows.
Anthers just bend over and drop their pollen on stigmata.

And others. This I can fix. If I had just asked them to define or fill in the blank or whatever, I never would have known.

I see this a lot too, especially with the reproductive structures. Having the stereotypical dicot plant in all of the textbooks isn't helping anyone learn about monocots, grasses and cereal grains. We collect a lot of grasses in lab to emphasize this and my students get quite tired of seeing another grass flower on the plant walks. I think it's important since many of them will need to decide what to do with the crabgrass or dallisgrass that's growing in their burmuda grass or fescue lawns at home. Come to think of it, I never have to discuss dandelion more than once though. They all know that weed.

[astrofraa]

If we didn't teach anything until we could teach it with complete accuracy, we'd never teach anything. 

Just to be clear, I was never suggesting teaching anything with "complete accuracy".  My concern was whether it was really necessary to teach them something that was actually wrong, or whether it was possible to teach them something not wrong (but incomplete), which could then be expanded upon, if they progressed to the point where that was useful.  I fully agree that trying to teach "complete accuracy" (if there even is such a thing, which I doubt) is a mistake.

Yours,

Astrofraa

[barcrossliar]

If we didn't teach anything until we could teach it with complete accuracy, we'd never teach anything. 

Just to be clear, I was never suggesting teaching anything with "complete accuracy".  My concern was whether it was really necessary to teach them something that was actually wrong, or whether it was possible to teach them something not wrong (but incomplete), which could then be expanded upon, if they progressed to the point where that was useful.  I fully agree that trying to teach "complete accuracy" (if there even is such a thing, which I doubt) is a mistake.

I agree that I made a more extreme statement than you did. 
Some things are easier to teach incompletely than others.  Most of my students come to my class with almost no understanding of basic science and will never take another science class after mine.  I can leave them with a picture that makes sense and leaves them thinking, "I can do this." or leave them mystified and scared. 

[frogfactory]

This is what happens when you let snowflakes graduate.

[galactic_hedgehog]

I have made a big effort to work on this concept of "what the heck does a graph mean?" and I think I'm making headway but it can be frustrating.

And even though we use graphing calculators to quickly look at the data, I still require a lot of graphing by hand using lots of graph paper. I don't believe a student can really learn to graph until they get down-and-dirty and put it all down on paper.

We definitely share the brain.  I hope your newest students catch on faster than my newest students appear to be. Right now, I'm just hoping that Monday's resubmission of their first graphing exercises mean that I only have to give the how-to-read-a-graph-spiel twice more next week.

I'm worried, 'cause it sounds like I share that brain as well, and I didn't think I had enough for one, let alone three.

[cc_alan]

I have made a big effort to work on this concept of "what the heck does a graph mean?" and I think I'm making headway but it can be frustrating.

And even though we use graphing calculators to quickly look at the data, I still require a lot of graphing by hand using lots of graph paper. I don't believe a student can really learn to graph until they get down-and-dirty and put it all down on paper.

We definitely share the brain.  I hope your newest students catch on faster than my newest students appear to be. Right now, I'm just hoping that Monday's resubmission of their first graphing exercises mean that I only have to give the how-to-read-a-graph-spiel twice more next week.

I'm worried, 'cause it sounds like I share that brain as well, and I didn't think I had enough for one, let alone three.

That's ok. When people ask me-

"What the eff were you thinking."

or

"Do you have your head up your @$$?"

I can just refer them to you or Polly.

Alan

[conjugate]

I have made a big effort to work on this concept of "what the heck does a graph mean?" and I think I'm making headway but it can be frustrating.

And even though we use graphing calculators to quickly look at the data, I still require a lot of graphing by hand using lots of graph paper. I don't believe a student can really learn to graph until they get down-and-dirty and put it all down on paper.

Graphing calculators also don't do a great job with everybody's nemesis, the piecewise-defined function.  It can be done, but it takes a lot of work to make it happen.  Of course, those don't arise often in chemistry, I imagine.