Damn – i was hoping we’d get to guess that.

But (a) does your diving board really flex 4 feet on the bounce? And (b) where do you find an 8 ft high diving board?

Mr. K, the board wouldn’t flex 4 feet, but your change in elevation would. You jump up a little just before you bounce on the board, approximately two feet high. The board dips a couple more feet, which gives you the four feet difference. We have an 8ft diving board where I live.

Nice. Can you throw in another few seconds and show the negative elevation?

Reminds me a bit of these graphs.

Okay. Bad tag in there somewhere: http://www.gphillymath.org/IMP1Supp/Overland.pdf

Looks good. What did you use to make the graph?

Dan, just because you don’t use IMP doesn’t mean you can’t use the graphs, does it?

I’ve got to echo Dan’s findings here on the “weak” students. When I’ve done similar activities, the students who are “weak” math students (symbolic manipulation) are often the ones who get the graphical representation. However they are both math. We just usually assess (and hence value) the symbolic manipulations.

How did you get the curved line on the graph? That’s a new one for me.

For those of us without Keynote, this is a nice option: http://www.apple.com/downloads/macosx/math_science/graphsketcher.html (mac only) for curve sketching.

I was in a grade 5 classroom recently and put up a picture of Mona Lisa. I had chopped it up into 150 or so pieces and put them back together randomly so it looked all pixelated. This was a class that was struggling with fraction,decimal,percent conversions and my purpose was to demonstrate that knowing all the pieces isn’t enough. You have to build connections to get a picture (next slide was reconstructed Mona Lisa).

Anyway, I popped up the pixelated version and 3 kids immediately yelled out “Mona Lisa”. One of them knew the artist was ‘Vinci or something’. You just never know…

You’ve got me in your store, Dan, but I’m still not buying. Once again, we seem to diverge on where perseverence should come into the assessment equation (and thanks for acknowledging my accurate read on that, however obliquely).

I believe there’s quite a bit to be said, for example, for “unrefined, brute intellectual force”. (By the way, I haven’t seen such a beautiful lace tablecloth thrown over a devaluation of effort in quite a long time).

And on the flip side, there’s no way that I would characterize a student as overarchingly “strong” who is too lazy to apply themselves to a difficult problem, no matter how many tools they’ve got. (I don’t like lace.)

:) :)

I don’t really feel like adding too much to the mix here except to say that I agree with Dan on this one. I think his last two replies really nailed the issue.

Dan, to answer the question you pose in comment #25, the answer is:

the fast food industry

“@Mark: Keynote handled the entire process. I wonder if the process is worth a screencast.”

Emphatically: yes!

Now if only we windows forced-users could get Keynote, I’d be in heaven.

So basically effort = mastery, is the equation?

Then I’m right back at failing to see where your criticism of assessment paradigms that factor in effort has any leg to stand on. For surely these use the same equation.

Or do they? I suspect that the key actually lies in what you are now calling “straight channeling” of effort.

What is “straight channeling” of effort, exactly? Why is it different from what might be happening in Ms. Newman’s class down the hall, whom you think *gyps* her kids by factoring effort into their assessment? And try to ignore her Berkenstocks, please. We don’t want to get emotional about this.

Oh, by all means, Dan– tap out if you’re dizzy. :) Although for the sake of not putting your readership in rigor mortis, if you want to move this conversation to email we can certainly do that. Your call.

Different dictionaries is probably accurate, which is why I threw Ms. Newman at you. Using the most common schema, can we ask, again, why her quarterly evaluation, which awards points in a discrete category called “effort,” is any different from yours, in which you simply subsume the same award into subcategories such as partial credit and verbal praise? (Verbal praise of effort, by the way, being empirically demonstrated to have as much, if not more, objective evaluative effect than grades?)

I’m not asking a leading question here– I really want to know what you perceive that difference to be.

And I also want to acknowledge that we’re probably never going to meet on whether “subjectivity”– whatever that actually means to you– has its place in a classroom. I’ve got the New York State Teacher of 2008 on my side with that one, but you know. Whatever. :)

I also

I’m trying to understand what Dina and Dan are disagreeing on. Let’s consider four students, one brilliant and diligent (A), one brilliant slacker (B), one bravely struggling student with limited number sense (C), and one innumerate student who does little about it (D). In Dan’s assessment scheme, A will pass with a high grade, B will make a bare pass but nevertheless move to the next class, D will fail, and C might get any grade from a C to an A, depending on lots of things. It seems any disagreement between Dina and Dan would be about what should happen to student B? No?

A math teacher who wants effort to significantly affect the grade permits retests, tests on predictable and clearly defined skills, lets the best score count, and makes it possible to retest until perfect scores are achieved. A math teacher who values brilliance over effort includes some tricky, surprising problems on tests to make sure that only the smartest students net an A, and may insist on averaging scores after retesting so that the grade “remembers” that a student once did not know. The former system rewards students of type C, but may make things too easy for students of type B — but on the other hand, with such a system student B is quickly passed on to a level where effort is actually necessary to pass. What am I leaving out?

H, I feel like I’ve been brought into the nurse’s office after a playground scuffle. :) Did you know drinking water drops your cortisol levels? No kidding. Who would have thought that allowing a riled-up student to go to the water fountain actually would increase his ability to function in class?

And this is precisely my point, it occurs to me. If I were Dan’s kid, running into class with a bloody scrape on my face and shaking, he would let me get a drink to drop my cortisol levels. I know he would. And I would come back and focus and do OK, because Dan, to use his own words, wants to “remove that which impedes my effort from elevating my grade,” and this is commendable.

But it is not objective. Nor it is emotionless. Compassion never is.

But Dan, as per his Faculty Room post, wants us to believe something else: that he “derives his grades from what a student knows and little else.” Yet here, he admits that effort, however directly or indirectly, factors in significantly. Indeed from every comment he’s made in this string, including his wholesale agreement about what happens to your theoretical kids A-D, this pure-as-the-driven-content-mastery assertion is false.

It’s false, but it is not the *problem*. Please understand that I’m not actually disagreeing with the way Dan grades. I mean, I could argue some larger points about needing to teach and evaluate kids as citizens and ethical beings, and yes, what to do with the type B student thing is a problem for me. But really, from all appearances, Dan’s system is overall commendable, responsible, and accurate.

What is objectionable to me is this: also per his FR post, Dan wants to cram inerrantly necessary daily evaluative decisions of compassion–decisions that do not *excuse* children’s effort levels, but *actualize* them– into this box labeled “emotional”,“subjective”, and therefore, “lousy”, for every teacher except, apparently, himself. And I just can’t get with that.

Dan, if this is not what you intend, or not what you are criticizing in other teachers, then I urge you to please get clear about that in your language, instead of encouraging false dichotomies that are designed to pitch your pedagogy as above reproach, several of which are floating around this blog today. I urge you to do this not leastways because of this fact: such design is unnecessary to justify your brilliance. I mean that.

But I’ve realized right about now that although I brought this to bear on the original weak/strong post, I’ve veered off quite a long ways elsewhere. (And anyway, Chris Lehmann has made this argument to Dan before, and better.) So I think the bell to indicate the end of the round has rung.

My take, as a math teacher, on Dan’s statements: if a student is willing to put forth effort then they will pass. This is what I am trained to do; my job as a professional is to figure out how to help each student succeed. They will make it over the hurdles in their brain with my help as long as they are willing to think and to work. It has nothing to do with rewarding effort with higher grades; the student becomes more successful mathematically *because* they put forh the effort. Students unwilling to engage their minds are the ones who fail.

This discussion is very interesting, thanks Dina and Dan (and any others :)

I teach CS at the college level, so I’m closer to Dan in content; I think the fact that there are right and wrong answers (although they may be more than one right answer) in our area colors our thinking greatly.

I agree with Dan’s ideals; the *final* grade should reflect only mastery of the material (knowledge); I seldom *explicitly* reward effort. However, effort normally leads to mastery, so I reward the obvious *consequence* of that effort.