I put this opener on the board three times today and each time the weakest student in each class figured it out first. In two classes, the weakest student was the only student to land it.
In one class it was the soft-spoken student whose father committed suicide earlier this year, who’s been in and out of class all year, whose eyes were bright like a torch after I told him, “Nice! Now hide that, hide that.”
danApril 21, 2008 - 5:54 pm -
PS. The answer is “climbing a diving board and jumping off.”
Mr. KApril 21, 2008 - 6:31 pm -
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?
JoeApril 21, 2008 - 6:43 pm -
Dan, great idea. One thing though, define “weak” for me.
RickApril 21, 2008 - 6:46 pm -
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.
danApril 21, 2008 - 6:55 pm -
Okay, so Mr. K sounds just like my kids. Glad Rick is cleaning up after me ’cause I was ready to modify the opener.
Joe, weak, lowest grade point average, Farthest Below Basic, the most in need of remediation. Alternate adjectives?
JackieBApril 21, 2008 - 7:04 pm -
Nice. Can you throw in another few seconds and show the negative elevation?
Reminds me a bit of these graphs.
JackieBApril 21, 2008 - 7:06 pm -
And the graphs on page three of this. I’ve gotten great discussions outta these.
JackieBApril 21, 2008 - 7:07 pm -
Okay. Bad tag in there somewhere: http://www.gphillymath.org/IMP1Supp/Overland.pdf
danApril 21, 2008 - 7:13 pm -
IMP was run out of my district on a train just before mine pulled into the station. Kinda sad in some respects. Totally deserved in others.
MarkApril 21, 2008 - 7:17 pm -
Looks good. What did you use to make the graph?
Dean ShareskiApril 21, 2008 - 7:28 pm -
I’d be curious to have you elaborate more on why this happened. Makes me wonder if you define “weak” as poor grades or something else. These are definitely moments worth some further investigation. I know, it’s nice moment, just leave it alone but I don’t want to miss the learning. Or is it so obvious I just can’t see it?
JackieBApril 21, 2008 - 7:43 pm -
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.
danApril 21, 2008 - 7:46 pm -
@Mark: Keynote handled the entire process. I wonder if the process is worth a screencast.
@Dean: damn, this “weak” thing is getting out of control. Not meant to be pejorative or indicative of some underlying teacher prejudice.
These were the kids who typically take the longest to complete these opener problems, who require the most one-on-one coaching, who have the lowest concept quiz scores.
If I tried to explain this phenomenon, I’d point out that there is no algorithm for these problems. A different interpretation underlies each graph, each of which requires a full brain-ransack. My kids who work quickly – tempted to call ’em “strong” except y’all’ll make me justify that one too – have a lower tolerance for problems which can’t be solved algorithmically.
In other words, some kids gave up ’cause the problem was more challenging than usual. The other kids – my weaker students – kept on staring at it, dumbfounded until they saw it, ’cause that’s what they do every day.
danApril 21, 2008 - 7:48 pm -
@Jackie, no, definitely. In fact, I have used that page. Just noticed it was from the curriculum my district blackballed.
Dean ShareskiApril 21, 2008 - 7:51 pm -
I wasn’t so much focused on the weak term as much as what why this type of activity seemed to capture a certain type of student. I think Jackie’s getting close to what I was assuming but given the amount of visuals you appear to do daily, this wouldn’t seem to be a particularly unusual event.
MarkApril 21, 2008 - 7:52 pm -
How did you get the curved line on the graph? That’s a new one for me.
danApril 21, 2008 - 7:55 pm -
Keynote lets you use Bezier curves, which is pretty ridiculously cool. Go to the Shapes palette, push past the rectangles and triangles and what-not, and there they are at the bottom.
JackieBApril 21, 2008 - 8:10 pm -
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.
JoeApril 22, 2008 - 2:52 am -
Dan, I think you getting closer, and definitely realize that you weren’t using “weak” as pejorative, but it’s definitely a loaded, deficit term, dropped in passing.
To me, you seem to be talking about how a smaller section of your learners acquire knowledge differently. I wonder why that happens like this? I see that happen all the time in my class as well. The kids that are the worst at “doing school” are typically the ones that benefit when I do things like this. Your “weak” students are capable of these more open-ended assignments. That’s strength in math man.
I had a great professor back in my college days that used to talk about how his “C” students were some of the smartest students he had. I think there’s a lot of truth to that. Understanding that and translating it into numbers for grade reports is where I fall down. I definitely struggle mightily with this though, and applaud you for showing your students some success with this activity.
Paul BApril 22, 2008 - 3:23 am -
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…
DinaApril 22, 2008 - 11:13 am -
Ironic. I have to connect this to your grading post over at Faculty Room (which I’d encourage folks to read), and as a result commend you for being far more precise about the term “weak” than most educators.
Let me throw this out, however. You begin by talking about visuals versus algorithims (JackieB’s point and confirmation), but then seem to take a right turn later in your comments (and I don’t choose the direction lightly). :)
You seem to imply that your “weak” kids got the graph not because they have a different learning style, or different learning strengths, but simply because they *persevered*: that is, they scraped away at the prison wall with the spoon long enough to make it out. “Cause that’s what they do every day,” you say.
You also imply by extension that if your “strong” kids had *just* stuck with it long enough, they too would have seized the answer.
And to put it bluntly, I just don’t know if this is an accurate interpretation of the phenomenon.
Am I way off base on this one?
danApril 22, 2008 - 12:32 pm -
I may have been a bit glib in my assessment, but only because I really don’t want to romanticize or otherwise excuse my student’s “weakness” as an “alternative learning modality.”
My stronger students have a bunch of tools in their toolbox for solving problems. When one of those problems doesn’t point quickly to an existing tool, or if it points to a sequence of tools, they have little patience for it.
My weak student has no tools in his box. He has missed weeks of instruction. He sees the problem, grabs a rock, starts whacking on it and, lo, his method sinks the nail. These problems lend themselves well to unrefined, brute intellectual force.
This doesn’t mean my weak student is merely “alternatively gifted.” I want all my students to fill their boxes with sturdy tools and have the perseverance and intelligence to ply them even in uncertain situations.
I’m not saying that alternative learning modalities aren’t ever mischaracterized as “weakness” just that they aren’t here.
Benjamin BaxterApril 22, 2008 - 1:41 pm -
I was thinking trampoline. Close enough.
DinaApril 22, 2008 - 5:40 pm -
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.)
danApril 22, 2008 - 7:50 pm -
Awright, humor me here:
If I emphasize perseverance in assessment and pass a kid who tried really hard but who doesn’t know a linear equation from a lion in the grass along to the next class where he is underequipped to learn those new skills, who exactly wins?
TonyApril 22, 2008 - 9:30 pm -
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.
DinaApril 23, 2008 - 5:19 am -
If I emphasize mastery in assessment, and pass a kid who is brilliant, but doesn’t know stamina from an Animoto video (cough), along to the next class where she is underequipped to stick to any kind of extended revision process in writing, or strategic, long-term approaches to navigating meaning in reading, who exactly wins?
Now, you’ll see right away that there’s a difference between our disciplines in that for reading and writing, effort to a degree IS mastery. There is never a piece of writing that can’t benefit from revision; never a book that doesn’t deepen its meaning from revisiting its content over time, in multiple ways.
But beyond that, Dan, let me put this out there: not so long ago you were arguing passionately from the premise that teachers are made, not born. This is a nearly *entirely* effort-based premise. How can you make such assertions and then use an assessment system that doesn’t place a value on effort? I don’t see a consistent ethic there.
But yeah…yeah, I know. I don’t mean to sound glib about this either. I’m not saying it’s easy. Lord knows *I* haven’t figured it out. I’m working on it in microcosm and have several larger pissy subvert-the-dominant paradigm answers that have to do with arbitrary age-level expectations of content mastery and grade-level promotion, amongst other things, and which are not satisfying, even to myself.
I’m saying only that I believe that addressing it, in however a flawed fashion, it is absolutely necessary.
kenApril 23, 2008 - 5:29 am -
Dan, to answer the question you pose in comment #25, the answer is:
the fast food industry
danApril 23, 2008 - 6:44 am -
@Dina, I said I don’t want to pass a kid who doesn’t know how to do anything and you’ve replied, “yeah, but what about this other kid who knows how to do things but has no perseverance,” which doesn’t really address the issue at all.
For whatever it’s worth:
During classwork, it doesn’t matter if you make it through two problems or twenty. It matters to me (and your grade) that you’ve worked hard, pushed hard against your boundaries, the entire time.
But a C- in this class certifies a basic comprehension of (eg.) Algebra. You have to know something eventually but I decline to lump myself in with all these teachers who do lame things in the name of the almighty grade for that simple conviction.
It doesn’t have to be like that and, in my classes, it isn’t.
@Ken, good to see you back in form.
TheInfamousJApril 23, 2008 - 7:12 am -
“@Mark: Keynote handled the entire process. I wonder if the process is worth a screencast.”
Now if only we windows forced-users could get Keynote, I’d be in heaven.
DinaApril 23, 2008 - 8:33 am -
It *doesn’t* address the issue? Under the assessment system you seem to be promoting, my brilliant kid passes and your sweat-it-out kid fails, but the kid who passes ends up just as deficient– particularly if you’re talking about E/LA– as the kid you retain. Who wins? My point: nobody. Except maybe McDonald’s, as Ken says, because I’m absolutely certain they’re also looking for smart people who will sacrifice quality for efficiency for management training.
But Dan, seriously, you keep changing the parameters in this conversation. You can’t say “it matters to me (and your grade) that you’ve pushed hard” and say you don’t assess effort in the next breath. Obviously, you *do*. Would you please elaborate clearly on how?
Let’s stick with this theoretical kid who sweats blood in your class, but doesn’t end up KNOWING anything, even after running him through your most differentiated and clever assessments. What do you do with such an animal? Do you fail him? Then how does his effort “matter” to his grade *at all*?
danApril 23, 2008 - 9:19 am -
This kid who sweats blood in my class but fails doesn’t exist. I don’t know what to do with this hypothetical.
DinaApril 23, 2008 - 9:54 am -
That’s what I thought. Now we’re cooking. *Why doesn’t he exist?*
Put a different way: when kids do fail your class, why do they fail?
danApril 23, 2008 - 1:19 pm -
Okay, one way this could go:
My assessment schema doesn’t factor effort in directly but it does take a student’s effort and channels it straight at a series of targets which in turn affect the student’s grade. There is very little resistance between effort and grade, though effort is not enough on its own.
sylvia martinezApril 23, 2008 - 6:44 pm -
I wonder if more/different kids would get this if you “played” this graph as a sound file. I heard it in my head when I looked at this.
School teaches kids how to do well at school. Getting a solution intuitively is not typically rewarded in schools, so it becomes a lost art, except to those stubborn kids who refuse to learn the lesson of school.
The kids who get good grades know that there is an answer, and most likely, they were given the answer (or at least a ton of clues) in the recent past. Intuition, looking at problems from a different angle, or out of the box thinking is not in their bag of tricks because they’ve learned it doesn’t do them any good.
I think your methods might be shaking some of your “good” students to their core. Keep it up!
DinaApril 23, 2008 - 7:01 pm -
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.
danApril 23, 2008 - 7:08 pm -
Help me understand how evaluating effort is anything but a subjective game.
In math, you either arrived at the right destination or you didn’t. If a student shed some beautiful tears along the way and took a problem down an interesting rabbit trail then I award partial credit and verbally complement the creativity, but that alone won’t promote her on to cooler and more complicated courses of study.
The best I can do, then, is remove that which impedes her effort from elevating her grade while at the same time remaining true to the convictions I’ve outlined ad nauseum here, there, and everywhere.
This feels like we’re debating from different dictionaries. I don’t mind, but if the room starts to spin on you, no hard feelings for tapping out.
DinaApril 24, 2008 - 8:55 am -
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. :)
DinaApril 24, 2008 - 8:56 am -
Never mind that last “I also.” Backspace leftover. :)
H.April 24, 2008 - 12:06 pm -
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?
danApril 24, 2008 - 1:02 pm -
DinaApril 24, 2008 - 3:55 pm -
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.
H.April 24, 2008 - 5:07 pm -
I suspect part of the clue to what I’m trying to understand is in this reference to “…decisions that do not *excuse* children’s effort levels, but *actualize* them…” Too busy to think more now, though, interesting as this is. In three weeks, maybe. Sigh.
TerriApril 24, 2008 - 7:53 pm -
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.
Sue KingApril 26, 2008 - 4:46 am -
What a great discussion (and one of the reasons I think edublogging is so powerful)!! As an administrator in a school where we are redesigning our grading practices, this exchange has given me insight into how complex changing and challenging a grading system is – so many varying thoughts, beliefs, etc. Just not as black and white as I have been thinking (though never have thought grading was ‘simple’). Then again, as a former math teacher, I can see how/why Dan’s comments had resonated with me. All of this has given me food for thought and more to think about as I work with my staff to examine our practices!
orlandoApril 30, 2008 - 11:28 am -
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.