The last few days of the term can be hell for most any teacher, but under Standards Based Grading (SBG), where every kid has the “opportunity to earn an A,” and thinks all they need to do is reassess their way to an A, which often translates into hanging out the teacher’s classroom working on problems I give them until they are satisfied, or give up in despair, and along the entire focus on learning we’ve been building all year long can fall away.

Here are a collection of random observations and thoughts that, because I’m in the middle of dealing with all my students’ perfection seeking, I haven’t had time to really hammer out into a deep connected understanding.

## The problem of perfection seeking in general

This past weekend, I got the following email:

I would like to enter the exam having showed understanding on absolutely everything. Is there any way that you could let me know the concepts that I have not yet showed understanding on so that I could look them over, make sure that I understand them, and then re-assess my understanding of them so that I could not only show understanding on everything, but also review any dicey subject matters that I need to go over. If you could please let me know the subjects I don’t have 3’s on, that’d be great.

Five years ago, I would have thought—”wow, this student really cares about physics. Let me look in my trusty gradebook and send them a detailed list of their scores on every concept and questions they can use to reassess them.” (This isn’t completely true. 5 years ago I would have said something, like “your sores on the previous exams were X, Y, and Z; they are fixed and cannot change, they show your lack of understanding of physics and will follow you forward throughout time. Now, your best hope is to study your past mistakes to do better on your exam, BWAHAHAHA!”).

Now, this email really got me thinking. This is a good student. They have a strong understanding of most of the ideas in physics. Why are they seeking 3’s on everything? What’s the deal here? This also got me thinking about a fascinating post I saw on the the awesome psychology of games blog—and a great post titled “Conceptual Consumption and Kicks to the Head.”

Here’s the basic gist: Dan Ariely coined the phrase conceptual consumption (pdf) for the idea that people are just as interested in consuming ideas and information as they are physical things. They want to possess “ideas” that are rare as status symbols in the same way they want a nice car or clothes. For some, this becomes a sort of “check off list” of “thing’s I’ve done.” And of course, on this check off list, knowing an idea is rare or difficult makes it all the more coveted. (If you’re wondering how this connects to video games, you really should go read the blog post and see how XBox live uses this phenomenon to get people to want to spend vast amounts of time replaying tedious and brutally hard sections of games like Halo:Reach all so that they can achieve the achievement of having beaten the solo campaign on epic difficulty.)

Despite the fact that I often find myself falling victim to conceptual consumption, especially in the age of twitter, blogs and the universe of ideas the internet exposes me to, this is precisely what I do not want for my students: I do not want them “checking off boxes” in my class that say they understand every concept. I do not want them waiting for me to tell them they understand every concept. And I do not want them to think learning is just a process of acquiring “achievements” that you collect to add to your “experience resume” as status indicators.

(Cue idealistic music) I want them to see to see learning as a process, I want them to see that just when you think you understand a concept, you realize how much more there is to understand, and that is a good thing. Precisely for this reason, it’s pointless to put together a list of “intellectual achievements” for you to achieve, since unlike Halo, the list of possibilities is endless, and the most important ones haven’t even been found yet. I want them to see that they can begin to measure their own understanding, and when they really achieve mastery, they will know it, without having me or Xbox live telling them so.

So why do I present them with a list of standards for each unit? And why aren’t there blank spaces at the bottom for the new standards we come up with along the way?

## How can we see risk-taking, failure and mistakes as investments?

A while ago, @mmhoward tweeted this:

The best way for my students to learn physics is by making mistakes. Lots of them. Its a truism student who survives the physics major knows to be true, and it’s shared all the way up the pantheon to the greats:

“An expert is a person who has made all the mistakes that can be made in a very narrow field.” —Neils Bohr

So here’s the challenge. My students can do corrections to test questions to demonstrate increased understanding and replace previous grades. They can also reassess standards outside of class. Often, it’s the case that in the process of doing corrections, or reassessing a standard, a student will reveal another misconception that shows they don’t have mastery of a different concept. What do you do in this situation? The right thing to do is tell them that this showed they didn’t understand that idea they thought they mastered, and lower their score on that other concept too.

As you can imagine, this can send perfection seeking students into a tailspin. “What? I’m correcting something and you’re lowering my grade?” And it contradicts the idea that we learn through making mistakes, and I want to encourage my students to make as many mistakes as possible. So how do I reward them for the investment they are making in doing corrections and exposing other misconceptions? Sure, some investments don’t pay off (really wish I had held onto those 10 shares of Apple stock I bought a five years ago, instead of selling them at break even), but I want my grading system to reward the kids who are tenaciously ferreting out misunderstandings of ideas that they thought they “knew”, rather than let them sit comfortably with their perfect scores on every idea and think they’ve figured out all there is to this subject.

Here’s a prime example (sidenote for the physics un-inclined: feel free to jump over the next few paragraphs, but don’t miss the bigger point about understanding the big idea I highlight later). A student wanted to reassess his understanding of how to solve kinematics problems. So I asked him to calculate the distance a car would travel if it were traveling at 20 m/s and came to a stop in 1.5s, assuming constant acceleration.

Here’s his response:

The answer would use the formula 1/2 deltav*deltat because of a triangle needed to find the displacement in the velocity vs. time graph. If you add numbers, you get 1/2*20m/s*1.5s which then gives you the final answer of a displacement of 15m.

This answer belies a few significant misconceptions. First, it relies too much on formulas. The formula $1/2 \Delta v \Delta t$ isn’t something I’ve taught them, and it shouldn’t be written in the pantheon of important physics formulas. Moreover, if you do the calculation a bit more rigorously, you find $\Delta v=v_f-v_i=0-20\:\textrm{m/s}=-20\:\textrm{m/s}$, but if you follow that through you’ll find that the formula above gives you a negative displacement, which makes no sense at all.

So I wrote my student back to explain this very point. And here was his response (he also included a graph similar to this—which is awesome).

The reason that I didn’t stay with the negative delta-v was to keep the numbers real. Yes, the change in the velocity was -20, but if you look at the green triangle that shows displacement, you would realize that an area can’t be negative. That’s when you must do the absolute value of delta-v, in order to keep the area of the triangle positive, and therefore the displacement positive as well.

Can you see the learning taking place? Here’s a kid who knows what the answer is graphically, but is hanging on to a formula, and when the formula doesn’t make sense, he throws out the negative because he knows the right answer from the graph. This is good understanding—far better than trying to pass off a stopping car goes backward because the formula says so, but it also shows he’s not really seeing the connection between the graph and the formula.

I’ll spare you the 5 additional back and forth messages it took to begin to clear this up, followed by a 1-on-1 conversation, but eventually the student realized that the number from the formula should be $-20\:\textrm{m/s}$, but he also needs to account for the distance the car travels because of its initial velocity.

Graphically, we see that the student was calculating the displacement that corresponds to the red triangle, and if he adds this negative displacement to the displacement represented by the area of the black box, he would get the a displacement of $15\:\textrm{m}$, the area of the green triangle.

And if he’d started with a more general formula, based on the complete picture from the graph, everything agrees perfectly.

$\begin{array}{rcl}\Delta x &=& v_0t+\frac{1}{2}\Delta t \Delta v \\ &=&20\:\textrm{m/s} \cdot 1.5\:\textrm{s}+\frac{1}{2}\left(-20\:\textrm{m/s} \right)1.5\:\textrm{s}\end{array}$
$\begin{array}{rcl}\Delta x&=& 15\:\textrm{m}\end{array}$

So what sort of grade should you assign a kid for making this breakthrough? And how much does he really own this breakthrough versus just doing stuff I’ve assigned so he can check off some boxes to earn achievements?

These are difficult questions that I’m wrestling with, and they bring me back to the big idea I’ve shared about grades before:

Let grades be the start of a conversation, and not the end.

1. December 15, 2010 8:06 pm

This web that you are immersed in on the grading issue is circular. I really don’t see a way out of the circular issue or argument. If you are truly interested in “mastery” above your interest in assigning a “grade,” I think you have to go for mastery, ignore the grade, and not put time constraints on the learning process. Now that may not be realistic given where you are. However, I think it might be the only way out of the argument you are having with yourself. Mastery of physics is important, but is mastery of every nuance important? Depends? Who is the student and what are their personal goals for the course? Do you have that information for each student and can you tailor your grading to their personal goals?

Good work on the blog posting. Very informative and good questions are being posted.

Bob R.

2. December 15, 2010 10:53 pm

Bob,
You raise some good questions, and they are issues I hope to discuss in our PLC. At the same time, I think the quest for total agreement and perfect “fairness” can be quite un-fruitful. Life really isn’t fair—Mr. X things sig figs are super important, and takes off points every time, Ms. Y doesn’t care. Mr. Z gives nothing but multiple choice tests with no partial credit, while Mr. A awards generous partial credit. Students constantly grouse about these differences, or the English teacher who is supposedly the “easy” grader, and the nit-picky “hard” grader who seems to give every paper a B-, but I think they learn to adapt to these differences, and this is a valuable lesson. After all, we’ll all end up working for a number of different bosses in our lifetimes, each of whom might emphasize different things, and our success will, in large part, determined by how we adapt to those varying demands. One of the benefits of teaching in an independent school, I think, is giving teachers the freedom to teach and grade in the manner they see fit, within reason, of course, so that each teacher maximizes her strengths. I worry that too much focus on standardization can lead to regression to the mean, and degrade the overall student experience.