# What does a grade mean, anyway?

Here’s the second part of math teacher Stephanie Sawyer’s thoughts on the math common core standards. If you only have time to check into this blog every few weeks, skip me and read her. This is great.

Here’s a briar patch I am stepping into! Grades are how everybody measures everything. Parents and students want “good grades” so they can get into the college of their choice. Teachers want their classes to have “good grades” so they don’t get called on the carpet by the administration, because “bad grades” are often interpreted as “bad teacher”. Colleges want to see “good grades” so that they be confident that the applicant can handle what is coming in college. The problem is that no one really knows what a grade is anymore.

The leads me to think of the cartoon – Mary has posted it here – that shows two panels, one in 1961 and one in 2011. In the 1961 panel, the parents and teacher are on the teacher side of the desk and are holding up a report card to the student saying “What’s the meaning of these marks?” In the 2011 panel, the parents are standing with the student facing the teacher across the desk, saying the same thing. What an interesting shift! Once, we thought the grade was determined by the student, but in the later panel, it seems the grade is determined by the teacher.

So, what is a grade? Since people like Alfie Kohn have actually written books about the subject, I will have to distill. (Disclaimer: I don’t agree with most of his conclusions, but Mr. Kohn provides lots of food for thought.) The answer is, a grade is different things to different people at different times. One definition goes that a grade reflects mastery of content taught. Another definition indicates that a grade reflects completion of tasks on a checklist. I have spoken with students who perceive a grade as a commodity – something one gets in exchange for work. In other words, if they just do enough stuff for me, I should reward them with an A or B, regardless of how much math they actually know. I have spoken with parents who use the first two definitions at different times: it should reflect “getting the work done” while the class is going on, but when the student can’t perform at the math benchmark level on the ACT, it becomes “doesn’t getting a B/A mean my student knew the material?”

And it is that last question, “Doesn’t getting a B/A mean that one knows the material?” that links grades with assessment. If we are to be completely honest with ourselves, a grade must be linked to assessments, which, when valid, measure mastery of content. And this will only become more important once a standardized assessment is adopted for measuring mastery of the Common Core Standards.

Colleges use transcript grades to evaluate students for admission. At the high-school level, we use grades as prerequisites for the next math course. If a student enters my Algebra II class with a B+ or A- in Algebra I, I expect that she has mastered Algebra I. Turns out that is not necessarily a valid conclusion. I’m sure that many readers of this blog have experienced this. You have a student who made A’s all through 7^{th}-grade math. He arrives in pre-algebra unable to do the most elementary mathematics operations. You have to wonder, how did he – or she – get that A?

Most teachers will tell you they count assessment as part of the grade. The thing is, the assessment is not always the major part of the grade. The pressure from above is very great to “get the kids through.” As bad grades reflect poorly on teachers, high dropout rates reflect poorly on administrators. So teachers come up with a grading formula that “gets the kids through.” But that tends to open a whole new can of worms for administrators: poor standardized test scores.

My principal sent me a link to a story last year about discrepancies between grades and end-of-course exams. Why weren’t the grades a predictor of performance? The answer to these educators was that many of the A and B students were the kids who didn’t necessarily learn content; they learned to “do school.”

Here’s how it works. You have a class where the grade is determined by the following formula: 50% comes from your homework average, 50% from assessments like tests and quizzes*. With this formula, good students who turn in all their homework on time can get a 100% homework average. But because they just want to get the work done, they aren’t really processing or learning. This same student makes a 65% test average. Fifty percent of 100 is 50, and fifty percent of 65 is 32.5; 50 + 32.5 = 82.5, and that is a solid B. See how easy this is? You can be a D student but get a B. How awesomely awesome is that? Why actually learn the math if you can get a good math grade without really learning any math?

Link the grade to assessments, and make the assessments a valid measure of the learning you want to occur. When this happens, I think the grade-standardized test correlation will rise. How could they not? If you are teaching students to learn the content in the standards, and their grade is a reflection of that learning, shouldn’t the logical consequence be that big standardized assessment will be just like your assessments? And wouldn’t the grade earned, based on your assessments, be a decent predictor of success on the big one?

I will share that my grading formula now counts homework as only 10%. I have a total of 4 categories, but assessment is now 75-80%, depending on the course. It was a little rocky at first, but I now have students who are really trying to learn math. Once they figured out that “doing the work” was no longer sufficient, some started to study. And think. And process. I can’t explain their turnarounds in any other way. I am talking about students who went from Ds and Fs on tests to Bs. I asked one of them what changed. He told me, “If you learn the math, the grade will follow.”

What else is there to say?

Judging by the 49 “valedictorians” at a Utah County high school, I’m not sure grades mean much now. That poor student who got one A- in his school life and was ranked #50. Ouch! Of course I bet the teacher looked like the one on the right when the parents came calling…

On the piece above, I have to say it is well written and brings out some good points. Grade inflation is rampant as my previous post would suggest and that example I gave is NOT an exaggeration. A Utah County school had nearly 50 students go through three years of high school with a 4.0 grade point average, a generation ago, one or two students would do that in a typical large high school.

My only problem basing things on “assessments” is not using them to determine grades but using a “variety” of assessments to determine learning. Perhaps math is limited this a bit, but not completely. Also, many subjects like the Social Sciences are a bit more subjective in determining what content is the most crucial where in math solving for X is more cut and dried. Bottom line, students need a variety of ways to show learning. And determining mastery is sometimes tricky.

Let’s take this example from sports. Who knows more about basketball–NY Knicks TV broadcaster Marv Albert or Utah Jazz legend Karl Malone? Of course, the obvious answer is Karl Malone, right? He knows how the play the game at the highest of all levels. But I would bet Marv Albert knows the rules better, the history of the game better, statistics better? But he might not be able a shoot a basketball consistently from ten feet out. So how would mastery of basketball be measured?

And in math, I view math, unlike most people I suppose, as a right-brained exercise. Math to me is a creative, right-brained thing, or it should be IMO. So maybe we put a lot of students in front of computers, like they do at our local high school, many could come up with the correct “answers” on these CRT tests, buy many of these students lack the knowledge to apply these skills in a meaningful, creative way. And to me, these students aren’t that much better at math than the students that can’t pass the CRT test in the first place.

The problem with standardized tests is that they don’t assess creativity or application too well. The assess only in one or two different modalities. SInce teachers and administrators are conscious about teaching to the test and getting good test scores, creativity and application is stifled. Of course, I don’t think we’ll truly grasp the incidious nature of this type of teaching and assessing for generations to come. The other sad thing about standardized testing is things like music, art and PE have been taken out of the curriculum at many schools, or they barely exist at all. Then we can complain why children watch reality television and are obese.