This last week I had two minor scrapes with grading, but when I sat down to write it up, this came out. I figured it was important to share some background, since grading is such an important issue to me.

Now that that’s out of the way, let me tell you about this week.

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I’m in the last year of a Masters program in math, so each term I take a couple courses at Hunter College. Hunter, like most colleges, gives letter grades to its students. That’s fine by me for the most part, mostly because I usually do well in school, especially when I’m studying math, my personal fave.

I guess I like my program in general, but my experiences have certainly been mixed. I’m extending my expertise by learning lots of stuff, and it feels really good to be surrounded by knowledgeable math nerds. On the other hand, a lot of the chalk-and-talk lectures are pretty boring, and the head of the program once said “my job is to beat you up.” Usually my job is to do the homework and regurgitate proofs on exams, which is not my ideal learning experience, but thankfully, I can do as expected, follow lectures, and also think on my own, make my own connections, and ask my own questions. This doesn’t make me a genius. It simply means math is where I connect with my “element.” *(Can you tell I’m reading Sir Ken Robinson’s book?)*

Homework is my chance to take on tough problems and share my mathematical work with my professor. These are graded, of course, and in my Real Analysis class, only 8 out of 10 will count for our grade, so last week, I simply didn’t do my homework. I put it off, then said “forget it.”

Systems like this all head the same way – towards me calculating what I can get away with not doing. (And I actually like math!) I totally could have done it, and it isn’t like grades made me *not* do the homework, But really, I can’t help but beat the system. In highly structured systematic schooling, I suspect students spend a considerable portion of their energies trying to outwit the designers. I’ve seen it at that boarding school, and I’ve done it all my life.

* * *

I spent a year in a graduate program for Education and in one of my classes, I had to create a powerpoint presentation as a major component of the course. Unfortunately, and somewhat ashamedly, I calculated that I wouldn’t need it to pass, so I wrote the teacher and explained I wouldn’t be doing it. I’m not proud of this, but it is one from a long list of similar stories.

At EdcampNYC a teacher asked about how Saint Ann’s worked without grades and said, “in a pass/fail class, students never try as hard as the do with grades.” He’s right, but that’s only when pass/fail is the alternative to grades. Outside of that system, a great deal is possible. Students can surprise you and themselves when school is simply about learning and development.

Salman Khan of Khan Academy was recently quoted as saying “school is a game,” (and by implication ‘I’m here to help you win.’) Grades and grading systems epitomize the game mentality of schooling. When school is about doing what it takes to make the grade, economizing energy and investment is what makes you successful. Really though, passionate, meaningful learning experiences requires the opposite relationship to investment. The more of you that’s there, the more you absorb.

* * *

Finally, Justin showed me a neat little game called RayRay that some of his fifth graders played for free-choice time. I suggest you try it out. I didn’t really get it at first, so I clicked around until I figured it out. I started thinking about group theory applications (Each table of n RayRays is a subgroup of (**Z**_{2})^{n}, so which subgroup is this?) and didn’t really focus on doing the puzzles perfectly. I was happy when I solved each one, and when I beat them all, I was proud, even if it *was *the easy level.

Then, out come the cute little RayRay’s in perfect formation to inform me of my “F” ranking. I was crushed, betrayed, and angry. I went back and tried to find simpler solutions, and earned a C. Then I gave up. I realize it’s just a game, and I have faith that I could improve, but honestly, do I really need to get an F on a dinky little flash game? My colleagues will tell you, I was actually affected by this. Am I just being thin-skinned, or is there something unnecessarily negative in grading like this?

* * *

Grades are not inherently evil, but if grades constitute the core of a feedback system, that system is inherently weak. The system can be scammed, and the feedback is less valuable. (*more proof here.)*

No grading system should allow you to dump the hard work that will help you grow in the ways you care to grow. No system should thoughtlessly hand out grades or ranks without meaningful, helpful feedback, and careful consideration.

When we communicate more freely, one person to another, we have a richer opportunity for understanding and growth. Really, what is the argument for grading? Can it possibly come out of a student-centered mentality?

I completely agree with the idea that the idea of beating the system is on most people’s minds and most kids. I was that kid who figured out how to beat the system and used it to my advantage as much as possible. I’m not a lazy person and was not a lazy student growing up, but many times in high school and in undergrad I found ways to work around things and make life easier. I currently see the same patterns developing in my second grade students and I hear comments that lead me to believe that this is a learned behavior at a very young age. I agree with communicating more freely and being open in a person to person conversation. We absolutely have a richer opportunity for understanding and growth.

Thanks for your comments, Chera. More than anything, schools teach culture, and the culture of shortcuts along the way to satisfying external standards seems quite unfortunate. I would love to build schools that support a culture of hard work along the way to satisfying internal standards – the kind that grow out of connection with deeply satisfying personal experiences.

Thanks again for your thoughts.

At Western Governors University, where I did my Masters in Teaching Mathematics, you were graded pass/fail. However, a pass was a B. So essentially you had to be competent in everything you did. You had to get at least a 3 out of 4 on every rubric component for every assignment. If you had one 2 out of 4, you had to revise your assignment.

Probably one of the best experiences I have ever had as a student. It probably would work for high school students.

I’m really glad to hear you liked that system. There is an aspect of “quality assurance” in it, that I can’t quite complain about.

“So essentially you had to be competent in everything you did.”That is the thing I wonder about. Is this how experts develop, or does it more likely stop people at the level of “competent?” (Even still, we could do with a good deal more competence in the world.) I suspect for passionate learners, there are times when no grade or competency level will satisfy – when you simply have to keep going, learning more, because you really really really care.

Thanks for the comment.

Forgot to click on notification.

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I don’t think grad school for math is structured on the idea that it is an ideal learning experience. The general goal seems to be that after you leave you’ll become a research mathematician. As such, you will generally work alone and have to teach yourself new material along the way to prove something that can be written into a paper which is publishable. Graduate school exists to teach you common techniques to prove certain types of problems in various fields (algebra, topology, analysis, etc.), test you comprehensively on advanced topics to assure you’ll be able to teach those same graduate classes someday and finally see if you can produce original work.

I found that sort of disappointing myself and asked some faculty about why they even assign grades. The overwhelming response was the university used it to for fellowships and TAships (at least where I was). I think the general perception of a master’s degree (or any degree) in the research math community (the people in charge of such programs) isn’t that its a mark of genius or a certificate of mathematical competence so the grades don’t really matter. The real test seems to be a jury of your peers–peer review for original work.

Original work should absolutely be the real test. However, I don’t think you need a masters degree or a PhD or bachelors or pre-calc or algebra 1 to do real mathematics. The way you’ve put it, (and the way lots of programs think about math education), real mathematics comes at the very end, only after you’ve built up the world’s largest foundation in service of something so distant at times it hardly seems to exist. You learn arithmetic as the foundation for algebra and geometry, as the foundation for analysis, as the foundation for calculus, and then you further abstract and wind your way through the

“common techniques to prove certain types of problems in various fields”,and then,“finally see if you can produce original work.”Though, original work seems to be the thing we care least about at each level.I’m simply of the opinion that original mathematics can be done at every stage of mathematical development. No doubt training and familiarity with the mathematical landscape are very important, but it’s not enough to string students along up the ladder with no sight of the real thing.

Am I wrong?