Monthly Archives: October 2011

[Grades]: More recent experiences

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.

* * *

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 (Z2)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.

The RayRays betray me - F on Easy

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?

[Grades]: Some personal history

I work at Saint Ann’s School, where grades are not allowed, but I used to work at a highly structured all-boys boarding school with what I would call an uber-grading culture.

Not only were students graded in each of their classes twelve times a year, but they were also given “effort grades” on everything from their academic classes to dorm life and sports.  These two combined to place the student in one of five groups that would determine their freedoms and privileges at school – everything from required breakfast and study hall down to when they could visit town or even go home for the weekend.

The school believed firmly that this was a very explicit and fair way to control boys and get them “on track.”  After all, all they had to do was put in more effort, and the marks would surely rise.  The sad truth is lots of guys were bottom group guys, term after term, and this became a part of the language used to describe students.

Though I loved and respected my colleagues (and many of those students), I perceived a systemic lacking in the intellectual culture and treatment of young people.

* * *

I grew up with grades, and did mostly fine with them.  I’m convinced that they shut down my dreams of being a poet (more on this another time), but I found academic success anyway.  Typically, if I did my homework and paid attention in class I could earn A’s and B’s, and that didn’t even involve taking notes, studying, or even doing the English or History readings most of the time!

Steve Miranda wrote a nice post recently about complete contracts and why they’re rarely used, except in school, of course.  Complete contracts indicate precisely what must be done, so the rest is omitted.  The simple fact is grades define “good enough,” and if I could earn B’s without even reading the books, and if I would rather spend my time biking, singing, playing piano, or tinkering with speakers and electronics, than why would I ever read those books?  I got my B.  That was good enough for me.

This is the behavior I observed in the “middle group” at that boarding school, and it’s the kind of thing that drives me crazy.  My relationship to everything I listed above (and more) was very different from my relationship to most school subjects, but it was there, on my own time, guided by my own instincts, that I had grown the most.

Can school be more like that?

* * *

People are always fascinated by Saint Ann’s.  How can a school work without grades?  How do the kids go to college?  How do their parents know how their doing?  How do the kids know?  I get these questions, especially the second one, all the time, but trust me.  Kids do go to college, and it does work.  In fact, Saint Ann’s is not so different from a more typical school, despite our love of the quirky, funky, odd, and eccentric.

Saint Ann’s is not the intellectual utopia it might seem, but based on my experience, I’d say we’re getting a lot of things right on the fundamental level.

By extending great autonomy and flexibility to the faculty, the school puts faith in the intellectual capacity of its teachers and their ability to inspire action and growth in their students.  By placing arts on equal footing, the school points towards a larger view of intelligence and potential.

The school believes in the almost sacred value of children, and that grading them or using grades to derive authority would be demeaning to the potential within them.  By eschewing grades and almost any strict sense of propriety in favor of passionate intellectual pursuits, the school has made plain that earning good grades and learning are not tied well together.

I could be equally critical on the small-scale, but for the foundations of a school, I’d say this is a great place to start.

Real World Math (Dan Meyer and stuff)

I spent a really invigorating and exciting day at EdcampNYC on Saturday, surrounded by passionate, motivated, active educators. I just want to thank everyone who came, especially the attendees at my session, Student Choice in the Classroom.

The sessions were posted by people who could facilitate, but not necessarily in response to attendee interest, and some were left underwhelmed by the offerings.  If I were designing EdcampBK, for instance, I would include a way for session requests – probably a quick and dirty version of class planning at PSCS.

I just wanted to grab these underwhelmed adults and say, “see how boring stuff is when it isn’t what you want?  That’s how our students feel everyday!”

* * *

At the end of our student choice session, I had a conversation with a teacher about her daughter, who was very interested in becoming a math teacher. The daughter spent lots of time in college preparing for this, but she decided to enter the business world instead, and come to teaching later in life.

“If I’m going to tell these kids about all of the real world applications of math in the business world, and all of the life and career paths that include math, I’d better have some experience with it first,” said the daughter.

Math is so COOL! Right?

First of all, if she just wants the money, I get it. No blame. No shame. I’ve seriously considered selling out lots of times, especially with student loans rocking my monthly budget. On the other hand, she brings up a good point. You don’t even need to look at a textbook like this to know that questions of “real world applicability” are always being asked. In the face of “when am I ever going to use this?” many teachers see winning over students and convincing them of relevance as hugely important for gaining their buy-in.

They’ve got that right!  Personal attachment and investment are what drive personal growth, but this is a very artificial look at math in the real world. Let alone that shade of orange and the hodge podge cover full of unrelated stuff, I suspect no one actually sees the world this way.  Ugh.

* * *

Here’s a better vision of real world math.

Dan Meyer is a former teacher, now doctoral fellow at Stanford working on curriculum design. You can check out his TED talk, but I’ll summarize. Dan’s trying to recontextualize mathematics by using videos and photos of REAL scenarios – the kind you can actually see.

Here’s a classic problem, revamped and improved.

You show that, and then ask the students what they’re wondering. “Does it go in?” perhaps. You can read all about Dan’s “three acts of a mathematical story” here, but act one should grab hold of the audience with something truly compelling. I’m all about that, for sure, but let me be critical.

Sometimes I get the feeling that Dan is close to merely repackaging the same old product in a more exciting way. I applaud his work and effort, but this is still pretty dull. Dan’s stuff is distinct from that textbook cover in two ways; It’s authentic, and it’s actually compelling (though not always and not for everyone). Furthermore, lots of teachers simply must teach this stuff, by law, so I’m extremely happy that he’s helping them do that, but the “math makeover” we need is about much more than repackaging.

It’s about the mathematical process (Dan gets this), and it’s about student interest and their questions. I get the sense that Dan only kind of gets this one, because the videos speak so directly towards one or perhaps a few very specific questions.  I try, instead, to bring students to mathematically rich and accessible environments, in which an abundance of questions can be pursued along various routes. This helps students develop the mathematical instincts already within them, on whatever terms they can negotiate.

* * *

But here’s what rocks about Dan Meyer and what I think “real world math” really is.

Dan is a very passionate mathematician, and he is sharing compelling math, directly from his own experience.  Seeing math in the world is something he actually does, and to share that with students is to help them do it themselves. If my kid were in his class (not that I have one), I would be thrilled that he got to learn from a passionate and empowered math nerd.

That’s what’s real about math in this world.  There are real human beings, called “mathematicians,” that spend a considerable portion of their time engaged in mathematical thought – asking questions, answering them, revising, explaining, sharing, tinkering, analyzing, wondering, dreaming, playing, failing, succeeding, and on and on.  This is what I want to share with students. Math is something that people do, including me, and it is something that they can do as well.

This is what I want to tell that daughter. You don’t have to go into business to understand real math. Simply immerse yourself in a mathematical life, be a mathematician (in your own way), and you will have plenty to share. The sad fact is that school-math discourages this notion by implying to students that math is math class (or for geniuses), particularly because so many so-called “real world applications” are wholly artificial and pseudocontextualized.  Furthermore, school tells us we need teachers, texts, and problem sets to do math, when this is far from the truth.

Real world math is simply mathematical thinking. It’s personal, it’s real, and it can happen to all of us.