Thursday, September 13, 2012

First Quiz!

I gave my first quiz today! This is super exciting because I have something to put in my grade book. We get to see my grading policy in action. :)

Actually, to be honest, I'm more excited about the quiz itself and the girls' work. SBG has forced me to re-evaluate the assessments I was giving out, and  revise them. Now I ask for more explanation. It's not enough to write the correct answer, or show some limited algebra. I'm also trying to find more creative ways to assess their understanding. For example, "What did this student do wrong, what should she have done and why?" is something I haven't used much. I should.  Their answers are very informative; I can pretty quickly see what they do know, and where the errors in their thinking are.

Now, to the grading!

Friday, September 7, 2012

Meet the Teacher's Grading Policy

Introducing the parents to my grading policy last night at Meet the Teacher Night went really well! Of course they had questions, of course they had concerns. Actually, the concerns were not quite the ones I expected. They were troubled that I was introducing this uncertainty in the senior year. No one really knows how this will work out. For seniors who depend on the first term grades to help cement their acceptance into the colleges they want, not knowing how the grading system works is really scary. (They know what the policy says - they don't know how it works. Experience is needed.) So the parental concerns were not that I was grading differently, but that grading difficulty is really scaring/stressing their daughters out in an already stressful year. 

The highlight of MtTN was when one mother pulled me aside after it was all over to talk about her concerns that her daughter hadn't really mastered the material in previous classes. Her response to my new grading system was along the lines of "I think this is wonderful! Why isn't everyone doing this? Why haven't they been using this in other math classes? It would have helped my daughter!"

Gotta admit - that was one response I wasn't expecting. At all. 

Tuesday, September 4, 2012

This is Math

"The important thing is not to stop questioning. Curiosity has its own reason for existing. One cannot help but be in awe when one contemplates the mysteries of eternity, of life, of the marvelous structure of reality." --Albert Einstein

"Each problem that I solved became a rule which served afterwards to solve other problems." --Rene Descartes

Somewhere, in and between these two quotes, is what mathematics means to me. It's not the techniques and the procedural ways to solve problems. It's not even knowing theorem after theorem. It's in the exploration I do myself, and the discoveries I make.

In my last two years of high school, I decided I was going to be a math teacher. As far as I was aware, I was good at math. I mean, really good. My mom loves to remind me how my HS math teacher, Mrs. C, told her how I would act as a translator for other students in the class, re-explaining during work time what Mrs. C had meant. I had almost no trouble getting it the first time. Math was recreating what the teacher had shown us on a variety of problems. Sometimes there was a cool little trick you needed. I liked those. They made me feel smart when I figured out what the trick was.

My first semester of college, I got a wake-up call. Sure, most of my math classes were recreating what the teacher was showing us, but one class stood out. Everything was open ended. We'd get a question (the first one was about ants and how their tunnels connected - hooray for graph theory!), and then we'd play around, trying to find an answer of some sort. David, the instructor, had some rules about the format of our notebooks and everyone having to share something in class each day, but he didn't seem to do much. (Now that I'm on the other end of the classroom, I know what a lie that was!) We met in study groups (required), shared with each other, got excited for each other's brilliant ideas, and hoped some rule we came up with would be named after us. (David started that, too.)

One of my group mates spent hours drawing and looking at graph after graph, counting vertices, faces and edges, until he came up with an equation relating them all. Our study group was so proud of his result - it was HUGE. I was envious of his dedication and discovery. (To this day, I think of it as the Wilmot Equation, not Euler's Formula.) That was math. That was what it meant to do math.

I promise I'm not really straying from my quotes. Yes, problems were given to us, but they were only the starting point. David encouraged us to extend and expand the problems, go down a variety of different paths, and ask more questions. We became curious, and more curious, as we found more answers. And every problem built upon the one before. The definitions, rules and explanations from one problem guided us and pushed us on the next one. Sometimes something forgotten would pop back up. It was like finding those little tricks, but so much bigger, so much more meaningful. There's nothing like it to make you feel like a genius and an idiot all at once.

That, my friends, is real math. Not school math. REAL MATH. Mathematicians-turning-coffee-into-theorems math.

How do we get it into our schools?

Personally, I stole the research log from David. (Though he helped a bit - so is it just borrowing? I'm not giving it back!) I pose open questions to my students, and let them try stuff, play around, suggest ideas and shoot them down. I'm nowhere near as accomplished at "doing nothing" as David was, but I'm working on it.  I make up questions related to calculus, and ask them to play with them. I've gotten some beautiful definitions of tangent lines and explanations of how curves can have slope (without me introducing the topic first!), and I've gotten frustrated, stuck in the mud spinning the tires students. (It varies, depending on how willing they are to throw out how they've defined Math for all of these years...) I'm learning, slowly and painfully, how to scaffold the questions without making them obviously leading. I've got a loooong way to go on that. I need more calculus teachers in my circle of friends, so I can pick their brains.

Here's the notebook guidelines I give my students:

Research Log Guidelines
(Based on the syllabus of David Olson)

The Big Reveal!

I've had a couple of posts now where I reference my new grading policy, but I haven't really said much about the details. I wanted to wait until I had all of the major pieces done. But I think if I wait much longer, I'll never get it posted.

To start, here's the explanation of how it all works. This is actually a subsection of my syllabus and procedures document. It isn't specifically mentioned here, because homework has its own section in the syllabus, but I do not grade homework. (Though I foresee a language shift in my future. Some assessments could be worked on at home, I think... so better to say I don't grade practice problems)

SBG Policy

A lot of these ideas aren't really mine. They come from the great minds of people like Sam Shah, Shawn Cornally, Frank Noschese, Joel Ochiltree, Dan Bowdoin... Shawn was kind enough to exchange emails with me, answering a bunch of questions I had. Many thanks, gentlemen!!

One piece that wasn't included in the policy above was how, at the end of the term, I was going to convert all the standards marks into a letter grade. (As the only person using SBG at my school this year, I still have to put a letter grade and a percentage on the final report card. But we may be moving to a school-wide grading policy - and this one has generated a lot of interest among the other faculty...) I was hoping I'd get more buy-in if the students had input on what was a fair conversion. The conversation quickly revealed a lot of their doubts and fears about this new policy. In the end, I came up with a compromise between my initial impulse (which was very strict) and their I-need-to-get-an-A-so-let's-make-this-easy ideas. (To be fair, I'm not really sure that's what they were thinking, but it's what it felt like!)

This is what it looks like:

Grade Conversion

I'm not really thrilled with the last bit about using my discretion to assign in-between grades, but it was the easiest way to account for the in-between percentages and the wide variety of combinations of marks. There's going to be around 60 skills for the term (broken into units of anywhere from 8 - 12 standards), which means to get an 80% (B-), they need to be about 90% proficient.

I'm going to use the table above to convert their standards marks for the term into a percentage, which goes into the 85% category. On the midterm and the final, I'll grade based on the standards that appear on each assessment, and convert their marks using the chart above into fixed percentages for the 7.5% categories.

So there it is. I'd love hear any thoughts you have. Especially if you've been here and done (something like) this before.

Thursday night is Meet the Teacher Night. I hope the parents are open to this!