While my grades in Algebra 1 and 2 may lead one to believe I knew what was going on, those classes were agonizing for me. I can still vividly remember the frustration I felt because nothing seemed to make any sense and my ability to memorize steps is sub-par. To this day I find it easier to remember only the formula for the volume of a sphere and then use calculus to find the formula for surface area rather than actually memorize to formula for surface area.
Strange, I know. But it works for me.
In my last post I was thinking about what it’s like to not know something. But in addition to not knowing, I think the utter confusion one can feel in a classroom is also something important to keep in mind while teaching and lesson planning and working with students. To that end my mental index popped out the card for a skit from the British sketch comedy show That Mitchell & Webb Look called Numberwang. Yes, yes, I know it sounds like I am leading you to a dark place on the internet, but I’m not. Look:
There are other episodes along with A History of Numberwang, which I recommend watching as well. Go ahead. I’ll wait.
I asked some tweeps if they had seen the skit before, and Carl Oliver came back with this:
As that kid without conceptual understanding in algebra, this skit is pretty much exactly what it was like in class for me. Confusing, almost no stated rules I understood, and at any moment the scene might change or I might be shoved in a box for not achieving Wangernumb.
Next time I go to make lessons for others, I need to keep this skit in mind and think about how I can plan for conceptual mental grappling and not just learned memorized performance in front of a live studio audience.
I’ve been poking at this video for a while as something for Mathagogy, but it’s closer to 4 minutes than 2 and not so much about math as it is about grading. As such, I’m going to put it here and do something else for the 2 minute math project.
PCMI instigated a lot of changes in my classroom. This video is about what I believe was the biggest change and something that I think caused a lot of positive cultural shifts: I stopped putting grades on the papers I handed back.
The paper I talk about is Working Inside the Black Box: Assessment for Learning in the Classroom by Paul Black, Christine Harrison, Clare Lee, Bethan Marshall, and Dylan Wiliam.
I used SBG as my quiz structure in all classes, so students were regularly getting 2-4 question quizzes handed back (I’m not a fan of collecting homework). Prior to the article they had a number corresponding to the rubric I used and some comments. After the article they had no numbers/grades and all of them had comments (right or wrong, often in the form of a question). The change in discussion post-handing papers back was huge, but it did take time to happen and was just one part of my ongoing campaign to figure out ways to get students talking math and recognizing each other as fellow learners.
Not putting grades on things that students expect to have grades is a big shift. There’s backlash from the kids to deal with who were used to getting instant status from their grades to deal with and it takes time to change culture. Do I recommend you go and try this right now at the end of the year? Not really. Do I think you should consider this as a change for next year? Definitely. Post any questions you have in the comments and I’ll get back to you. Thanks for watching 🙂
Follow up: Emily Steinmetz over at Crazy in Math gave dropping the grades a go in favor of some student grading. Read her breakdown here.
The Math Forum does a lot of cool stuff. Just click the link and look at some of the tabs. If you’ve never checkout out their Problems of the Week, I highly recommend.
I bring this group up now because I’m doing an online course with them on Differentiated Math Instruction. While working through the reading, I came across this sentence:
Well-chosen problems can often replace regular exercises and assignments and accomplish multiple curricular goals more effectively.
I am very interested in the selection of problems to replace the hum-drum ‘turn to page p394, complete 1.31 odd’ where possible. Interaction, debate, making links across topics (within and outside of math!), and problems that can engage students coming from multiple backgrounds are all things I want in a classroom. Looking forward to the rest of the course.
So Anne put up a challenge and I thought ‘why not?’
Last Saturday marked the end of a project that had been haunting my steps for a while and being free of those shackles makes the whole world seem just a little bit brighter. This next month will be a time of significant information consumption as I work through a bunch of NCTM books (Principles to Actions, Visible Learning, 5 Practices, Fostering Algebraic Thinking), read lots of blog posts, learn how to use an iPad (hello, dark side!), prep for PCMI, and develop some PD sessions for middle grades and the NCTM HS Interactive Institute.
So for the next month I’m going to try to dedicate time every day to something small and interesting that I have read/found/am playing with.
Today: Henri Picciotto’s Acceleration Posts (1/30)
I’ll start out with stating I am not a fan of separate honors classes in school and that acceleration makes me twitchy. I was accelerated along the honors math track and I developed some great rote learning skills that completely failed me in Calc 1 in college as my most excellent prof would have none of that (Thank goodness for Russ Gordon). I became a math major not because of my high school classes but rather because of an amazing 6th grade math experience and Russ Gordon’s class.
Henri lays out some discussion-worthy ideas around acceleration and honors. Tradition and parents who want sparkly transcripts are a huge challenge here. Colleges that only look at transcripts and not the actual kids are also a problem. Had a I math department, I would be interested in having some group discussions around these ideas. As it stands, I’m going to bring these to PCMI and try and get a conversation going to help further my own understanding and get others thinking about what acceleration means.
So go read Henri’s 4 posts on acceleration (I also recommend the rest of his blog). I love posts that pose questions that would shake up tradition and status quo. If we can’t defend what we have, perhaps we shouldn’t keep it? And not keeping something means working to figure out a replacement that is better, not just ‘something else’.
Like many teachers, I occasionally get notes or drop-ins from former students. And I don’t care how old they are; they will always be my kids. With the advent of the Facebooks, I have several that I occasionally hear from after they’ve graduated. I especially like the ones that apologize to me for not taking more math in college. Kinda adorable.
Last night I got a missive from one of my darlings worried about her math final. If she doesn’t pass it, she’ll fail the class. This is her first semester in college. The note was short, and she ended it with
Why am I so bad at the maths?! D:
I wrote back the following:
For me, maths was more about accepting a different way of thinking than anything else and that can be the hard part. We’re not brought up in a logic-based society. So much of high school math is focused on procedural thinking–if A, then do B & C, and ta-da! And that’s not really math. That’s more like advanced baking. Useful, to be sure, but not a way of thinking. Since I don’t use those types of problems as my main push in classes it’s also why the typical A-maths kids don’t like me for a few months–they’ve never really had to think for understanding before.
And that right there is the key. Maths makes sense. It’s the Queen of Science for a reason. If you think what you are doing in math does not make sense or is magical, than we need to figure out a different way for you to think about it. Luckily, there are a lot of ways to think about maths that are successful. Unluckily, finding the way that works for your brain can be grueling.
I got through high school using procedural skill (the If A, then do B stuff). I hit a brick wall in my first maths class in college because it didn’t work with that professor. I had to show him how I was making sense of the maths and since I wasn’t really making any sense I didn’t have anything to give him. There were a lot of nights spent in the math study room and I didn’t really get the thinking needed to understand, but I was moving that way. Slowly.
Sophomore year was when it was finally clicking that I needed to build my own understanding so I could stop playing the memorization game (it wasn’t possible to pass some of my classes via pure-memorization as no ones memory is that good. And I was taking Latin at the time so my memory banks were full up with vocabulary).
So yeah, maths is hard if you’re taking the memorize ever permutation of a problem and how to solve it route. Figuring out the patterns behind the maths is a challenge, but it pays a lot of dividends. If you ever want to chat about your stuff, just let me know. I have skype and I use google hangouts quite a bit for my work. Just remember: I am 3 hours ahead of you 🙂
What I did in class wasn’t enough to get her to where she needed to be to be successful in college maths. I still focus too much on the procedural at times, but every year I moved more and more away from that as I built up skills toward a teaching style I never saw in high school maths. I’m curious to see how much my classroom skills will atrophe while I am out of one or if the level of ed-research, blogs, and consulting work I do will help me hold steady. One can only hope.
I miss my kids.
IM&E hosted a thing at Berkeley October 12-14. I was working with middle grades folks and asked to give the final plenary talk entitled ‘Call to Action’. I chose to talk about the profession of teaching and how I think we get more teachers engaging with teaching as professionals. I’ve tried to type up what I said in the talk based on my copious notes, powerpoint, and memory below the cut. I know it’s not exact and I suspect my memory is editing to make me sound better, but I don’t have a video recording (thank Gauss) so it will have to do. I’ll warn you it’s longish, but I would love to hear your thoughts on professionalize and education in the comments.
Oh, and this is the tweet that spurred much of my ideas for the talk. Or rather, had me re-writing much of my ideas for the talk.
My interpretation of her words regarding teachers as professionals:
Don’t let anyone call you a ‘natural’. They may mean it as a compliment, but it diminishes the intellectual work that we do as professionals to become as good as we have to be to educate our children.