Sunday 4 November 2012

Math Teaching Roundup - Part 2

In my prior post, I mentioned some of the good things that I think I've been doing in the class during Term 1 of Semester 1. Feel free to read that first, I'll wait. There, see? I kind of know what I'm doing. But I'm still struggling in places. Maybe some of you will even see yourself in me? And maybe you have coping strategies that are working?

Part 2 - The Not So Good

First, just an overall remark. I know that, for me, teaching works much better with a lecture style. Not that I talk the whole period (though see #1 below), just that I have trouble thinking up, and dealing with, more chaotic environments. The ones with lots of group work, or activities - in fact, they stress me out as they occur, even ignoring the issues of setup. I know, I know, this is something I need to work on, and I'm not advocating "chalk and talk" or anything, but... euh, some days I wonder if I'd have been better positioned as a post-secondary professor.  Which is more an overall mentality thing. Less broad issues include...


Absolute Value Barred
Okay, I don't think any student has ever said this to me, but sometimes I find myself thinking it, so some of them might be too. I swear I'm a little ADD. It's not that I get way off track (well, not very often). It's not that I don't stop and let them work through a few problems (homework or otherwise) when needed, or to let them discover certain things on their own.

It's more like I can't bear the thought of ten seconds of silence.

I've been (trying to) get better at this. Waiting longer than five seconds for students to think about a problem, for instance, before rephrasing it. Or there's times I them to start in on their homework, and five seconds later I'm all, "oh, and remember we have a quiz tomorrow" or "right, and make sure you're simplifying for the first question, not evaluating it" or "by the way, how does my tie look today" and, yeah, shut up, sir. (Okay, so maybe not that last remark.)

Once the students are working on something, and discussing themselves, we're fine. And I grant part of the problem is that if I don't say something when it occurs to me, it's probably gone, and I'll remember it at lunch and go ARGH, meant to ask if anyone else wanted to sign up for the math contests... hope I remember tomorrow. But part of it is I need to know when to STOP, and let students think, or work. I'm trying to count numbers in my head. Work in progress.


It's killing me. As I mentioned in the 'good', it's pretty easy to grab some valid student work because I spend up to two hours totaling. THAT'S ON TOP OF THE MARKING TIME. I mark the tests in four hours. Now add two more for totals, because I'm not counting points here. I'm looking at it holistically, looking at the overall expectations for the curriculum document, and assessing whether that's a 75% or really just a 72%.

Don't get me wrong. I am ALL FOR this. I've seen the studies, I'm nodding about a lot of stuff on Dan Meyer's blog (and those of others), and I'm trying to implement pieces of it to the best of my ability. But speaking as something of a perfectionist, IT'S KILLING ME. (Slowly.) Some bright people in our math department have devised a point system to run in tandem... for instance, all tests are out of 24, and getting an 18/24 might mean 75%, but it might be 72% depending on what aspects of the test they did and didn't get.

The system seems to be most useful at separating out the fail and near perfect cases, allowing one to concentrate more on the middle ground. For some, it's working well. But I think it would take me just as long for me to figure out how to allocate the 24 points initially, as it would to mark the fail/near perfect cases anyway... plus my mentality tends to be pretty black and white. (Hot and cold, yes and no, in and out, up and down...)  So for me, my suspicion is that shading points into a level system would lead me to (more) madness.

But two extra hours? And I'm not exaggerating by much here... with 29 students, that's only about four minutes per paper, maybe a minute for looking over each page. Some do take less. But then factor in the fact that after doing this 10 times I'm staring at the ceiling, or wondering if The Sam Tsui has a new Medley song up yet, or counting how many Gangnam Style videos there are out there, or... okay fine, if I cut ALL that out, maybe we're down to just over an hour. But isn't that about 45 minutes too long? Particularly since I'm not even marking the stuff at this point?

I'm going to throw in this paragraph to potentially ruffle some feathers. I'm going to claim this is easier, or at least more familiar, for those who mark subjects like English and Social Sciences. When they go through teacher's college, there's probably instruction on why that essay should be a 68% and not a 72%. But being good at math, and having the connection to numbers that I do, makes it harder for me to say "these solutions are a 75% and no more!". (This far, no further! You.. shall not.. pass!) Now, don't get me wrong, I was an editor for my university newspaper, and marking English isn't simple either. But I feel like there's more adaptability in how they think about things. Feel free to prove me wrong, or merely offer some tips below in the comments.

In the meantime, this is killing me. Someone. Help. Please.


I struggle with this every year too. My class is arranged with desks in pairs, facing the SmartBoard. No problem. I've also been blessed this Semester with groups that are mixed college level or above, thus generally task oriented, and disinclined to jab the person next to them with a pencil. Good. So what's the problem?
Circe thought she might even doodle a mustache

Students at the back potentially tuning out. Students who start to work with the person next to them, to the exclusion of everyone else in the room. Students who struggle that end up next to other students who can't help them - or who CAN help them, but then the information may only ever flow one way. The logical solution to this is, of course, to change up the seating plan, but there's some students who need to be nearer the front, some who need to be nearer the door, some who cannot be placed next to their sworn enemy... I have trouble coordinating all this, particularly when there's a good chance I wasn't aware of the identity of the sworn enemy.

There's also the fact that I can't change the seating plan in September. Because I am LOUSY with names. In a prior year, I arranged students alphabetically by first name on Day 1... I'm on the fence as to whether that helped me learn faster or not. Thing is, I learn spatially, facial recognition comes later, and only after that does the name hook in. (I'm also bad with body language.) Yeah, I'm the guy you'd have this conversation with at a Professional Development Day:
YOU: So, how was your last session?
ME: Uhm, good, uh... sorry, you look familiar but...
YOU: We taught together at the same school last year and sat next to each other during the keynote this morning.
ME: RIGHT! ...your name is on the tip of my tongue.
YOU: I'm still wearing my nametag.

Now, once I have name/face association, it's in there... assuming I encounter you regularly. Give it two years, they'll disassociate; I'll likely recognize your name, and your face, but may not make the link. In committees, I often take the position of secretary, and I'm not sure if that's to help me forge the links, or just for added irony. So... so where was I? Aha, seating. Yeah, so changing the seating plan every week would be a bit of a nightmare. But by October, once I'm comfortable, the students are kind of entrenched.

I have a possible fix here though, which only just occurred to me this past Thursday. Seat-Switch Fridays. On Friday, you sit next to someone new. I have no idea how it will go over long term, whether they'll take the same other seat next Friday when I do this, whether they'll actually make connections with someone new, or whether they'll start jabbing people with pencils. My hope is it helps with the learning. Something to revisit.


I know, what teacher doesn't have this on their list. But over the last couple of years, I think I've started to become less productive at home. (Is it because I actually live in a house now?) When I get home, I can often rationalize away doing prep or marking in favour of the dishes, or mowing the lawn, or going online, or wouldn't you know it, spending time with my wife.

But what this means is that I'm spending more time at school, until 7pm, 8pm, even later. Granted, I have three courses to prep this year, only two of which I've taught in the past, but... yeah, I don't know, should I simply be leaving early and setting aside the hours of 7pm to 8pm at the house for schoolwork? Does that work for people? Because I'm not sure it would work for me - if it's not absolutely needed for the next day, I'm too good with excuses. So, something else I'm tossing out there. Because I can't see my method holding up forever, or being particularly healthy.

And there we go. I think that's the main stuff. If anything else occurs to me, maybe I'll do another one of these around the end of 2012. In the meantime, look for me the week of November 12th, when I attempt A Day In The Life, with thanks to the other math educators who came up with the idea.

(Math personification graphics not guaranteed for the next "Day In" post... unless people really want them?)


  1. 1) Shushing: (^_^) Would writing down the reminders in a file to display on the smart board help any? You could set it up the night before or in between classes and put the file up on the board at the beginning and end of class. Might help get the pesky details straight without having to follow the memory chain while getting the students to do their work.

    The slow count of ten in a language of your choice should help there with letting the students get started on a problem. If it'll help, try counting in a foreign language, to give more time as you remember the right word.

    2) Marking levels: Math doesn't strike me as being fuzzy on numbers (except where fuzzy numbers are being studied). But, when creating the tests, can you break down the steps so that each step is worth x and add those up to get the total mark for the question? It's one thing to know the answer (1 point), but explicitly going through all the solution steps, even if the result of step is wrong, getting a mark or two for having the right idea shows that the student is applying the lessons. If you want, I can try sending a cousin who teaches Classics in university to the blog to see if she can help here.

    3) Seating: All I can suggest is nametags. Unless class participation is a part of the mark, let the students make up names that aren't obscene and aren't a copy of their neighbour's. Works with letting the students shuffle around weekly, too. Or, if numbers are easier, assign each a number. :D

    4) Work-life balance: This is major, but workloads differ from person to person. I can definitely say that when work takes over your life, it sucks. You do need time to de-stress and spend time with friends and family. I just can't think of a way for you to do that without telling you to stop driving and take the bus so you can mark during the commute. (I've seen where you teach - it'll take more time to get there by bus.) Is it possible to set up an office at home where the only thing you do in it is mark? Sometimes, just having a physical door to go through that signals the transition from home to work can help the psychological part, and also lets you step away from work by leaving the home office. Other than that, no idea.

    And if it's not too late, I'd like to see the Math-tans make appearances in your "Day In" post. :)

  2. 1) It's possible, though I was using the reminders more as another example; it's more I ask "What kind of sampling works best here?" and then pause for blank stares, and then "Well, do we have a grouping scenario?" possibly before their minds have tracked that far. Worse, if they expect me to do stuff like that, they may stop the initial thinking altogether. For reminders I should start carrying post-its around with me... though I can never seem to remember 'seven' in Japanese so maybe that's something too.

    2) Anything with points is the old system. Anything that relates to "getting a mark or two" is right out. Because the thing is, if they demonstrate their ability to factor in this question, you can forgive a similar glitch in an earlier question - they'd get those "points" back. So I don't want to be tracking said points. But if they can't demonstrate using domain and range anywhere, then that's a strike and they're probably not getting 70%. Unless it's the ONLY problem, in which case maybe 72%? Sigh.

    3) Class participation is part of their learning strategies, we continue to mark those on levels separate from the mark... but anyway. Yeah, I just feel awkward having to do nametags. With the confusion Friday of three periods in a row along with the Remembrance Day assembly I also didn't think to do the seat switch thing. Despite thinking about it Thurs. night. Darn it!

    4) I can't see myself marking on a bus anyway. >.< And I have an 'office' at home but it's multipurpose. I will consider that though. Thanks for the ideas.

    Also, starting to think you're my number one Math-tans fan and you're not even involved in high school math on a daily basis - huh, maybe I totally misjudged my target audience. I need more people like you. :)