Saturday, 3 November 2012

Math Teaching Roundup - Part 1

Meant to post something to start October. Obviously didn't happen. But now, as Term 1 of Semester 1 ends, I've decided I should at least do a roundup. Just to get things straight in my head, and maybe someone out there will find something useful - or expand on this for me, or in Part 2 (tomorrow) be able to provide me with solutions to my difficulties. For the record, I'm currently teaching high school mathematics in Ontario, Canada - your curriculum expectations may vary, but very probably the math is the same.

Part 1 - The Good

Going to start with the positive, aka what's working, since October was a bit of a negative month for me in general. Plus, this way anyone who is meeting me for the first time here might get a better impression of me than they would otherwise! Though yes, you'll see I personify math in my spare time, so I grant you will find me a bit weird regardless.


This year, I've started taking up quizzes right after the students write them. (Quizzes are assessed, not evaluated for marks.) It means building in an extra 10 minutes, so there's now less than half a period for a lesson or doing other work, however:

Lyn gives positive feedback for m>0
-It's immediate feedback, allowing them to correct their thinking now, rather than not remembering what they were thinking when they first wrote it.
-It's peer or self-evaluation (I encourage swapping papers with their neighbour, but up to them) and they can ask whether something that's slightly different on the quiz they have is correct or not, rather than just accept that they got it right/wrong.
-It makes the quizzes faster for me to go through that evening; yes, I do still take them in, to flag communication errors or problems with middle steps that may have otherwise been missed.

Taking the papers in also means I can record the level, not for a mark but just so I have evidence of where they're at, so that I know who I should try to target during review (in the absence of other questions). I tell them to switch to pen for marking, and not to erase any mistakes, just make the corrections so that they see where they went wrong. I think they're doing this; any who don't are only sabotaging themselves for the test anyway.

In all the blog browsing I've been doing since jumping on twitter, I even saw there's someone out there (sorry, forget who) that just has 'solution binders' (with provided pens), and students can go there to check their work whenever they finish. I'm not at that point yet; in fact, I often don't have a formal solution written up for the quiz (see #2)... I've grabbed random questions from prior assessments and then solved them on the fly when taking them up. (With some informal notes as to where I changed numbers.) Not sure if I will go to binders either, as I like that the students can all hear how a different method may be correct.


Not the X-Ray that Reci expected
Speaking of not having a formal solution written up... these days, for tests I usually have a lot of scribbled notes on changes from prior versions. So rather than writing that up formally for students to use in making corrections, I made copies of (correct) student solutions. Obviously taking the names off, and (in case there's handwriting experts out there?) I asked the students to tell me individually if they don't want to potentially be selected as an exemplar model.

I don't just copy most of a single test either; for a four page test, I'm looking at about eight different students (a half page of correct work each). I'm trying to use the high level achieving tests only as a last resort too, to mix it up. Again, it's the sort of thing that requires an additional 10 minutes (outside class), and this one's harder to tell if it's having much of an impact aside from me not writing up formal solutions. (Yes, only about 10 extra minutes for copying/pasting, because I can identify the papers I want to use during the 2 HOURS it takes me to total them. Not mark. Total. That one's going in the PART 2 - NOT GOOD part of the Roundup.)

Still, I like the idea that they're not just seeing how *I'd* write up the solution, but how their peers are able to express the mathematics in a similar way. Or sometimes a completely different way that is better than mine.


Expona has a powerful voice

Okay, so this one isn't new; I was doing it last year. But I didn't have Grade 11 classes then, thus I'm working with some different material this time. In brief, I parody a current or classic tune by rewriting the lyrics to review mathematical concepts, and prepare a powerpoint so students can follow along as I sing the lyrics, including sketches where applicable. It takes a while, but it's fun!

I think they find it fun too, and after one run through of "I Need A Zero", at least one student was remarking on it a week later (and I only sang it once). The trick is to pick one of those 'earworm' style songs - though the disadvantage (if you can call it that) is I can no longer hear the original lyrics properly myself anymore. >.<  Bonus if you can find a call-and-response song to get them more involved ("Vertex" by Pet Shop Boys is awesome for this). Failing that, try to get them in on the Chorus, which returns at least a couple of times.

I'm looking forward to Trigonmetry this year. I hope I have time to prepare a mashup of "Ace of Base", "Kristina Maria" and "Kreesha Turner" for all the trig ratios, to use for review purposes. The one thing that makes me think a bit is when students from last year say they miss my songs. On the one hand, yay for pulling them in, on the other, I hope they're not using it as a point of comparison to other members of our math department (who are all awesome and doing their own things that I'd struggle with).


"I still prefer a vertical component using surds."
Yes, those would be my accompanying graphics, which I also spoofed in my "Mystery Teacher Two Thousand" entry on Khan Academy. Meaning yes, I do toss the images into my SmartBoard lessons on occasion. The jury's still out on whether that's useful, or merely weird. But perhaps I can call success for one aspect: Transformations.

A vertical stretch of 3... does that make the parabola look larger or smaller? Well, tug up on Para's bunny ears. They'll get closer together. If the value is less than 1, you're not tugging up, you're pushing down, so they'll bow out further apart. Horizontal compression works similarly, coming at the ears from the sides. Root's hair almost works better for that though, as you can see how pushing in requires the end to expand upwards.

There's still confusion, as always, about how a vertical stretch might end up modeling the same image as a (different) horizontal compression... but I think I'm getting somewhere with this model, or at least I think this connection is helping. (Or maybe I'm overthinking?) Well, I'm at least making things more interesting here too... on a notebook check I saw one student had doodled a couple of the faces. Much better than I can draw them, I might add.

-Yes, as a student pointed out, Maud's hair doesn't seem quite right; he has hat hair.
-Yes, Para and Root are dating because they're inverses. (And the basic line is a self-inverse, but then, Lyn's too young to date.)
-Also, Sine isn't going to like me when I start modeling transformations on her... hm, maybe I shouldn't be looking forward to Trigonometry.
"Cut that out, sis..."


Since I teach on a SmartBoard (with orientation issues...), I save all the lessons, convert to pdf, and upload to a website, along with referencing the homework of the day.  In principle, this is good.  I've expanded it out from last year to include all three of my classes, rather than just MDM Data Management.  Students can go to the site when they've been away, or want a refresher - and they have been doing so. I've heard this from some of them (usually when I miss an update), as well as one set of parents on interview night. I've kept the front page as being interesting newspaper articles too, which, maybe some keen people will also check out.

On the other hand... it's still very utilitarian. I also sometimes find myself saying, "I'll post this on the web later" if we don't get to an example in class, or a couple students don't quite get time to copy something down. Which is not yet a crutch, but it's like it's giving me an out if my pacing is off.

On the third hand... there's an element to a flipped classroom here, which has it's benefits. Read the lesson at home, come in with questions and we'll discuss it more there. Plus, then you're not seeing it for the first time in class. But who really does that, particularly when I'm not steering things that way? Besides, students learn differently, so for some, seeing my lesson in advance without any verbal component isn't necessarily beneficial.

I guess my point here is, while what I have is good, I feel like I should be doing more somehow... not unlike how I feel about my peripheral participation in math on Twitter. Leading me in to some of the bad stuff I've been doing, or at least, where I feel I need more help. That will be in part 2.

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