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Busy times

This one isn’t going to be mathsy. Sorry. Just thought I’d share a little bit of what’s been happening with me lately. I really won’t be offended if you tune out now 🙂

My twitter description currently reads: Secondary maths teacher. Church musician. Hockey coach. Suspected human being. Obviously, this blog focusses on the first one, but the middle two combined last weekend to create some of the busiest few days of my life. (I don’t really have any evidence of the last one…)

So despite the fact I’m really not athletic at all, I coach our town’s junior hockey team (that’s field hockey for any international readers). Saturday was our Grand Final, which our club hosted, and we were playing in it. After finishing 1-1 at full time, we clinched the winning goal in extra time! Third premiership in a row!

The team immediately celebrated by spraying their coach (and maths teacher) with their water bottles:

One of the mothers decided I should be holding streamers for the photos. I’m not sure why. I must’ve been pretty happy, because I don’t usually grin like that when I’m soaking wet 🙂

The water thing seems to be their standard celebration. This is the same moment from a year ago:

See? I was getting water dumped on my head before it was cool.

Saturday evening was spent helping host our hockey association’s Grand Final Dinner, and Sunday lunchtime was our club’s presentations. So a lot of hockey for one weekend. As much as I enjoy the game, I’m happy the season’s over for now and I get my Saturdays back again.

For the record, I also play hockey, but my team has a proud tradition of choking in the first few weeks of the finals.

Sunday afternoon was spent preparing for my church’s monthly night service, which we very creatively call “Night Church”. I head up the music team, for which I play piano and guitar, and pretend that I can sing. My friend who was singing with me last night is a keen photographer, so she got this pic of me practicing:

Unfortunately I look pretty ridiculous with the guitar pick hanging out of my mouth.

So there you go, a little taste of what I do when I’m not teaching.

 
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Exam pressure

In theory last night’s #OzMathsChat was about Inquiry Based Learning, but we got sidetracked pretty quickly. Oh well, I’m sure we’ll come back to it sometime 🙂

Someone mentioned the difficulty in using inquiry in Year 12 classes because of the pressure to get through everything before the exams. The conversation moved to the way our senior secondary certificates are structured, and the possible negative effects that has on mathematics teaching in the classroom. I was fairly quiet last night because others had basically the same ideas as me, but I’d like to take some time to reflect on it a bit more.

It’s undeniable that I teach my Year 12s differently to my Year 9s. With lower years, I feel I have the time to play around with ideas, to set kids to discover mathematical concepts themselves and to ‘waste’ lessons on arguing whether a square should be allowed to be called a rectangle (yeah, this did actually happen recently).

But the constant pressure to “cover everything before the exam” makes it all too easy to fall into the old pattern of lecture-then-questions-then-exam-practice. And that’s not just me, the kids come into class expecting lessons to be like that. Having discussions is like pulling teeth. Whenever I try to include more investigation type activities, the looks on the kids faces basically say “Come on Mr. Carter, just tell us the answer so we can get back to the textbook exercises.” Not that they want to do the exercises, but anything that doesn’t look like exam questions feels like a waste of time.

Which is a problem. Because doing exam questions doesn’t feel like doing mathematics to me.

Then there’s the way the calculator impacts the class. The calculator requirement is so explicit in Victoria it’s even in the subject name: Mathematical Methods (CAS). TI really do have a great deal going. I’d love the freedom to use whatever tools I want, such as Desmos, Geogebra or just coloured paper for that matter. But no, the exam requires the calculator so we need to practice using the calculator.

I really do admire the US teachers who have to deal with high-stakes testing at every grade. The very existance of the exam changes the approach teachers and students take to maths, whether they like it or not. Last night, primary teachers also mentioned similar pressure to ensure kids are “ready for high school”, something I’d never really thought of before (that could be because I’m in a P-12 school).

Then there’s NAPLAN. I think it’s probably best if I don’t say anything about that.

So, enough ranting. What do we do? There needs to be a culture change, so that learning is the primary driver in the senior secondary classroom, not assessment. We can’t deny the importance of that assessment – the kids do depend on it for university entry after all.

But good teaching and learning is good teaching and learning – the existance of the exam doesn’t change that. The culture change needs to begin with us, the teachers who believe in it. The exams are not going away any time soon. But surely if we produce students who actually understand mathematical thinking and discovery, they can do just as well, if not better, than the kids who only know how to reproduce rules and examples.

Yes, the exams push hard. But we can push back. And in my classroom, that begins with me.

 
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The distributive law

Teaching the distributive law is an interesting prospect. Because really, if students know how to multiply numbers with more than one digit they already use the distributive law, even if they don’t know it. But if you write this on a board:

a•(b + c) = a•b + a•c

and expect kids to understand it, you’ll be met with blank looks. The challenge is not in knowing the law, but in connecting it to prior understanding of numerical multiplication and extending that understanding to algebra.

When Year 9 and I started our unit on Expanding and Factorising (which admittedly was weeks ago, we’re nearly finished the next unit now), I posed a seemingly simple question: what is 29 × 4? The class worked in groups, and I enforced a couple of rules: they couldn’t use calculators and they couldn’t use the standard written algorithm.


Looking back now, I really should’ve created a better graphic than just drawing on the IWB…

Most were clearly happy with themselves for finding the answer, but I ruined that by writing 116 on the board as we came back together as a class. Just giving me the answer was no longer good enough. The groups needed to explain how they got their answers.

As a side note, I find this a constant struggle with my students. How do I get them to unlearn the idea that “getting the answer” is everything, and think more in terms of understanding the problem?

Anyway, it turned out that amongst the groups there were a few different methods used.

I think most readers will know where this is going. Though the methods used were different, they were all dependent on the distributive law. I presented some of their solutions to them in a different form.

This was a good launching point for talking about expanding. After the class did a couple more numerical examples, we started introducing variables into it.

Of course, I was silly enough to do that part on the whiteboard instead of the IWB, so I don’t have an image of it 🙁

Often with algebra, we are teaching rules and patterns that students already know are true, but they are not familiar with the language and structure of algebra. Yes, expanding 2(x+3) is an abstract idea, but 29×4 is itself an abstraction, really. A useful strategy is to help students realise that algebra is often just a layer of abstraction over concepts they already know and understand.

 
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#OzMathsChat

A few weeks ago, @DianeMaths tweeted out the idea of a regular maths chat in a timezone friendly to Australian teachers. At the time, I was the only one to respond, but we were both really keen, so we decided to start one!

#OzMathsChat starts Tuesday (that’s right – Tomorrow!) at 8:30 pm AEST (GMT+10). As long as you’re interested in maths education at any level, we would love to have you there.

Don’t let the name make you think it’s only for Australia. There are many other regular twitter maths chats around the world, but none (that we could find) at a time suitable for us in our isolated part of the planet. But if our weird timezone doesn’t put you off, you’re more than welcome!

And even if you can’t make it, we’d love you to retweet or pass the message on to anyone else you think might be interested.

 
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Discrete Probability Posters

At the start of this term, I said I was going to make more of an effort to make posters and decorations, particularly for the video conferencing room where I teach Year 12 Maths Methods. That hasn’t really happened as much as I’d hoped.

But seeing all the new year classroom posts from the northern hemisphere has reminded me again how bare some of my walls are. Given I’ve just started Probability with Year 12, here’s a set of posters on Discrete Probability Distributions I put together today. I plan to follow these up with a set for Continuous Distributions soon.

Downloads

If you want to edit the document, you’ll want the font Matiz.