## Thursday, June 27, 2013

### Thoughts on the MTBoS - from a Relative Newbie

I think I've been composing parts of this post for a while. It finally came in for a landing this week. Let me say at the outset that I have the utmost respect for the people of the Global Math Meeting!

A couple of nights ago, at the weekly Global Math Meeting, there was a discussion about the Math Twitter Blogosphere (MTBoS), which seems to have set off a kind of virtual earthquake - tweets, posts, and probably emails have been rippling through the lines ever since - for some examples, read here, here, here, and here. The discussion at the meeting was supposed to be centered around how the MTBoS can grow, and be more welcoming for newbies. That discussion, and the resulting ones, really shook me up and to explain why, I have to go back to.....

My first GMM meeting:

I started attending this amazing weekly online gathering of math teachers near the end of 2012, when I was invited, by the superhero-like Megan Golding, to give a ten minute presentation about how I flip my math class. There were other presenters, which is why it was only a ten-minuter. I have to say that when I entered the virtual room, I was immediately intimidated, for many reasons. But the online environment was not one of those reasons, because I teach in exactly that kind of space, so I'm used to it. What got me was how many people showed up for the talk, plus WHO they were, I mean, there were some NAMES. People whose blogs I've been reading, and probably you've been reading forever, really, really brilliant, famous, brilliant people.  I should have been tipped off when I saw that it was Kate Nowak who gave Megan my name.....

Anyway, Megan, being the great moderator that she is, advised the presenters to ignore the chat window because it would be distracting, and that she would monitor it for questions etc, which I really appreciated. As an online teacher, I know how hard it can be to maintain focus, keep the flow AND keep your eye on the chat window. It's similar to when a brick-and-mortar classroom teacher reads the room - you want to be able to say what you want to say while you scan faces for reactions, but in the online environment, where there's no eye contact or body language to go on, it means having to split your brain into two halves - the one that's presenting and the one that's reading. So I prepared myself to forget about who was there, let Megan have my back, and to ignore the chat.

Bring it on.

That lasted about 2 seconds, because what showed up in this chat window was unlike anything I'd ever experienced in my class. I wasn't prepared for the banter. A lot of joking and cajoling went on between the audience members, and it was immediately clear that these people were long-time friends, had a high level of comfort with each other, were even smarter than I had imagined, and were here for socializing as much as they were for math stuff. Unnerving for a GMM newbie, but fascinating nevertheless.

But I have to say, this made me feel like nobody was actually listening to me. I'm sure it wasn't the case, and nobody intended to do that, but there it is. Some of the presenters seemed able to jump right in with their own portable comfort zone, but I don't have one of those. And me being me, I blamed myself - after all, if I were interesting enough, there wouldn't be any banter, would there?

You'd think I would never go back, right? Wrong. I put on my big-girl pants and kept going. (Megan alone was enough of a draw for me, for she is the nicest person in North America.)

I haven't missed more than 2 or 3 GMM's since then. My shaky experience as a presenter was way overpowered by the brilliance of the ideas I heard week after week - interactive notebooks, gaming, lesson bonfire - to name a few. Not to mention that these people could probably all be stand-up comedian/comediennes, and mostly not to mention that I have become friends with some really wonderful people there. The GMM seems like a group of friends who happen to be math teachers taking turns sharing their ideas and making each other laugh. I look forward to each one, even though I'm still pretty much lurking. Although this post would be the definition of not lurking.....

The Antichoir

At any rate, I was just getting comfortable when earlier this week I saw tweets from a few members about flipping, which had been my topic way back in December. Tweets that I felt were unkind, and not representative of the open-mindedness and sensitivity that teachers strive to model for their students. The thread eventually circled back to become fairer, but I thought back to that first meeting - is that why there had been all the banter? I had been preaching not to the choir, but the antichoir?

Then came the meeting about MTBoS, which was called Choose Your Lunch Table. The title reminded me of a particularly clique-y staff to which I used to belong, but I could not have been happier to read the intro:
The #MTBoS can be an intimidating place for newcomers. Many seasoned veterans of the MathTwitterBlogoSphere have developed friendships and professional working relationships over the course of its lifespan. How can newcomers become an integral part of this community and feel at home? Let's drive the #MTBoS forward!
Those words alone were the reassurance I needed that the GMM was NOT the antichoir, and not even a clique, but a group of people engaged in a genuine attempt at group self-assessment.

But during the GMM, the discussion wove in and out of things like - Why are we trying to grow, it's not about the numbers, how can we decide for others who aren't here, people have different expectations, some people feel intimidated to blog, some get more attention than others, etc etc.  It was a great discussion, but it continued on into subsequent posts and counterposts, of which this is one. Many feelings emerged that surprised me - I wasn't the only one who felt intimidated, for example. I guess hurt feelings happen all the time, to everyone, unintentionally and even unwittingly.

I realized that just like our students, we all need the relationship to come first, and the learning second.

My thoughts, FINALLY geez:
• On welcoming: Before welcoming new people, make sure the ones that are already there feel it. I do now, but it took some time. And pants.
• On blogging: Sure, we all have to be tough in the TwitterBlogoSphere. It's a daily chant for me: Blog for yourself and don't expect a million retweets or comments, because it's not about that. It's about reflecting on your practice, improving, and documenting your journey. I do it in public just on the off chance that someone else will be interested, but that's not the goal. I have to accept the fact that when I put myself out there in front of the world, I might be ignored by the world. It's okay, I'll still learn something.The flip side is that if and when I do get attention, it's the ultimate, most authentic tip of the hat. No one wants to change that, because no one wants a charity comment, or a pity tweet.
• On communicating: The thing is, in the TwitterBlogoSphere, just like in the virtual classroom in which I teach everyday, all those tweets, posts, comments, in other words, WORDS, take the place of body language and eye contact.  The more evidence there is in those words that they come from a caring soul, who's more interested in being kind than in being right, the better and more long-lasting the impact. And there is no doubt in my mind that the MTBoS is a community of such people.
• And they're also hilarious.

## Sunday, June 9, 2013

### Life, Twitter, and General Weirdness

Twitter, like life, is just too weird and wonderful to explain. However, here's my attempt:

Last Friday, after finishing my classes for this school year, I was absolutely fried, with achy shoulders, neck, and throbbing mouse-wrist, all the result of having been on my computer non-stop for one practically sleep-free week. I was about to close up shop and head out to my garden for some quiet, green, life-affirming tech-free time, but first tweeted something, I have to admit, without much thought. Just kind of putting a punctuation mark to the week, on-my-way-out-the-door type of thing.

Here's the tweet, and as of today, here's what's happened with it:

26 retweets and 9 favourites. That might not seem like a lot to some of you, but it's huge to me, not to mention life-affirming. Not just because I went from feeling pretty dead to pretty happy, not just because of the amazing conversations and ideas I've had since then, and not just because I got to add all kinds of great people to my PLN, but also because it illustrates the nature of twitter that's so hard to explain to people who aren't on twitter.

If a living organism were a conversation, it would look like twitter. Utterly unpredictable, instinctive, multi-faceted, energy-consuming AND generating, changing direction instantaneously, constantly mixing and remixing, growing or dying depending on infinitely many factors....but ultimately striving to become better and stronger, on the way to becoming part of a much bigger, richer tapestry. Except on twitter, instead of genes being exchanged, it's ideas.

And why would anyone choose NOT to participate in that? You can either stay alone on your own little rock, surviving on what's always worked in the past, or you can jump into the idea pool and thrive. Everybody wins, and everybody's got something to share, but the thing is, you may be the last person to know it until you go for it.

And that 140 character thing that seems so limiting? Yeah, well, genes only get to use 4 (ATGC), and look where that got us!

## Monday, June 3, 2013

### How One Student Stopped Me From Dropping the Ball

Every year, June review time is when I drop the ball. I usually give out all kinds of review packages and old exams, together with answer keys, and say to my students "Here you go, my part's done, now it's up to you - good luck!" I also drone on and on during the last few classes about all the bazillions of things we did all year, during which time I literally put myself to sleep. I do this because my brain swirls with these kinds of thoughts: "Well I can't possibly go over everything anyway...If they don't know it now they never will....They need to do the work now not me....and anyway this is SO BORING!"  Basically, I drop the ball on the field and say, here it is, if you want it, come get it.

But that's not the same thing as passing the ball, so that someone else benefits from your momentum. This year, I tried to pass the ball. What made that happen? One student's words.

A couple of weeks ago, I asked my students for some input on how they wanted to review for their June exams. They gave me their ideas via a google form. Here are a few:
The best way for me to review is to gather all my notes and start rewriting down the rules to remember them but mostly...practice , practice , practice!
Review packages, those are the best thing for me to review a whole year's worth of stuff.
My ideal review would be to actually review everything we did since the beginning of the year and not only do practice..... I think we would just need to refresh everything in our minds.
do some problems from every chapter but i know you know how to do the best review ever :)
That last one is the one that did it. "I know you know how to do the best review ever." That came from a student who has put in an effort of 200% all year, and more importantly, has always taken the time to tell me how much he appreciates my efforts, so he had my ear. When I read that, all those swirling, bored, tired, I'm-now-dropping-the-ball thoughts thudded to the floor. I did NOT want to let this student, or any of my students, down.

So I put together some overviews that actually did make it interesting, at least for me, who has seen it all before a zillion times. Based on their reactions, it didn't work perfectly, and I already see lots of places to improve. But I feel better about this than anything I've ever done at this time of year in my entire career.

First, I must mention, that all year we've used a graphic organizer for each of the functions we've studied. I call it the Wheel of Function (get it? Wheel of Fortune?....sigh....). Every time we finish a new function, we go around the wheel of function and summarize it using these headings, so this is not the first time I've tried to give them a Big Picture of some sort:

But this time, it became the Wheel of FunctionS:

I used the wheel to make activities that would:
• cover a heck of a lot of material in a very short time
• meet them halfway in terms of content - start with activities at the lower end of Bloom, then work our way up
• get them up to speed so they can do the practice they need/want
• deepen understanding for some
• cause understanding for others
• at the very least make them do some review during class if nowhere else
Here are some that we did, and some that I came up with afterwards, with the instructions I gave as captions. By the way, these were all given to them in powerpoint format, so that they could move the tiles around:

 Match the groups of graphs to the function rule Then get into more detail:
 Move each tile into the appropriate column

Properties:
After more matching, look at the properties from a comparative point of view, leading to some Higher-Order-Thinking: There are similarities between log and square root function domains, so why is the only difference the inclusive/exclusive brackets? Or - The exponential and log graphs look very similar - how can you tell the difference between them?

Definitions of basic functions:

For this one I had them all writing on the board, just for variety. It was interesting to see how little everyone remembered. And frightening. It was a great opportunity to go over the algebra behind how we simplified them, and there was an aha moment for at least one student who said she hadn't noticed that we never did simplify the trig functions. Next year, maybe we will by using identities (AT LAST SOMETHING USEFUL HAS COME FROM IDENTITIES!!!)

 Fill in the simplified form for each function
Solving equations and finding intercepts:

Before getting into the nitty-gritty algebra, an overview of What to Expect When You're Solving an Equation. (I think next time, I'll have them fill in the orange part first.) The idea behind the purple part was that for some equations, it's obvious when there's no solution - for example, if a quadratic equation has no solution, some kids find out only when they try to take the square root of a negative number, and their calculator lets them know. But for some equations, it's easy to miss when there is no solution, because the algebra doesn't always alert you, for example, in this equation,     $\sqrt{x + 3} = -1$   it's very tempting to square both sides, but the fact is that there is no solution to it. I wanted them to be on the alert for those situations, as well as to realize, perhaps for the first time in their math lives, that linear equations ALWAYS have a solution, as do logarithmic ones:

 1. Fill in the number of intercepts that the given function can have: none, 1, 2, or infinitely many. 2. Indicate whether it's obvious when the given type of equation has no solution, and what it looks like when that is the case.

......that last one needs work. Not clear.

That was last week. Today I showed them this series of slides, in which I tried to summarize probably way too much about solving inequations and finding the rule for a function, again from a visual and comparative point of view:

I think I may have exploded a few heads......including my own. But I will definitely use it next year, and if you see a way to make it better, please feel free to comment.

Bottom line, I am so grateful to all my students, especially Mr. 200%, whom I shall call Albert today, and he'll know why.

Thanks for reminding me, Albert, that even though my job description is "Teacher", you and your peers truly deserve that title.

And oh yes: Catch!