Wednesday, July 2, 2014

Big Ideas at Flipcon14

Flipcon14 took place in Mars, Pennsylvania June 23-25, and I'm happy to say I was there. I had previously attended Flipcon12 in Chicago. My perception may be a little skewed, but it felt like this conference had a Big Idea feel to it that I don't remember from the Chicago one, maybe because I was still a relative beginner then. Where did this feeling come from?

First from the keynote speaker, Molly Schroeder. She said these three words:

Think - Make - Improve.

That's what all these teachers have been doing with their own work, with other teachers' work, and it's what we want our kids to do.

Later, Brian Gervase said this, which I just had to tweet:
Throughout the conference, I found that even though most of the sessions I attended were not specific to math, what I heard was nevertheless applicable to any subject. Big concrete ideas that are making their way through the Think - Make - Improve cycle, taking on new colours as they move into different subject areas, then branching out further, in a sort of learning fractal.

A rundown of what went down, and my takeaways:

Day 1: Session A: Andrew Thomasson & Cheryl Morris:

Creativity: Biggest takeaway for me was that routine is a significant factor to creativity. Counter intuitive for me! I always thought it happens when it happens, you can't schedule it. Blogging, for example - whenever I've heard people say they stick to a blogging schedule, I've thought, well not me, I wait to be inspired. But it turns out there is evidence that routine really does help people be more creative.

Gradual release of responsibility: The year begins with bootcamp, and ends with work for which the student assumes full responsibility. During bootcamp, the essential skills are covered, like how to watch a video, how to talk to peers, how to take notes. For math class, it will be about those exact same things, plus using Geogebra and Desmos. 

Opportunities to practice: no grades for these, simply practice on the essential skills but building in variety, such as taking notes from a variety of media, video, text, or a website. Perfect for what I'm planning for next year - giving my students more geogebra and less direct instruction, so they'll need to take notes from their own explorations with geogebra.

Grammarly: Cheryl showed how she uses this tool with her students. She feeds the students' text to grammarly, which it then scans it for grammatical or spelling errors, then it reports how many errors there are. It's up to the kids to find them and fix them! I'm going to do the same with math examples, maybe even create a geogebra with mistakes in it, and have them find and fix them. I can train them to use geogebra at the same time, kill two birds with one stone if you will.

Networking by subject
This was a great idea - one entire slot of time devoted to informal chatting amongst people who teach the same subject. Of course, I headed to one of the math rooms. We organized ourselves into groups by level, and I ended up in a circle of about 10 people who teach senior high. We had a great time just sharing our questions, ideas, general thoughts. There was a teacher there who had come all the way from China (if I recall correctly)!

This was just the right amount of subject-specific stuff for me. And even this discussion yielded some generalizations - via Steve Kelly, for example, about how kids organize themselves into groups according to their ability, which usually turns out to be about 4 different levels.

Soon after this, I started to feel overwhelmed, even though it was still day 1. I expressed this to Steve Kelly, who was kind enough to tweet it out:
Session B: Book panel:
Next it was time for all the coauthors of this wonderful book:

to join Jason Bretzmann, our publisher and tireless supporter, for the panel discussion he organized. Jason gave a wonderful presentation about the book, and had some questions for us all to take turns answering. It was an honour to be included in this group of talented people.

Does it kind of look like Jason has a halo? Just saying.

That evening we were all bused to the beautiful Carnegie Science Center in downtown Pittsburgh. I have to say, I had no idea that Pittsburgh was such a beautiful city! Our view from the science centre cafeteria was stunning - we were sitting in a valley, where two rivers become one, surrounded by an astonishing amount of greenery. Lots of huge yellow bridges, too! We had a great time eating, learning, and DANCING. Michelle Karpovich said it best:

Day 2: Session C: Jonathan Thomas-Palmer
Videos: Jonathan makes physics videos full-time, so he's pretty good at it. He used to teach, and flip his class using videos, but found too many students did not watch them, so decided to make them so good that they would WANT to watch them. He gave us tips on making engaging videos.

Audio is of prime importance, get a really good mic, check your audio level, don't film outside
Talking head should be doing more than just talking - pick up stuff, point to parts of presentation, anything to vary. Don't film with light behind you.
Frequent visual changes ie text popping up that paraphrases what speaker has just said, arrows, callouts

Jon cautioned against trying to make something like this, with one person playing multiple characters:

....unless you have a professional grade software. Darn. That looks really fun.

Session D: Brian Gervase
This was one of those sessions that got me so worked up that I didn't take any notes. I spent this session either tweeting what I was hearing Brian say or just picking my jaw up from the floor, being stunned that someone else could speak my thoughts so eloquently and passionately. Brian's session was called Flipped Assessments. He uses mastery with his classes. Here are some of the tweets I managed to make, apart from the one at the top of this post:

Anyone who knows me at all knows what my favourite math edtech tool is, and at one point during the session I became afraid I might lose what little professional composure I still had:

As it turned out, Brian ran out of time in his session, which is probably for the best, because he later replied:
Session E: Crystal Kirch
Crystal explained her WSQ system, which she uses in her math class.  I had read about it, and had even tried a form of it before, but it's always way better to hear things explained f2f and see it for yourself. Crystal's talk, like all of her writing, isn't just about the details of what and how she does the WSQ, or the TWIRL, it's much deeper and further-reaching. Brian said it best:
Crystal also spoke of routine in her class, just as Andrew and Cheryl did. Bigger ideas included Organization, Accountability, Processing, Feedback, and Discussion, all features of her classroom, which we can all use, regardless of what we teach.

Session F: Stacy Lovdahl and Eric Marcos
Stacy gets her students to create videos as projects, and Eric's students create videos to help their peers' understanding. In either case, the underlying idea is purpose. Kids learn best when they're making something that they see the purpose of. Think - Make- Improve must be happening constantly when kids make videos. There are other benefits, though, such as kid-friendly language, both in the video and in the feedback other kids can then give:

One example of the benefits of student-created videos was Stacy's - you get 16 kids to each create a video showing an example of a chemical change, and boom, not only did they engage in their learning, have a purpose, but they also now have 16 examples! My favourite rationale for kids to present their learning this way instead of in front of the class is here:

Biggest takeaway, biggest idea from Flipcon14:

There is so much variety in what teachers who "flip" are doing, that the word really doesn't mean anything anymore. But I will still use it because:

Friday, May 23, 2014

There's knowing and then there's KNOWing


My students did this activity yesterday, in which they unwittingly drew a parabola using geometry instead of algebra. So they "knew" about the focus and directrix of a parabola, and that all the points on a parabola are the same distance from the focus as they are from the directrix. And they "knew" the formula c = 1/(4a).

But I had a sneaking feeling they didn't really KNOW, you know?


So today I showed them this:

...and asked "Which point is the focus of this parabola?" There were guesses for each of the colours. Some said they all could be the focus. Bingo. They know what it is but not what it isn't. That's not KNOWing.

"If the pink one is the focus, then which line has to be the directrix?"

Everyone went with the pink line of course, but their reasons were varied:  because the colour matches, because it's the farthest away, because it's the same distance from the vertex as the pink dot.

Right. We've just established that as soon as you have a focus, you also have a directrix - they work as a team. That's a slightly bigger picture. Also I need to knock it off with the colour coding.


"Is it possible that any one of these could be the focus, as long as we pair it with the correct directrix?" Some said yes, some said no. 

Time to test out their hypotheses. I had everyone make a dot somewhere on the parabola with their initials.

"Draw L1 and L2 for your point using the green focus/directrix."

The board looked something like this:

It was very fortunate that K picked the vertex for her point!

"Does anyone's point have L1 = L2?"

K's did, no one else's though. 

"Well does that mean the green point is the focus or isn't the focus?"

Great discussion on why it isn't - it's not good enough to have one point on the parabola with L1 = L2, they ALL have to have it. They knew that yesterday, but this was knowing on a different level. I think the fact that each person "owned" a different point reinforces the all or nothing idea here.

Then each person picked a new points, and we tested out the blue pair. As soon as ONE person's point didn't work, the reaction was immediate - it can't be the right pair. 

Now they knew that there is only ONE possible location for the focus and directrix of a parabola. Move anything and it doesn't have the L1 = L2 property.


We finally tested the pink pair and found it to be the actual focus and directrix. Now they knew where it was and where it wasn't, and there's only one possibility for the former.

Way to drop the ball McSquared:

The final point I wanted to make was the connection between what they just did and the formula c = 1/4a. Not the algebraic connection, but the bigger, deeper one:
The numbers are connected like this: Change the value of a, and you'll change the value of c, and vice versa.
The things are connected like this: Change the parabola, and you change the focus and vice versa.

Unfortunately, that part was just me talking, which I'll replace next time with them doing something, not sure what. Something involving matching parabolas with c values and focus/directrix was time to zoom out here and I dropped the ball, but I'll pick it up next year.

But I do think I helped them to KNOW, you know?

Friday, May 9, 2014

Developing the standard rule of an ellipse

This activity was inspired by two people: Teresa Ryan, a fabulous math teacher tweep, and Amanda R., one of my students. A few days ago, Theresa tweeted this
and that question started the cogs turning. Around the same time, I had my students playing around with circles on desmos. Amanda happened to type in the equation 2x² + 2y² = 1, and notice that it had a smaller radius than our unit circle. That lead to a nice discussion as to why the radius was less than one, and then why it was equal to the square root of 1/2.

So today, again, all of this kind of gel-ed on my way into class. Here are my guiding questions, and their collective answers:

Open a desmos or ggb, and get the unit circle to show up.

Now type in 2x² + 2y² = 1. Tell me what you get, (smaller circle), what's the approximate radius? (0.7)

Type in another equation like this, which = 1, but make an even smaller circle appear, and write your equation on the eboard, plus the approximate radius.

Find pattern: as coeffs get bigger, circle gets smaller.

And what's the relation between the coefficient and the radius? Radius is the square root of one over the coefficient.

Okay, if bigger coefficients make smaller circles, what coefficients will make bigger circles? (1/2 or 1/3)

Type those in, measure the approximate radius, and write on eboard:

Is it okay if we write these equations this way instead? Are they equivalent?

Now how can we calculate the radius from the rule? It's always the square root of the number in the denominator.

Which denominator? Well, it doesn't matter. Doh. They're the same.

Oh right. I didn't notice that. Well type one in that doesn't have the same number under each term, what do you get? An ellipse!

Tell me your equations and the dimensions of your ellipses:

Unfortunately I didn't take a snip of this, but the variety was wonderful, some ellipses were horizontal, some vertical, it was absolutely no big deal for them to see that the number under the x always governed the width and the one under the y governed the height, plus that a square rooting was involved.

From there it was a piece of cake to generalize to the standard form of the ellipse! We did a bit of practice where I gave them the rule and they graphed, and vice-versa. It felt like I'd covered 2-3 days' worth of concepts just today.

Thanks Teresa and Amanda!

Tuesday, May 6, 2014

New Intro to Locus and Circles

All of this actually happened today, although, well, maybe not all during the same class. So it's piece-wise true...

Part 1: Locus intro:

This was the first day of our last chapter, conics. I wanted to begin with the idea of the locus of a point. But I didn't want to actually tell them what a locus is, I wanted to show them, then get them to tell me.

I got this idea on my way into class, which by the way there has to be something to why that happens so often at that exact time. Anyway, I thought of a use for one of my geogebras that was not at all what I had intended it for. This video explains what I had intended it for, and what I ended up doing instead:

By the way, if you're interested, here's that geogebra. Next I asked my students what they thought a locus was. Here are a few samples, word for word:
  • The path of a point followed by a specific function
  • a locus is the path a point takes
  • The path of a point of a function
  • The trace of a moving point
Their words, not mine. Which, collectively, touched on all of the key points - that it's a path, that it's created by a point, that the point is moving, that as it moves, the point is following some kind of rule.

Part 2: The circle as a locus:

I then wove all of these locus ideas into this geogebra, made by the brilliant Jennifer Silverman:
How beautiful is this?

I let them play with it a bit, to draw a few circles, then identify which of these virtual things was the locus, which was the moving point P, and what rule that point was following as it moved. Here are their answers, again collectively:

What is the locus? The circle is the locus! (Just that right there was huge. All these years I've been the one saying that, and approximately no one was really seeing the circle any differently than they had always seen it - as a static thing.)

Which point traced this locus? The point at the tip of the pencil.

What rule did the point follow as it moved? It stayed the same distance from the red pin.

Then we formalized that into the locus definition of the circle, which for the first time since I've ever taught it, I didn't have to dictate or get them to fill in the blanks on pre-made notes. Okay, I did give them the word equidistant.

Part 3: The rule of the circle

Next I wanted to move onto the Cartesian coordinate system, so we reviewed that:
  • the rule for the unit circle is x² + y² = 1
  • where that rule came from (right triangle inside circle)
  • that really the 1 in the rule was 1².
 I gave them this desmos:  and had them work on that in groups. Just like when they're using geogebra, there is no need for me to tell them if they're right or not. If it is, they'll see a circle with the right radius. Again, there were no notes, no me telling them what the rule is. It took some trial and error, but eventually everyone noticed that the radius has to be squared in the rule. After a bit we regrouped, discussed, even a few things that I hadn't expected would come up:
  • Why is the radius squared in the rule? Why isn't it just x² + y² = r?
  • Is it possible to get a circle that's even smaller than the unit circle?
  • One student noticed that  2x² + 2y² = 1 gave a smaller circle than the unit circle.  Why would that be?
On the way out, I had another idea. I need to write this down so I'll remember it all next year. That was 9 hours ago!

Sunday, April 27, 2014

Our Third All-School Twitter Chat

This past week, the teachers, students, and principal of LearnQuebec's online school had our third all-school twitter chat. Three is a magic number. Once you've done something three times, it starts to become a habit. You also start to notice trends, behaviours, what works best, and what doesn't. Most importantly, you get an idea of how it's evolving, if it's gaining traction, and we are all now convinced we are onto something!

A little background: 
Our classroom (students' names appear in chat area at
lower left, hidden here of course.)

  • We're synchronous online classroom teachers. Our students are in brick and mortar schools all day but when it's time for Math, Science, Physics, or Chemistry, they get online with us. They are from all over Quebec, many in remote areas. We're all pretty used to interacting live online, in fact, we pretty much crave it due to the lack of f2f time.
  • By "all-school", I mean all of our teachers, all of our students, and our principal.
  • 3/5 of the teachers already use Twitter with their students, so most of them already had accounts and were comfortable using it.
  • At the beginning of each year, we get permission from the parents of our students to be online in many sites - google drive, twitter, blogs, geogebratube....and the list just keeps growing every year. So that part was already taken care of.
  • For non-Tweeters: A twitter chat is what happens when a bunch of people all get on Twitter at the same time to tweet at each other. It's like a party that happens online, except that you can actually have way more conversations with way more people at a twitter chat than you could ever manage at a party.

The story so far:

We started having these twitter chats in February of this year. Our purpose was to create a stronger sense of community amongst our online students, whom we almost never get to see face to face, and who almost never get to see each other. Here's a quick synopsis of the first two chats:

Chat 1: Feb. 5, 2014:  If you'd like to read all the details of this wonderful event, including the actual tweets that happened that night, I blogged all about it here. If you'd rather not read that whole chapter, allow me to summarize: It was great! We decided on 5 questions, the theme of which was online learning - the one thing that unites all of us. The participation rate was very encouraging - we had about 35% of them there, and by the end of the evening, there were about 700 tweets with the #lqchat hashtag. The staff were all so thrilled by the event that we spontaneously had a staff meeting immediately afterward to debrief! We were so blown away by how enthusiastic our students were about the opportunity to interact this way. It took a while to calm down! My takeaway was that every human needs to connect, regardless of age, academic interest, or what medium you use. Where there's a will, there's a way.

Chat 2: March 12, 2014:  Unfortunately, I didn't blog about this one, not because it wasn't great or important though! You can see the complete chat here, separated into questions. Summary: This time we used some of our students' suggestions for chat topics, like career plans. The theme was still online-based, but also looking to the future - theirs and ours. Once again, the staff met afterwards to take it all in together. Chats can be quite overwhelming. Not only is the sheer volume of tweets impossible to keep up with, but the stimulation generated by all the ideas and connections can be quite overpowering as well. We had about the same amount of participation, and we were once again thrilled by it all. As a side note, suddenly there was more tweeting happening on a daily basis from some of the more reluctant tweeters on our staff! My takeaway - sometimes to get from A to B you have to aim for C, and then unexpectedly end up at B on your way there.

Our latest chapter:

Chat 3: April 22, 2014: This time, we asked for the students ideas in a more concrete way. Peggy Drolet made a google spreadsheet for them in which to give their input. The staff met, and together came up with the questions, using as many of their suggestions as possible, while keeping it safe, appropriate, non-academic, and interesting. Unfortunately, as I write this, Storify is not fully cooperating, at the moment, in giving us the full set of tweets for all the questions, so I have had to take a few snips to give you an idea of the flavour of the responses.


Here the Storify for the prechat chatting that took place. As it happened, that night there was also a very important hockey game happening at the exact same time as our chat. This hockey game happened to involve the Montreal Canadians. Have I mentioned we are all Canadians? Living in Quebec? So, of course, we get a little excited about hockey. More than a few people were, um, multi-tasking during the chat! These happened before and during the chat:

And finally here are the actual chat questions, with a few of the answers:

Q1 What is the happiest/proudest you have ever been in your life?

Q2 What is the coolest thing about math/science?

Q3 What is your favorite pastime/hobby?

Q4 What tech tool is your favourite & why?

Q5 What about you would people find the most surprising?

Q6 What is something you are not learning presently in school that you want to learn?

This last question took an interesting turn toward the end:

A few other things that happened:

An idea for us all to do our own version of Pharrell's Happy video!

Lots of personalities, senses of humour revealed:

Our fabulous principal, as always, was there and supportive like a boss (get it? haha)

Finally, the day after the chat, we all asked our students to type their reactions on the eboard in class. I have taken snips of those and put them on this padlet wall, word for word. Yup, I really think we're onto something!