IB

IB, you be, we all be...

The Wall Street Journal had an article on schools going International Baccalaureate by By Caroline Porter and Stephanie Banchero. Joan Smith, a good family friend is a former principal of IB schools (including having started one) and now travels the country training teachers in schools that are becoming IB. I sent the article on to her and she had cogent comments. (As you would expect.)

The article is behind a soft pay wall. (My access came through ASCD's SmartBrief (free sign up), which is often worthwhile.

Some salient points and figures:

• Houston, Chicago, Tampa, Fla., and other cities are embracing the International Baccalaureate program
• there are 1,651 IB programs in the U.S.—including 1,493 public schools—up from 503 in 2003. About 90% of them are in public schools
• IB programs emphasize individual and group projects governed by a philosophy of "international mindedness."
• some parents are concerned that IB programs are too theoretical. "It's frustrating to see that instead of doing spelling bees or history reports, they are spending about six weeks of time focusing on poverty or saving white tigers"
• Schools typically incur a cost of $150,000 or so to prepare for the program, which could include expanding lab or library space. They also must pay the IB group about $10,000 in annual fees plus $700 per student for tests given in 11th and 12th grades, as well as teacher-training fees.

Joanie responds:

This is true--the programs are growing very, very rapidly across the US and Canada. It's a pretty good interview, though the reporter misses the reality that the content of the curriculum is dictated by the district; the IB teaches teachers how to deliver it through inquiry and higher level thinking so that kids actually learn. I have never found a state or district curriculum at odds with the requirements of the IB, which are broad expectations in all subjects and the Primary program and the Middle Years program do not have outside assessments like the Diploma does.
Any news on GV engaging in this? I'm glad to help in any way you need.

The parents who complain about not having spelling bees and other things they remember from when they attended school are pretty clueless about how little is learned from those activities. The kids who excel and enjoy those are the linguistic learners, who represent about 15% of any classroom! The rigorous expectations of the IB programs raise test scores without the rote memorization, mindless skill and drill, etc. that is happening in so many of our failing schools today.

I would add that the costs incurred vary by program. The fees are most expensive for the Diploma Program (11th and 12th grade) because there are external as well as internal assessments over the two years of the program. The assessments are balanced with 50% of the final mark dependent on the exams in May of each year. The papers set are usually two or three separate exams including essay, multiple choice, etc., not unlike A.P. exams. The beauty of the program is that teachers are involved in the marks on internal assessments. The Primary and Middle Years Programs are less expensive but are amazing programs! (added here from the comments)

What I often see in successful professional development is a vision that is shared by the teachers and an increased sense of agency, that they have the authority to make changes that result in deeper learning. IB isn't magical, but it does connect to what we know about motivation and learning.

Flow

I must have three unfinished blogposts to get through, but this is what I keep coming back to this week.

Natasha Lewis Harrington is a doctoral psychology student who writes about my favorite game (Magic: the Gathering) in her spare time. Sometimes she crosses the stream to great effect. Like this week, when she wrote about why this game is so good at encouraging creativity among players. It's applying the work of (let me copy and paste here) Mihaly Csikzentmihalyi (specifically Creativity: Flow and the Psychology of Discovery and Invention [Google book preview]) to the question of how can we learn to engage more. I think it's well readable by non-Magic players, so please do peruse.

Here's the quick take:

(The little bit of art is from Flickr, Paolo Colacino who does what he calls generative art. Quite neat.)

Csikzentmihalyi has a TED talk about leaving boredom:


Why is this gripping me so? Because of the divide between math as taught and math as it could be.

Math, as it is often taught, violates all three of these principles. (1) We tell you the problems to do, (3) we insist on solo mastery and uniformity of method.

Wait, that's only two.

I'm wondering if I have, in my need to change (1) and (3), more than occasionally neglected (2). Is that the procedural knowledge which I de-emphasize?  I usually do that in an attempt to get the pendulum swinging in the other direction, but in doing so am I denying needed support?

Maybe not. Maybe Learning the System in mathematics is not the procedural stuff. Maybe it's the processes, hidden behind the procedural emphasis. (The processes now appearing with their new band, the Standards for Mathematical Practice.)

Of course, there's hope. Teachers like Fawn Nguyen, Michael Pershan and Andrew Stadel are knocking this engagement issue out of the park on all three principles.

But, as Dave Coffey has cautioned, and convinced me, we need to teach our students to take control of their own engagement. So when they leave Jim Pai's classroom, they can be engaged the next year, too.

That's empowerment, and that's what I want for my students.

Student Voice

Touching documentary from our local PBS, WGVU. They capture admininstrators, teachers, and student voices.  Nicole, starting around 18, in particular, is full of determination and will.

Watch Get Your Diploma. Get Your Dream. on PBS. See more from WGVU Presents.

When I see something like this, it drives me crazy that we can't convince our society to invest in these students, or the teachers that have answered the vocation to mentor them.

Find It!

Design
The call: a game for 5th graders just starting with fraction multiplication.

I look at my games. Fraction version of the Product Game... great fun, but more for practice than introduction. The crazy Ant Man game ... fun, good for calculator use, but also dividing fractions, so probably not time for that. Hmph.

Answer the question
(this was the first one)

Get it right to get a chance to
shoot past the goalie.

I look around on the web. Googled fraction multiplication game and got a lot of really awful drill "games." Glgkh - they left an awful taste. Some are obviously just quick flash mass production, but there are a couple that people really put time into looks and animation. For a quiz set to 8-bit music.


So, I'm on my own. Often with introduction time I try to think about representation. One of the things to love about fractions are all the many representations.  I think the discrete models are underused, so I thought about about students claiming fractions of a common pot (similar to the GeoGebra percent game I posted recently) - but it was difficult to figure out how to keep to intuitive numbers and overcome the disproportionate effect of going first. Also, I had trouble thinking of a game context that would get students to see it as a fraction of a fraction instead of a fraction of a whole number.

Then I thought about the area model. I imagined carving up a rectangle, having kids carve up rectangles. Scoring a total... connecting two points... then I had a connection. Cutting down bit by bit, it felt like searching for something. I tried a 12x12 grid, and my first pass at a mechanic worked pretty well: rolling a die to get halves, thirds, fourths. I thought of a context - searching for a lost hiker. Too scary if you've been lost? Finding a lost pet... maybe. It was a little too direct. Is it a competition? It was starting to feel like Battleship (a fine game), and that was good. I tried finding multiple objects; 2, 3, 4... and 4 was right. Oh! They could come up with the context - and that would give them the opportunity to add rules of their own. That's worth a try!

Here's the handout on Google docs: Find It!

Playing
I launched the game with my own context:

They managed to find all three, before... well before nothing. I was pleasantly surprised by how engaged they were just trying to find the rings. Like spontaneous applause when someone found one. (Playing with the whole class, I have them pass the die to someone who's ready of the other gender. Usually works.) Afterwards, I shared how maybe I needed more rules. Or the Mandarin's searching also. Or if you roll two 5's the Mandarin finds a ring. Or...

It was clear this was going to work because there was immediately a crowd of students trying to tell me their context, Minecraft, aliens, how it fit into the story she's writing about two wolves who turn into humans. It was exciting. They experimented with more than 3 objects and asked me why I had chosen three.

The wolfgirls.

Quite complex. This was played on two boards,
with interaction between the heroes and villains.

The minecraft game.
This had hazards as well as the goal.

The zombie game, which also had a hazard.
You had three lives, and had to find the zombie solution
before you lost all the people in your party.

The playing went well also. I was impressed by students ability to divide regions equally, and the many ways they found to do it. They started inventing their own terminology for how they were doing it, like the strips or plus method for dividing into four.  They used horizontal and vertical divides, and one group experimented with non rectangular regions. One group played like Battleship, competing to find all three before the other team did.

In feedback, everyone gave the game a thumbs up (mostly) or so-so. (Rare to have one that no one dislikes.) They liked the Battleship connection, the feeling of searching and the multiple objects to find. They were very excited to tell about their context and rules variations.


Game Evaluation

1. Goal(s) - good - experience with representation, dividing up rectangular pieces into equal parts. Plus a context for future questions and rephrasing.
2. Structure - works well.
3. Strategy - puzzle like. Choice in which region to divide up with which fraction. Choices for where you hide the objects. Not the strongest element of the game, though.
4. Interaction - good and so-so. One person/team being the mechanic for revealing spots and checking the other team's work on dividing was good mathematically. But Battleship isn't strong on player interaction.
5. Surprise - die roll, so okay.
6. Catch-Up ... depends on the variation. It's a bit methodical doing the search, but there's no time element in the basic version. The chance to get lucky with a search or a roll will help.
7. Inertia - works for this. Students were anxious to play more.
8. Rules - toughest element is the dividing up equally. Once you've got that idea, rest is simple.
9. Context - here's the winner. Students being able to set their own context was very engaging for a vast majority.

Percent Game Remixing

In yesterday's post on a percent game, I shared two great GeoGebra sketches that students found. I remixed each of them a little, so I thought I'd share them here.

dhabecker's neat rational number arranging sketch lets students place arrows to try to put fractions, decimals, and percents in order. He has a very clever way to check if the randomly generated numbers are in the right spots.  It notifies students when they've got all 4 right, and I wanted to them to be able to check their answer along the way. So - thinking of Mastermind - I thought about what if it can give the number correctly placed? Since I was doing that I added a reset button and a bit of color. Next I would add a fifth number, as that makes so many more permutations possible.








On GeoGebraTube:
download or applet. (Unfortunately doesn't seem to work in HTML5, because the polygons won't move.)









The other sketch I modified was David Cox's great percent estimation sketch.  Almost immediately on trying it on the Smartboard, the students turned it into a game.

So I turned it into a game with turns and scoring. There's 6 rounds. I thought about forcing players to take turns going first but ultimately just decided to ask them to.

Next  I would be interested in seeing it go from a percent number line to another quantity. So the game asks you to find 38%, but the number line goes from 0 to 630. The percent and the whole would change each time. Worth a go? Probably that's in my head because of David's nice double numberline percent sketch.

On GeoGebraTube:
download or mobile-ready applet.


As always, I'd be interested in feedback on either one of these.

But I'd also be interested in what could help develop a remix culture in GeoGebra.  I learned it (am learning it) mostly on my own by experimentation, from suggestions on Twitter, and googling stuff from the online help. But in the Learning Creative Learning class they put a big emphasis on remixing as a way to learn that gives a lot of support to learners. With my middle school GeoGebraists, they are struggling to do work of value all on their own.

Are you a remixer by nature? What would it take to get you trying it in GeoGebra?

Percent Game

I was thinking about percents and ways to gain experience with them, in preparation for GeoGebra work with middle school students.

Found a couple of neat percent sketches on GeoGebra...

Nice visualization from jholcomb.
(By the way, GeoGebra has gotten input boxes to work in the HTML5/mobile device. Good going!)

Slick discount problem visualization from Anthony Or (orchiming).

Nice double numberline visualization from David Cox.

But as I looked, the idea for a game came to me, just to give percent experiences. There's no context, really, it's just a race game. No strategy, just rolling random percentages. But the mechanic of smaller roll goes first creates some nice percentage situations, and a lot of games wind up surprisingly tight.

I debated having the students find the percentages to subtract, but decided to make it optional.  There's a short video of how the game works below.

Here it is on GeoGebraTube, for download or for mobile applet.






The test game came out extremely close - most games will be shorter than that. It can be surprisingly suspenseful, though.  All students found it pretty playable, and some got very into it. I think the best benefit might be from playing and then using as a context for problems.

Searching through GeoGebraTube, students found two sketches particularly of interest.

Arrange Fractions, Decimals and Percents by dhabecker (who has quite a few rational number sketches), which lets students arrange form numbers of different form from least to greatest. A few students got quite engrossed in this sketch, and the feel of the sketch is terrific - very much like pieces snapping in place.

Estimating Percents by David Cox, which lets students make a first estimate and then a second estimate with the tens showing. Students were happy to see their % error improve from 1st to second guess, and got better quickly through playing. They also made an impromptu game out of it, and I think that would be fun.



Do you know a GeoGebra Percents sketch that you think supports students' understanding?

Here's the results collected so far. Thanks!

PS> there's a follow up post to this one with two more GeoGebra percent activities.

Penrose Tiles

From Wikipedia,
Professor Penrose

Quasiperiodic tessellations are my favorite bit of recreational math. They came up in my thesis non-recreationally, and the best bit of Mathematica I ever wrote was to generate them for various different rotational symmetries.

Recently the Penrose magnets came from the successful kickstarter. (I can't tell from their website if they are available anywhere now.) It was fun to see tweeps sharing getting theirs. @MrHonner posted a picture that started the jealousy.  This is a picture of my son's attempt to tile with them.


A recent GeoGebra project got me using the RigidPolygon[] tool for the first time, and later I realized that this would enable me to make them in GeoGebra.  The construction of the kites and darts is easy with the regular polygon tool. I couldn't make a tool to make copies, because it wanted too much information. I remembered the advice Kathryn Peake was giving to David Wees on Twitter for a sketch: make a button.

So the first sketch was the tiles without matching rules.

Purists, like Edmund Harriss (@gelada) in that Twitter conversation,  will correctly point out that these are not Penrose tiles but they can be used to make a Penrose tiling.

Without the matching rules it's really easy to get yourself in trouble.

Here's the GeoGebraTube page. Unfortunately the applet doesn't work well in the HTML5 version, since you can make new tiles, but they can't be moved. Fine in the Java applet, though.



It took me a bit to figure out how to construct the tile alterations to provide the matching rules, but the upside is that it is customizable, so that now you can make the tiles into shapes that are pleasing to you. I can see how Dr. Penrose wound up with chickens, though.

Here's the GeoGebraTube page.

I did get to meet Dr. Penrose when he was working with my advisor - very fun and charming man. As well as obviously brilliant; nice when things work out that way.

From David Austin's fun slides
Playing Penrose's Tile Game

In the sketch on GGBtube, I share some places to learn more about these:

• My favorite: my colleague David Austin's two articles, Penrose Tiles Talk Across Miles and Penrose Tilings Tied Up in Ribbons.
• Don't miss Dave's whiz-bang Java Rhomb Tiler. It is serious fun.
• Quick basics and images at http://intendo.com/penrose 
• A GeoGebra sketch to look at the motions in the rhomb tiling from jwelker.

If you get a chance to try either of my sketches, I'd love to know what you think!