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Archive for the 'tech enthusiasm' Category

Motion Math: Pizza!

I caught Motion Math's latest game at their booth at NCTM. It's pretty irresistible. Kids are in the pizza business. They get to name their pizzas whatever they want, create them with whatever ingredients they want, and sell them for whatever price they want. Then the game goes all Sim-like on the kid. Customers come in and start buying up pizzas. The student practices multiplication at the cash register. Eventually the day is done and the student tallies up her profit or loss.

The game builds in just enough market behavior to make it a fun introduction to running your own business but not so much market behavior you're collecting W-9s from your employees or dealing with health inspectors. Customers get annoyed if you price your pizzas too high. You run out of pizzas if you price them too low. They request new ingredients, which you can go buy at the market.

It's great math and great gameplay from one of my favorite game designers in math education. Highly recommended.

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Bowen Kerins:

This game is terrific, with plenty of variety and thoughtful math. There’s even work on unit rates available when a second vendor opens, and one is offering 20 sardines for $4 while the other offers 90 sardines for $20.

tl;dr – This is about a new digital lesson I made with Christopher Danielson and our friends at Desmos. It's called Waterline and its best feature is that it shares data from student to student rather than just from student to teacher. I'll show you what I mean while simultaneously badgering publishers of digital textbooks. (As I do.)

Think about the stretches of time when your smartphone or tablet is in airplane mode.

Without any connection to the Internet, you can read articles you've saved but you can't visit any links inside those articles. You can't text your friends. You can't share photos of cats wearing mittens or tweet your funny thoughts to anybody.

In airplane mode, your phone is worth less. You paid for the wireless antenna in your tablet. Perhaps you're paying for an extra data plan. Airplane mode shuts both of them down and dials the return on those investments down to zero.

Airplane mode sucks.

Most digital textbooks are in airplane mode:

  • Textbooks authored in Apple's iBooks Author don't send data from the student's iPad anywhere else. Not to her teacher and not to other students.
  • HMH Fuse includes some basic student response functionality, sending data from the student to the teacher, but not between students.
  • In the Los Angeles Unified iPad rollout, administrators were surprised to find that "300 students at three high schools almost immediately removed security filters so they could freely browse the Internet." Well of course they did. Airplane mode sucks.

The prize I'm chasing is curriculum where students share with other students, where I see your thoughts and you see mine and we both become smarter and life becomes more interesting because of that interaction. That's how the rest of the Internet works because the Internet is out of airplane mode.

Here's one example. In Waterline we ask students first to draw the height of the water in a glass against time. We echo their graph back to them in the same way we did in Function Carnival.

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But then we ask the students to create their own glass.

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Once they successfully draw the graph of their own glass, they get to put it in the class cupboard.

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Now they see their glass in a cupboard right alongside glasses invented by their friends. They can click on those new glasses and graph them. The teacher sees all of this from her dashboard. Everyone can see which glasses are harder to graph and which are easier, setting up a useful conversation later about why.

We piloted this lesson in a local school and asked them what their favorite part of the lesson was. This creating and sharing feature was the consensus winner.

A selection:

  • Making my own because it was my own.
  • Trying to create your own glass because you can make it into any size you want.
  • Designing my own glass because I was able to experiment and see how different shapes of the glass affects how fast the glass filled up.
  • My favorite part of the activity was making my own glass and making my other peers and try and estimate my glass.
  • My favorite part of the activity was solving other people's glasses because some were weird shapes and I wanted to challenge myself.

Jere Confrey claimed in her NCSM session that "students are our most underutilized resource in schools." I'd like to know exactly what she meant by that very tweetable quotation, but I think I see it in the student who said, "I also liked trying out other's glasses because we could see other's glasses and see how other people solved the problem."

I know we aren't suffering from too many interactions like that in our digital curricula. They're hard to create and they're hard to find. I also know we won't get more of them until teachers and administrators like you ask publishers more often to take their textbooks out of airplane mode.

David Cox sent his students through Function Carnival where they tried to graph the motion of different carnival rides. (Try it!)

Every student's initial graph was wrong. No one got it exactly right the first time. But Function Carnival doesn't display a percent score or hint tokens or some kind of Bayesian probability they'll get the next graph right. It just shows students what their graph means for that ride. Then it lets them revise.

David Cox screen-recorded the teacher view of all his students' graphs. This is the result. I love it.

BTW. I'm hardly unbiased here, having played a supporting role in the development of Function Carnival.

Today Desmos is releasing Function Carnival, an online math happytime we spent several months developing in collaboration with Christopher Danielson. Christopher and I drafted an announcement over at Desmos which summarizes some research on function misconceptions and details our efforts at addressing them. I hope you'll read it but I don't want to recap it here.

Instead, I'd like to be explicit about three claims we're making about online math education with Function Carnival.

1. We can ask students to do lots more than fill in blanks and select from multiple choices.

Currently, students select from a very limited buffet line of experiences when they try to learn math online. They watch videos. They answer questions about what they watched in the videos. If the answer is a real number, they're asked to fill in a blank. If the answer is less structured than a real number, we often turn to multiple choice items. If the answer is something even less structured, something like an argument or a conjecture … well … students don't really do those kinds of things when they learn math online, do they?

With Function Carnival, we ask students to graph something they see, to draw a graph by clicking with their mouse or tapping with their finger.

We also ask students to make arguments about incorrect graphs.

I'd like to know another online math curriculum that assigns students the tasks of drawing graphs and arguing about them. I'm sure it exists. I'm sure it isn't common.

2. We can give students more useful feedback than "right/wrong" with structured hints.

Currently, students submit an answer and they're told if it's right or wrong. If it's wrong, they're given an algorithmically generated hint (the computer recognizes you probably got your answer by multiplying by a fraction instead of by its reciprocal and suggests you check that) or they're shown one step at a time of a worked example ("Here's the first step for solving a proportion. Do you want another?").

This is fine to a certain extent. The answers to many mathematical questions are either right or wrong and worked examples can be helpful. But a lot of math questions have many correct answers with many ways to find those answers and many better ways to help students with wrong answers than by showing them steps from a worked example.

For example, with Function Carnival, when students draw an incorrect graph, we don't tell them they're right or wrong, though that'd be pretty simple. Instead, we echo their graph back at them. We bring in a second cannon man that floats along with their graph and they watch the difference between their cannon man and the target cannon man. Echoing. (Or "recursive feedback" to use Okita and Schwartz's term.)

When I taught with Function Carnival in two San Jose classrooms, the result was students who would iterate and refine their graphs and often experience useful realizations along the way that made future graphs easier to draw.

3. We can give teachers better feedback than columns filled with percentages and colors.

Our goal here isn't to distill student learning into percentages and colors but to empower teachers with good data that help them remediate student misconceptions during class and orchestrate productive mathematical discussions at the end of class. So we take in all these student graphs and instead of calculating a best-fit score and allowing teachers to sort it, we built filters for common misconceptions. We can quickly show a teacher which students evoke those misconceptions about function graphs and then suggest conversation starters.

A bonus claim to play us out:

4. This stuff is really hard to do well.

Maybe capturing 50% the quality of our best brick-and-mortar classrooms at 25% the cost and offering it to 10,000% more people will win the day. Before we reach that point, though, let's put together some existence proofs of online math activities that capture more quality, if also at greater cost. Let's run hard and bury a shoulder in the mushy boundary of what we call online math education, then back up a few feet and explore the territory we just revealed. Function Carnival is our contribution today.

I updated 101questions today to include a single major new feature: a lesson editor.

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Creating webpages like this soaks up too much of my time. I have to upload files in three different places. Changing a single word in the lesson means firing up an FTP client. Changing anything about an image takes ten minutes at least. None of this is creative work.

So I put together the task editor I want to use. You can add supporting materials — photos, videos, questions, teacher notes, student notes, links, and more. You can re-order them quickly, all from the browser. More fun is that other users can download them quickly. Click the "Download" button and Internet pixies will zip all the resources up and send the file to your computer.

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I've been using it for a couple of weeks and I'd like you to use it also.

I've added other features some of you have asked for:

Better tagging.

You can add tags like "pizza" or "basketball" or "money." You can type a few key mathematical terms into the Common Core search bar and it will locate standards for you. Of course, all of this will make the search engine much smarter.

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A smarter search engine.

People e-mail now and then telling me in kind terms how awful this spreadsheet is. I'm in total agreement. Unless you're fluent in Common Core shorthand, it's impossible to find tomorrow's topic today. So now you can head to my page on 101questions, click Search, and then click "Search this user." Type in what you're looking for. Click "Has lesson" to narrow down my material to everything that's been a little more developed. Click the grade boxes to tighten the results down even more.

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Try it out. Add some tags to your old material. Leave me some comments here. I'll need as much useful criticism as you can offer. Let's make this great together.

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