Month: April 2014

Total 12 Posts

Waterline & Taking Textbooks Out Of Airplane Mode

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.

“Think About Your Favorite Problem From A Unit”

Bob Lochel, responding to commenter Jenni who wondered how, when, and where to integrate tasks into a unit:

In my years as math coach, the most efficient piece of advice I would give to teachers is this: think about your favorite problem from a unit, the problem you look forward to, or that problem which is number 158 in the last section which you know will generate all kinds of discussion. Without fail, this problem is often done last, as the summary of all ideas in the unit. Okay, why not do it first? Keep it simmering in the background, flesh it out as ideas are developed and pratice occurs. It often doesn’t take a sledgehammer to make a good unit great.

Bar Trivia for Math Teachers

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The Desmos/Mathalicious happy hour in New Orleans on Friday was a great end to a long week of conferencing with math teachers, math ed professors, and the occasional vendor. My unofficial crowd estimate puts it at something like 50x the size of their 2014 event in Denver, CO.

The Desmos team and I wrote up some happy hour questions which were fun enough that several people requested the complete list. You should feel free to use them also. Please address complaints, quibbles, or corrections to Bill McCallum c/o Illustrative Math.

1. Math Homophones

All of the answers in this round are well-known mathematical words or phrases. (Example: “It lies under the mantle and belongs to use all” is also known as the “Common Core.”)

  1. Bad news at the dentist for Salman. (A: concavity.)
  2. A ski run you feel really good about. (A: positive slope.)
  3. A lady’s partner who’s gotten some sun. (A: tangent.)
  4. Messages you send in the same direction. (A: parallelograms.)
  5. Treads on the Red October. (A: subtraction.)
  6. Mickey’s British mother-in-law. (A: minimum.)
  7. It said, “please come aboard two by two”. (A: arcsine.)
  8. A change to a military banner. (A: standard deviation.)
  9. Louisiana Governor Huey drawn and quartered. (A: long division.)
  10. An airplane bathroom that is not vacant. (A: hypotenuse.)

Bonus:

  • Answer to the question, “Have you seen a letter jacket belonging to one of the protagonists from Monsters University?” (A: isosceles.)
  • A condition in which you become a better dancer after having a organic beer. (A: natural logarithm.)
  • A matching outfit you’d wear in freezing cold weather. (A: polar coordinates.)

2. Kids Say The Darnedest Things

We asked four hundred 3-5th graders some questions about math. You’re going to tell us what they said. We asked them …

  1. … who invented the Cartesian plane, a) Albert Einstein, b) Carter Von Ludvig, c) Rene Descartes, d) Eric Cartman, e) none of the above? What percent said the correct answer? (A: 9%.)
  2. … to name any mathematician. Name the top four answers for one point each. (A: In order of descending popularity, Albert Einstein, my teacher, Eric Cartman, Carter Von Ludvig.)
  3. … which is there more of, a) feet in a mile or b) pounds in a ton? What percent said the correct answer? (A: 57%.)
  4. … what their favorite number was. Name the top four favorite numbers of elementary students? (A: In order of descending popularity, 7, 10, 8, 11.)
  5. … which would you rather have: $100 or a stack of quarters from the floor to the top of your head? Which was the winner? (A: $100. That got 67% of the vote. Did they choose well?)
  6. … which was heavier, a) a ton of bricks, b) a ton of feathers, or c) a ton of kittens. What percent said “kittens?” (A: 5% The winner was a ton of bricks at 93%. Good job, kids.)
  7. … what was faster, a) the speed of light, b) the speed of sound, c) the speed of wind, or d) the speed of kittens. What percent said “sound”? (A: 25%.)
  8. … if zero was a) even, b) odd, or c) neither. What was the most popular answer? (A: In order of descending popularity, Even [46%], Odd [10%], neither [44%].)
  9. … what the biggest number is. Name the top four most popular answers for one point each. (A: In order of descending popularity, infinity, one hundred million, one billion, googleplex.)
  10. … to name the shape of a stop sign. Name any of the top four most popular answers for one point each. (A: In order of descending popularity, octagon, hexagon, pentagon, hectogon.)

3. Common Critters

Even though your students may struggle to meet the Common Core State Standards, some members of the animal kingdom are doing just fine. We’re going to match a standard to an animal. You tell us if the statement is backed up by a scientific study or if we just made it up.

  1. Salamanders can “identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.” (A: True.)
  2. Ants can measure lengths indirectly and by iterating length units. (A: True.)
  3. Goats can prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. (A: False.)
  4. Chickens can fluently add and subtract within 5. (A: True.)
  5. Octopuses can tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. (A: False.)
  6. Dolphins can construct viable arguments and critique the reasoning of others. (A: False.)
  7. Crows can use appropriate tools strategically.(A: True.)
  8. Owls can count out a number of objects from 1-20. (A: False.)
  9. Parrots can correctly name shapes regardless of their orientations or overall size. (A: True.)
  10. Spiders can apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (A: False.)

4. Music Round

We’re going to play 10-second clips of famous songs. You need to name the number that features prominently in the song.

  1. “99 Problems,” Jay Z. (A: 99.)
  2. “22,” Taylor Swift. (A: 22.)
  3. “Jenny,” Tommy Tutone. (A: 8,675,309.)
  4. “Take Five,” Dave Brubeck. (A: 5.)
  5. “Summer of ’69,” Bryan Adams. (A: 69.)
  6. “Seasons of Love,” Cast of Rent. (A: 525,600.)
  7. “A Thousand Miles,” Vanessa Carlton. (A: 1,000.)
  8. “Sixteen Candles,” The Crests. (A: 16.)
  9. “100 Years,” Five for Fighting. (A: 100.)
  10. “American Pie,” Don McLean. (A: π.)

My Opening Keynote for CUE 2014

I opened up the Computer-Using Educators annual conference in Palm Springs last month. That talk made its way online this week.

I started by describing why edtech presentations often make me aggravated. Then I described my “edtech mission statement,” which helps me through those presentations and helps me make tough choices for my limited resources.

BTW. I was also interviewed at CUE for the Infinite Thinking Machine with Mark Hammons.

Featured Comment

Michael Pershan:

LOL. Funny stuff!

High praise.

“Oh, you think you have a rule? See if you can wreck it.”

David Cox:

I’m noticing that more kids are gaining confidence in looking for patterns, forming hypotheses and then seeing if they can make the hypothesis fail. The phrase that seems to be gaining ground when it comes to hypothesis testing is “wreck it” – as in, “Oh, you think you have a rule? See if you can wreck it.”

There are two things I love about this:

  1. The phrase “see if you can wreck it,” and the toddler-knocking-down-a-tower-of-blocks spirit of destruction it conveys.
  2. The fact that you are supposed to wreck your own conjecture. Your conjecture isn’t something you’re supposed to protect from your peers and your teacher as though it were an extension of your ego. It’s supposed to get wrecked. That’s okay! In fact, you’re supposed to wreck it.

BTW. When David Cox finds a free moment to blog, he makes it count. Now he’s linked up this spherical Voronoi diagram that shows every airport in the world and the regions of points that are closer to them than every other airport. “Instead of having to teach things like perpendicular bisectors and systems of equations,” he says, “I just wish we could do things like this.”

Of course you need perpendicular bisectors to make a Voronoi diagram, so David’s in luck.