I’ve been trading e-mails over the last few weeks with Dave Major, a teacher in Dubai who also knows how to use code to make dreams come true.
For instance, I wrote a mushy love ode to the Taco Cart task of my dreams. Dave Major made it real.
Then I asked him to create an activity I described in this talk at 28:01. We ask students to create a triangle with certain specifications. They submit their triangle and then they see quickly and easily whether or not everyone else created the same triangle from the same specs. If they did, we should prove that it’s impossible to create another triangle. If they didn’t, then we have a counterexample and we can axe the hypothesis.
Dave put it together. You should check it out. He’s giving you a look at the math textbook of the future, several years early.
I keep thinking of learning a programming language, but didn’t quite have a reason why. I think I have one now.
cb1601ejOctober 22, 2012 - 8:21 am -
Checking whether the traingle is correct can also be done.
David WeesOctober 22, 2012 - 8:47 am -
Timothy RussellOctober 22, 2012 - 9:24 am -
Nice examples! Wish I had easy access to computers for the whole class for this. Might actually have to try to reserve a coveted computer lab if I can just to let the students work through this.
My only concern is rounding. I could make a triangle that has a different decimal value for the far side as some triangles and still have met the requirements. Is that something the computer should calculate to verify, should it have more decimals so we have to make the triangles more precise or is that something the teacher needs to address?
Dan MeyerOctober 22, 2012 - 9:34 am -
We were trying to strike a balance here. Force students to three decimal accuracy and the triangles will all look really, really congruent. It’ll just be really, really hard to make the triangle in the first place. Dave originally rounded to the nearest unit. It didn’t look right. I asked him to round to the nearest tenth and here we are.
josh g.October 22, 2012 - 10:05 am -
David, the major thing missing in Geogebra is the data sharing. There’s no way to have students submit data to a central server and have it shared with the whole class as far as I know.
David WeesOctober 22, 2012 - 10:18 am -
josh g.October 22, 2012 - 10:39 am -
The plot thickens!
Carl MalartreOctober 22, 2012 - 4:08 pm -
Nice job Dave! Keep the good work!
Chris RobinsonOctober 22, 2012 - 4:17 pm -
Michael POctober 22, 2012 - 6:39 pm -
Beautiful. Small bug: my triangle’s angles added up to 181. But, beautiful.
Chris RobinsonOctober 23, 2012 - 4:37 am -
How do you see these digital textbooks fitting with math instruction? Will they be used more individually with students (i.e. self-instruction) or in whole-class/small group instruction? I’m really intrigued by this form of curriculum, but wonder if there almost needs to be a class mode/individual mode.
AndrewOctober 23, 2012 - 12:54 pm -
Maybe in the future math students will use tablets rather than graphing calculators. An old Ti-83 is still quite expensive. When tablet prices come down and students are using them I see such work that Dave has shown being valuable to a teacher.
Perhaps new math teachers will be expected to have some useful programming knowledge and can contribute such digital textbooks. I keep thinking of learning a programming language, but didn’t know quite have a reason why. I think I have one now.
Dan MeyerOctober 24, 2012 - 1:30 pm -
Big big question. It’s kind of a logistical nightmare. I think the best approach I can take is to make the textbook fully self-contained so that individuals, self-learners, homeschoolers could learn from it.
But a skilled teacher could only make that kind of curriculum better, facilitating dialog around the prompts that the “textbook” doesn’t easily support, offering shorter explanations that are timed better than whatever the “textbook” included at whatever time it decided to include it.
Andrew StadelOctober 24, 2012 - 8:05 pm -
That was so much fun! Props Dave. Keep up the great work. Man, I would have learned math so much better in school with this type of interaction.
cb1601ejOctober 26, 2012 - 1:33 pm -
@6 yes, and you can even embed these in collab s/w like VMT (Virtual Math Teams) or storing student constructions, including checking correctness. I’m often suprprised that so many people don’t know this.
Dan MeyerOctober 26, 2012 - 1:42 pm -
My guess? The Geogebra / Java crowd overestimates the quality of the user experience.
Alex RobertsonOctober 28, 2012 - 6:20 pm -
I’ve recently discovered desmos.com as a graphing tool for my students and came across this graph that relates to your taco cart problem. I didn’t create it, but thought you might find it interesting:
StaciaOctober 31, 2012 - 8:31 pm -
I love this app! For those of us already teaching online things like this triangle example are awesome. My husband’s a programmer and I’m a teacher, both of us passionate for online education.
I think in the future students will have something like an iPad for their book and they would be able to manipulate images like these triangles, or use a pen to write a problem. In the classroom there could be log-ins so that all the students are connected to the teacher and each other. The “books” will have more of an interactive quality, which will help the individual/homeschooler.
This is awesome!
P.S. Alex, I haven’t come across desmos.com before, is there a way to graph the equation? Instead of typing it in having the student plot the point and slope, actually create the line and then double check it by typing it in? That would be amazing as an online teacher!