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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.

Featured Comment

Andrew:

I keep thinking of learning a programming language, but didn’t quite have a reason why. I think I have one now.

19 Responses to “Dave Major Shows You The Future Of Math Textbooks”

  1. on 22 Oct 2012 at 8:21 amcb1601ej

    Checking whether the traingle is correct can also be done.

  2. on 22 Oct 2012 at 8:47 amDavid Wees

    I checked it out in Firefox, Google Chrome, and Internet Explorer. Some hits & misses depending on which task & which browser, but as for the activities themselves, they look good. I think you can build both of these activities in Geogebra as well, (including recording the result using some external JavaScript) so that may be something to consider.

  3. on 22 Oct 2012 at 9:24 amTimothy Russell

    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?

  4. on 22 Oct 2012 at 9:34 amDan Meyer

    Timothy:

    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?

    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.

  5. on 22 Oct 2012 at 10:05 amjosh g.

    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.

  6. on 22 Oct 2012 at 10:18 amDavid Wees

    Josh G.

    You can program that capability into a Geogebra worksheet using JavaScript. See http://online.math.uh.edu/HoustonACT/GeoGebraWorkshop/WebPages/GeoGebra_JavaScript_Methods.html for the various methods available.

  7. on 22 Oct 2012 at 10:39 amjosh g.

    The plot thickens!

  8. on 22 Oct 2012 at 4:08 pmCarl Malartre

    Nice job Dave! Keep the good work!

  9. on 22 Oct 2012 at 4:17 pmChris Robinson

    I like the fact it can all be done with JavaScript, HTML5, and a pretty simple database setup. No need for other apps, although I’m still a fan of GeoGebra. Alright, gotta go bone up on my coding.

  10. on 22 Oct 2012 at 6:39 pmMichael P

    Beautiful. Small bug: my triangle’s angles added up to 181. But, beautiful.

  11. on 23 Oct 2012 at 4:37 amChris Robinson

    Dan,

    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.

  12. on 23 Oct 2012 at 12:54 pmAndrew

    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.

  13. on 24 Oct 2012 at 1:30 pmDan Meyer

    Chris:

    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.

    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.

  14. on 24 Oct 2012 at 8:05 pmAndrew Stadel

    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.

  15. on 26 Oct 2012 at 1:33 pmcb1601ej

    @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.

  16. on 26 Oct 2012 at 1:42 pmDan Meyer

    cb1601ej:

    I’m often suprprised that so many people don’t know this.

    My guess? The Geogebra / Java crowd overestimates the quality of the user experience.

  17. on 28 Oct 2012 at 6:20 pmAlex Robertson

    Dan,
    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:
    https://www.desmos.com/calculator/mxsu0bpdws

  18. on 31 Oct 2012 at 8:31 pmStacia

    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!

  19. [...] easily with his open source ActivePrompt project. While Dave Major and I continue to bat around very specific implementations of digital curricula, Riley has created an extremely open framework, useful for all kinds of [...]