In Design I Trust

[BTW: Updated the supporting graphics for clarity.]

In trying to teach really difficult material – so, math, or any math-based science, I guess – the look of the material rivals the material itself for importance.

The weird thing I realized while breaking several traffic laws on the way to work this morning is that there are no large design decisions. Even when the look of the thing changes drastically – from one field to its inverse, for example – the decision was small, the action simple.

Which Is Clearer?

Why It Matters

This makes graphic design a defining aspect of my teaching philosophy, something indicative of the larger whole. My enthusiasm for design points at my belief that small decisions lead to exponential gains, that the sum of my small color, opacity, and alignment choices will lead to a huge net win for my kids, that the math will be exponentially clearer, that we’ll unwaste huge stores of time.

Video Is King

Therefore, if I had unlimited time and capital to create a curriculum, I’d use video, because with video, you make those incremental decisions thirty times every second. If those decisions are made carelessly, of course, the result will be utterly disastrous, turgid, limp, and boring – a medium unearned – as I’m sure you’ve witnessed. The inverse is also true, though, and that awareness is now taking me down some interesting paths.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. Hmm, I stared at your two examples until my eyes became turgid, before finally concluding that it has something to do with different colors. Guess my partial color blindness means that my own exponential gains are all to the zeroth power….

  2. The gradients always bother me, too. Activity, but no information? Or simply that they are present in so many Powerpoint presentations that are done poorly in other ways, and I have bad associations? I have no idea.

    But the larger point here is so very true. When I go to look up some proof in the math library, and I find that the first book in whose index I can locate it was printed in the days of typewritten manuscripts (as opposed to the current method of all LaTeX all the time), I almost always keep looking. It’s a huge struggle to read through text in a distracting font with spacing that doesn’t actively promote comprehension, while also trying to follow a chain of reasoning that (most likely) I failed to quite understand in class.

  3. Yay! Color!

    Now that I have my projector, and a tablet hooked up to laptop/projector, I use color a LOT to teach prealgebra.

    I’ve noticed it makes a huge difference – especially with my SpEd kids and my ELLs. The difference is even more dramatic with the kids who use colored pencils (the way they’re supposed to) in their notes.

  4. What are you up to with Big Tree Learning (or, Brightstorm)? If you’re involved, nice to hear they have someone who actually understands video.

    I saw one of their videos a while back and it was scarily bad.

  5. Whenever I show a Keynote/PPt slide that is text-centric on the board to my students, I always go with a black slide punctuated by white text (sometimes the Mac-ish ‘salmon’ if I use Keynote and need an off-set color for word that become iconic rather than just being legible).

    Since I rarely let slides be dominated by text — save to put up strong student examples of successful thesis statements, for instance — I want the kids to immediately ‘respond’ to a different visual experience the moment the projector is turned on. In essence: ‘reading’ is replaced with ‘observing’ (although not in the passive sort of way).

    Like you, I have come to believe that small design decisions seem to carry the most punch over time.

    BTW, I’m also jumping on T. Hoffman’s bandwagon with regards to his curiosity re: the use of the gradient.

    Is that an intentional design choice or is it more of a quick-n-easy, low-level default setting when you use Keynote? Not an outright critique, mind you, but I am curious given what its value is given how sophisticated the majority of your design choices.

    Is gradient the new black in the dy/dan lexicon?

  6. It’d probably be pretty gauche of me to suggest y’all consider the forest for the trees in this post that’s all about the importance of trees but, still, the gradient? Really?

  7. I’m with the other partially-color-blind individual. Though I don’t think it is my inability to distinguish between blue and black, so much as that the font wasn’t thick enough.

    When I work with my students, I make sure that the font has a thicker line to it so they really, really, cannot help but catch the color.

    Two off-topic questions oh Dan, master of all math teaching:

    (1) Can I use the division symbol on solution sets for high school work? I’ve been having trouble finding a way to indicate that the line above the fraction bar was, in fact, the reduced form of the earlier operation.

    (2) My chemistry students don’t learn (or re-learn in a “it sticks now way) how to get x out of the denominator until about third quarter in Algebra 2, yet I need them to be able to solve for the volume in a density equation (D=m/v) in the first unit of Chemistry. If you have any tips on how I can teach it so that it sticks, please, please email me. Oh, and other commentators, feel free to help me as well. I think this is one of those math-teacher tricks that I’d love to be privy to.

  8. I’m with Jackie on cross-cancellation.

    Incidentally, I re-uploaded the graphic to better illustrate my point and uploaded a couple more to show how small choices with a) lines and b) alignment can each make math much clearer.

  9. Gradient is a choice. A ‘design’ choice, actually.

    It’s also a default template built by others (quite often), so it’s an easy grab, hence my curiosity as to why it works for you when you have a field of pre-built options and also have the ability to push well beyond what most can do…and what it implies from your design-centric eye.

    Just curious. Truly.

    FWIW: Trees and forest are pretty vital in each other’s world. Hard to swing an ax or rope/tire at one without grabbing the other in the process.

  10. re: gradient

    I use a dark background with light text. I add a slight gradient to mimic the effect of overhead lighting on the rest of the walls. The hope is that it causes less dissonance with the rest of the room, but I’m probably just blowing hot air.

  11. p.s.

    Isn’t there some better word to use than “cross” anything? My kids always confuse cross canceling for cross multiplying, which are two almost opposite actions.

  12. Yep, Mr. K you’re right. I try to remember to say “clear the fraction(s)”. They usually don’t know what I mean and respond with something like “Oh, the bow-tie thing?”

    Yeah. That’s helpful. Who tells them this stuff? Bow-tie method?

  13. @Jackie Sadly, I think it’s often elementary school teachers who set these sort of inaccurate or misleading terms and such into motion. (I say this as an elementary school teacher.) It often comes from too shallow of an understanding of the math which results in too simplistic of an explanation or strategy.

    That said, I haven’t figured out any good way to remedy the situation. Elementary school teachers have a wide range of topics and subjects to teach and can’t be experts on them all. So they/we often rely on a math textbook rather than having to really understand the concepts.