Redesigned: Darren Kuropatwa

Darren Kuropatwa:

I’d genuinely appreciate any suggestions you may have about improving this particular slide deck or my approach in general.

I can’t resist that kind of invitation. Tom Woodward recently performed a complete presentation redesign for Alice Mercer but I don’t have that kind of stamina. I have selected, instead, just one slide. Whether Darren agrees with my notes or not, this kind of exercise is supremely useful for anybody looking to nail down her own aesthetic. (ie. How would you handle Darren’s slide?)

Darren’s Slide

My Revisions

Problems I’ll try to solve:

  1. There is a lot of text, most of which should be spoken.
  2. There is a lot of information, which should be unpacked over several slides. The marginal cost of extra slides is $ We’ll use that.
  3. There aren’t any visuals, and visuals are what make projectors and presentation software worth the trouble.

First, when I recommend visuals, I am not recommending this:

or this:

I am recommending a real visual. People recognize high-bandwidth, meaningful imagery when they see it and stock photography isn’t that. I am also recommending that Darren speak the text he has on the screen, striking up a conversation between him and his class.

To review the changes so far:

Darren has a visually compelling prompt on his hands (“Which route does Dave take?”) with no visuals. What is the best way to illustrate this? I fired up Google Maps and located Toronto, which is where I assume all Canadians live, and forced two routes from the same location. Take screenshots.

He could put the routes on separate slides or, using some intermediate Photoshop, color-code them on the same slide.

At this point, I’d ask the class to tell me which route Dave should take. Just a guess. No math on the screen. Just a bet. Which is faster? Maybe they know the local topography. Maybe they know the traffic. Maybe they know the two-lane roads. Kids who are timid in mathematical discussions will be emboldened to participate here. They can do this one.

You tell them that Dave drove each route for one work week and timed the trips. You ask them to tell you the best route.

This is where Darren nails it. He knows his students will go straight for mean, which they just learned, but he has forced both means to 31 minutesa fact which Darren tells his students in the text of the problem, a fact which I would withhold and let them discover for themselves. Necessity is the mother of all invention, and they need to see the necessity for measures of dispersion.. This will propel an interesting question, “Okay, so now how do we decide?” Students will mull it over and eventually decide that the blue route is more unpredictable while the green route is more consistent, which will motivate the definition:

Thanks. This sort of exercise helps me define my own aesthetic and reconnects me to what I love about visual literacy in the math classroom so I’m grateful to Darren for his explicit permission to mess with his workPersonally, I think that anytime anybody posts their slides publicly like this, their work should be fair game for reproof, correction, and instruction. Those who think otherwise are squandering the enormous professional development opportunity we have with these blog things..

Photo Credits:

  1. Speedster.
  2. Mister D.
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. holy cows on fire, man! I think I need to take the rest of the day off just to digest the awesomeness. As a visual person, this was a great demonstration of what you are pushing toward and has given me some ideas for my own room.

    I’m definitely guilty of too much text and it is something I work on constantly.

    Thanks for the post :) And thanks to Darren for the request!

  2. I would recommend using Google Map’s traffic overlay as well. Washington DC has some great traffic patterns for this question (as does NYC). The question of going through vs. around and variance (show the traffic patterns from different times of day to get variety in the “red” zones). Great way to motivate them to ask for the times, rather than present the times.

    Also – when looking at the traffic maps – what qualifies as red? yellow? is it based on number of cars (which increases probability of an accident or slow down) or is it based on actual traffic speed?

    Lots of good questions that can all be used to motivate the same statistical measure, and at the same time show that how statistics are presented are just as important as the statistics themselves.

  3. Dan, thank you. I LOVE that you did this and what you’ve done with this.

    The screen shots and Google maps are a great idea. The thing for me is balancing creating 3 or 4 lessons like this every day and finding the time to do it all. My approach has been incremental, as you saw by looking through the two slide decks. Next years’ class will benefit from the makeover you’ve shared here using this one slide.

    And I’ll be carefully thinking through the future slides I make.


  4. Don’t confuse me, okay?

    And this sort of design process admittedly takes a fat lot of time. As I have internalized an aesthetic over the last few years, it has become incrementally easier but, still, a fat lot of time.

  5. The key after you have the ‘new and improved’ is to store it so you can find it next time you want it. That goes back to your (dan) desire to have a repository for everyboy’s ‘good stuff’.

    I guess you could have a file saving system that corresponded with the textbook or your notes or whatever. Like a slide-dewey-decimal-system.

  6. Yes, yes, a thousand times yes.

    This post is everything great about your blog in a single issue. Visual design, written style, total applicability to the classroom. For once, the math is at a level we primary folk get to teach about, too. I’m passing this on!

  7. I wanted to ask David Cox’s question seeing as I’m working on designing a unit on factoring. And I think this is just out of ignorance, and having never taught it before (lack of expertise) but I don’t have lined up some awesome real life applications. So far, I’ve shown kids a video of a dude high diving from 172 feet (pretty intense) and we did some estimation-mumbo jumbo to calculate the number of seconds he had to anticipate his impact. So I had the visuals, but as far as something that really ties in with the strategy, with the exception of contriving some rectangle area stuff, I’m lost for a really solid visual image, one that seems that it would find its’ way up here.

    Lingering question how do you teach really dry procedural knowledge? So the challenge is, what does the rest of the lesson look like, the part when you are teaching kids to crunch numbers and manipulate variables?

  8. I wonder about the ‘dry’ stuff too. Though I’ve generally been inspired by such blogs as Kate’s f(t) with regards to that. If a dry topic can’t be driven visually, then at least some sort of ‘fun’ practice work could be done.

    Though it does beg the larger question, what is the purpose of the dry stuff for the majority of kids?

    Dan: keep up the great work, you’re helping to reshape the way I think about teaching.

  9. Glad this made for valuable reading. I promise the exercise was as valuable to me.

    @Nancy, my computer’s indexing feature is usually sufficient for pulling up old content. I punch in (eg.) “solving linear equations standard form” and get within a couple of minutes of what I’m looking for in last year’s files.

    @David, Nick, kevin, a cornerstone of my classroom aesthetic is “building conversations around mathematical objects,” a cornerstone which is applicable (though less fun) even when a concept lacks “real life application.” (ie. Nick’s “dry procedural knowledge.”) This aesthetic forces me to build my slides around images (not text, which I push slowly into the conversation) even if that image is just an equation.

    For instance, I’m going to give my students y=x^2+5x-7 on a slide this Wednesday. I’ll ask them to tell me everything they can about that function. Most of them will reliably deliver a) the axis of symmetry, b) the vertex, and c) the fact that it has two intercepts. They will attempt to deliver those intercepts through factoring but that will be impossible. This mathematical object and the conversation surrounding it will then motivate the quadratic formula.

    Three things, to summarize,

    1) it’s very, very, easy to eff up the real-world application concepts too. That we do them right, nurturing a spirit of curiosity and inquiry classroom-wide, makes the procedural stuff immensely easier, more satisfying.

    2) necessity is the mother of all invention. If there are two intercepts and none of our tools are powerful enough to find them, then we need new tools. I don’t typically start a new concept with “today we’re going to learn about something called ‘the quadratic formula’.” I give them a problem they think they can solve but can’t.

    3) a classroom aesthetic, consistently applied, yields extremely cool results. This, of course, makes no sense if you have never pondered your classroom aesthetic.

  10. @Nancy Since I’ve started using a SMARTboard I save and categorize my lessons by course and unit. The next time through a particular course I pull up the old slides and push forward incrementally in their design. I’ve shared last years lessons here. Feel free to grab anything that looks interesting.

    @Dan I like your idea of developing a classroom aesthetic based on “building conversations around mathematical objects.” I’m going to use that more deliberately in the future.

  11. @Dan I’ll just say it, the problem I have is that I would like to work less and not more, though I would like to be better not worse. So there. You mentioned the fat lot of time it takes to pull this off, and I find myself saying that about other things I’m doing. So I guess subconsciously I’ve made the decision that 1st year teaching this stuff I have bigger fish to fry than the visual aesthetic. Though I know that’s not the meat of this. It’s hard to say that something is more of a priority than student engagement and conceptual understanding (is that an ok buzzword?). That something though, for now, is simply clarity of presentation. That I am able to get the class through concepts like, say factoring, or proofs involving trig ratios and the like without having everyone’s hair fall out. Beyond that, I think once comfort with the material has been achieved, the next big gap must be the engagement factor. I wish I was better at doing both at the same time.

    @Darren Looking at those slides, I’m tempted to say that they might function better (and more Dan-ly) if you printed them off for students. I think for a presentation, text rich is overload, but your HS kids are fine readers (I assume) so they’d probably be happy to have some nicely thought out definitions or example problems ready on the page to attack with their own thoughts etc. I find presentations are far more engaging if there’s something going with it, something guiding kids/adults towards where you want their thinking. This also lends itself towards getting rid of the images (they don’t print well). You could possibly push the images in your presentations (at least the ones you want to keep) to new slides, put the text on old ones, then print the text slides, and project the images.

  12. @Nick I very much like the idea of using more visuals in my teaching. Step by step, I’m working on it. I love these sort of discussions, I learn lots this way. I thought I might throw out a couple of points to frame how the slides are used in my class.

    Kids don’t take too many notes in my classes. The slides are published to the class blog (example) each day, tagged as “slides” and “whatever unit they relate to”. The notes are always there for them when needed.

    I try to minimize the amount of time I spend at the front of the room. I colour code my slides (purple = instructional, white = student work). As I’m planning my lesson if I see more than two purple slides in a row I know I need to break that up with a white one. I sometimes break this rule when the slides are intended to be displayed in quick succession.

    Kids are typically sitting in groups of 3 or 4. They work through each problem collaboratively and then one student goes up to the board to write the solution and then explain it to the rest of thee class. I’m typically at the back of the room or circulating mostly listening to the conversations and interjecting with the odd question here or there to push their thinking forward.

    While I do some presenting when teaching I do my best teaching when not presenting.

    Everything written on the board is preserved (taking advantage of that “marginal cost of extra slides” Dan mentioned) even, especially, the mistakes (so you might see the same problem repeated on 3 or 4 slides if we had that many different solutions or approaches to the problem). Each day one student will summarize what was learned in class by publishing what I call a Scribe Post to the class blog.

    I love talking about instructional design. IMHO instructional design & presentation design have an intersection, each is informed by the other for the better, but they’re different.

  13. Oh, I forgot to mention, I’m trying to cut down on the amount of paper we use. You can see how that fits in with the way I structure my class and orchestrate my students participation. ;-)

  14. Okay, you had me on this one until the end. Somehow this one disappointed me.

    I think it’s because the concept ends up on some very “soft” math. I like the start but all you can end it on is a discussion of range? (And I guess you mean the statistical range, which is a distinction most teachers don’t make and certainly our state standardized test doesn’t, causing confusion in the future for students when they have to worry about domain and a completely different sort of range.)

    Let me fiddle with end part and get back to you.