a/k/a *Redesigned: Dan Meyer*

**Then**

**Now**

Something I have been completely wrong about is the best way to use slide software in a math class. A few years ago I wrote a design series explaining how I use color theory, grid systems, etc., to clarify complex procedures, but the whole thing turns out to be simultaneously a) a lot more fun and b) a lot less time-consuming than that.

My reversal in slide design reflects a shift in my math pedagogy also. Far more important to me now than “developing fluency with complex procedures” is “developing a strong framework for interpreting unfamiliar mathematics and the world.”

I’m not trying to set up a false dichotomy here. We do both. Both are important. But all too often slides like that first one, with the classroom dialogue and solution method predetermined, cordon off classroom dialogue and student reflection onto very narrow paths. That kind of pedagogy does nothing to unify mathematics, tending, instead, to position complex procedures in isolation from each other, which is a very confusing way to learn math and a very laborious way to teach it.

Instead, I want my students to focus without distraction on a) how new questions are similar to old questions, b) how tougher questions demand tougher procedural skills, asking themselves c) which of their older tools can they adapt to these tougher questions?

For example, I put six equations on separate slides, equations we have seen. I asked, “how many answers are there?” One. Two. Zero. Etc.

Then I put up an inequality, tweaking the problem slightly, and quickly.

They told me there were lots of answers. I asked my students to start listing them. “7, 6, 5, 4.2, 4.1, 4,” etc.This became tiresome *quickly* and made the introduction of a graph – a *picture* of all those answers – clear and necessary.

Slide software makes it easy to sequence these mathematical objects, ordering and re-ordering them to promote contrasts and complements. Slide software lets me sequence these mathematical objects quickly, from anywhere on the globe, from photos and videos I take, from movies my students watch, from textbooks too. Graphic design is useful to mathematics, but I am happy to have discovered certain constraints on that usefulness and, simultaneously, higher fruit hanging elsewhere.

It is the curation of this mathematical media that interests me now, though I reserve the right to return to this space shortly and reverse myself again.

## 9 Comments

## David Petersen

May 28, 2009 - 6:24 am -If you are keeping it as simple as this, what is the point of using slides anyways? Especially if you are reorganizing on the fly or responding to student questions that might not go in quite the order planned, why not just use the old chalk and slate method?

Maybe I’m just short-sighted, but I can see why the computer might help with Slide 1 (Then) since you could show the numbers being plugged in to the equation. The rest of what you’ve shown seem (to me) to be just using tech to use tech (or save the planet by not using chalk? or not getting hands dirty? or allow you to move around the classroom?).

I do understand your point of having a more organic-type discussion of the problem rather than algorithmic lecturing. I also see that with the right questions you can lead the discussion in helpful directions, but when a student has an idea you wish to explore a little before getting back on track, slides seem somewhat limiting to me.

## josh g.

May 28, 2009 - 8:25 am -I’m still a student teacher / newbie, but I’ve had this kind of design shift on my mind after doing a lesson with an Info Tech 9 class on some basic PowerPoint design principles. Quick web research on people’s recommended do’s and don’ts kept coming up with seemingly extreme ideas like “no more than 6 words per slide”, and using a separate handout if you need your audience to retain details (as opposed to a printout of your slides).

At first I wrote this off as appropriate for marketing but not for teaching; now I’m not so sure. It’s cool to see that someone is making this transition based on classroom experience.

David: I can still see some advantages to using slides like this. It’s quicker to switch back and forth, and you can focus attention on one equation at a time more easily. (If I were doing this on the board, I’d end up with 4-5 things written on the board at once and try to point to one or the other – still workable but not as visually obvious to the student.)

You could also use a mix; keep the big ideas and main focus in concise slides, but use the whiteboard when you want to demonstrate rough work. (I’m not sure I like the idea of working out solutions ahead of time on a slide anyway; it doesn’t model the actual process very well.)

## Peter

May 28, 2009 - 8:43 am -Now this is what teaching is for me. Getting ‘them’ to discuss and think about mathematics.

I had a great lesson monday when i asked my pupils ‘How will division work for complex numbers?’ (we started the lesson with how to multiply them which was very easy). No slides just a blank blackboard. I did have a computer with Geogebra ready, prepared for if they wanted to investigate the geometrical ‘meaning’ of multiplication.

My job was moderating the discussion and asking questions about their suggestions (“Sure?” (yes even when they are right), “Can you explain to your neighbour?”, “Can you rephrase in mathematics?”, “Can you think of an exception?”). Leaving long pauzes to let them think it through, and talk it through. The one being most uneasy with the silence and the pace was me.

And they did it. It took them 2 hours, but they did everything from introducing the distance to the origin and the angle to finding a formula for z^{-1} if z=a+bi. They were great and both teacher and pupils left the class with a smile and eager to tackle the next problem: powers and roots.

And i can not see how I could have used slides. Don’t they limit you? Where do they help?

## Michael

May 28, 2009 - 9:21 am -I wish I had a projector and computer to present slides. All I have is a whiteboard.

Slides allows the teacher to focus students attention to really important information rather than being distracted by something else on the board. I also agree with Josh G. about how slides can be quickly accessed if needed.

However, can something be said for effective use of board work where important ideas are maintained on the board for students to refer to while thinking about the problem at hand? For instance, suppose the problem was talking about the absolute value of x is less than 5, if the solution of the absolute value of x equals 5 and the solution of x is less than 5 and the solution of x is less than -5, then perhaps students can use those ideas to create a whole new idea for the problem at hand. Again, the pieces are there on the board for students to synthesize without the prompting of the teacher to use such useful information, necessarily.

How can this opportunity be done using a slide presentation program? Since I don’t use it as regularly as others, like Dan, I call on such people to share their experience.

Great pedagogy topic!

## Nate M

May 28, 2009 - 10:41 am -For myself, I use a wacom wireless tablet combined with powerpoint to become my digital whiteboard. I use slides similar to Dan to focus the students and begin discussion. As students propose ideas through discussion, I pass them the tablet and have them solve it on the slide. The great thing about using powerpoint in this way as I can print the slides for missing students, save them to pull them up later in review for tests, or post them on the classroom blog for students to reference on their own.

I understand the “using tech for the sake of using tech argument”, but in some cases these simple changes like this can take the learning to places a heavy piece of slate on a wall cannot go.

## Robert Jones

May 28, 2009 - 12:01 pm -I feel I should warn you, Dan, that I find this blog post interesting and entirely pleasing in tone. I think you must be doing something wrong ;-)

## Chuck

May 28, 2009 - 9:18 pm -Technical question: how do you get ‘them’ to discuss it? Is it a whole-group conversation or do you use pair-shares or something else? I like to facilitate these types of discussions too, as best I can, but often it feels like the high-skilled kids take over and the lower-skilled kids disengage…

## Dan Meyer

May 29, 2009 - 7:38 am -Joshhas this mostly right. It’s speed. It’s the ability to preserve, shuffle, and re-organize a sequence of mathematical objects instantaneously (rather than scrawling one out, erasing it, and then starting again.) Slide software highlights the minute changes in consecutive mathematical objects (an equality changing to an inequality, in this case) in a way I couldn’t really reproduce in my overhead transparency days.I can also pull these mathematical objects from anywhere in any form. I don’t know how to reproduce any of my WCYWDT? lessons with chalk and slate, for instance.

And: because I project onto a whiteboard, I have never had to tell a curious student, “Sorry, we can’t talk about that, it isn’t on the slide.”

I have no idea how slide software could improve your lesson on complex numbers. Your review sounds great. Slide software, like dynamic geometry software, is just one tool in a complete pedagogical arsenal. How can I quickly sequence five videos, three images, and an equation, for instance, using only dynamic geometry software?

My experience is the same. Typically, I ask the students to engage with the mathematical object on a piece of notepaper and to talk to a neighbor, all while I float around, tune in, offer an observation, a question, or a challenge, and tune out. It’s far from perfect and I’m open to suggestions.

## Robin Schwartz

June 3, 2009 - 4:54 am -Hi Dan:

Your slides are awesome — have you used the TI-83/4 as a complementary learning tool for this content?

Robin