The lightning and the lottery

I almost spit up my coffee when I got to the punchline on this one.

From Tony Pratt:

I’m a first year teacher (4th Grade) in the New Orleans Recovery School District. The one common thread that I’ve noticed between the lessons that have stuck was a relation to something the kids were familiar with or interested in. I frequently relate math lessons to the beloved Saints and create bizarre scenarios to maintain student interest. The best and most interesting story, however, came from a colleague. He was teaching the concept of probability and went into a long monologue about how small of a probability you have to win the lottery. He relayed the particularly sticky stat that it is more likely that you will be struck by lightning than win the lottery. The lesson was memorable enough that several students went home and told family members.
One student, Jarred, relayed his story, “I saw my uncle buying lottery tickets last night. I told him that he was more likely to be struck by lightning than he was to win the lottery and that buying lottery tickets was a bad idea because of probability.”
“What did he say?”
“He told me to get the F out of his face.”

Digital signal processing, made to stick

[Preamble] If you ask someone to think of a sticky idea, a lot of times they’ll blurt out a slogan. “Wassssup!” “Just do it.” And, no question, these are sticky ideas. But because people tend to associate the notion of “stickiness” with things like slogans — i.e., short, punchy, cleverisms — they have a hard time imagining that stickiness could apply to really complex things. Stickiness is for marketers, not for engineers or scientists, or so goes the thinking.

Well, no. Chip and I may be largely to blame for this misperception — the word ‘sticky’ we’ve embraced is itself clever and vaguely marketingish. But sticky just refers to an idea that was understood, remembered, and changed something (opinions, behaviors, values). So the fact that someone is a practicing nuclear scientist means that, at some point, nuclear science concepts stuck. Which in turn means that a nuclear science teacher found an artful way to communicate really hard concepts.

Because of this backstory, we were thrilled to get a note from Andrew Singer, who teaches a digital signal processing (DSP) course at the University of Illinois at Urbana-Champaign. Professor Singer and I ran across each other as a result of a talk I gave on campus. He had read Made to Stick and shared some changes he had made to his course curriculum as a result. And, as you’ll see, slogans are not his bag. He deals with really complex topics that must be communicated to really smart people. After Chip and I got his note, we exchanged “Wow!” emails with each other. [/Preamble]

I teach a course on digital signal processing to juniors and seniors in electrical engineering at the University of Illinois. This is a course that describes the mathematics and theory behind applications like digital modems, HDTVs and MP3 players. Basically, whenever “signals”, that is information they you care about, are “processed” using a computer, cell phone, or anything that samples or “digitizes” the signals of interest, digital signal processing is used.

Needless to say, the theory that I need to teach the students makes this largely a math course for upper level engineering students. However, as you know, motivating students to learn more mathematics for mathematics sake (especially for non-math majors) is no easy task. I’ve struggled over the years in coming up with means to increase their interest and maintain this throughout the course so that I can supply them with the tools they need to be productive and successful engineers.

As a young faculty member, I used boundless enthusiasm and energy in my lectures, which managed to maintain their interest in my lectures, but this didn’t necessarily translate into deepening their understanding of the material. They would pay attention to what I was saying, since I embedded anecdotes of my time in industry or interjected jokes into the discourse, but in the end, the “smart students” did well, and the “not as smart” students did less well, and the results in terms of what I could discern they had learned, based on their exams and finals, was about the same. I did find over the last 10 years a number of things that did help to engage students in the learning process that did translate into broader and deeper understanding. It was after reading M2S that I saw the connection with the themes of your book and understood more broadly why these techniques worked. The problem that a professor has is a deep case of the Curse of Knowledge. Not only has it been a long time since we did not understand what we are trying to teach to students who have not yet grasped the concepts, but we have also taught it so many times, that there is a sense of “I’ve taught this 100 times, haven’t you understood it yet?” This is of course not a conscious phenomenon, but nonetheless, something that we all must battle.In the course of reading your book, I have also been re-writing the course lecture notes for this digital signal processing course and have been focussed on (using your term) “finding the core” of the course. I had come up with, over the last few years, a core set of ideas that I thought focussed on what it means to have taken and understood digital signal processing. When a student from the university of Illinois interviews at a company and says “I took digital signal processing from Prof. Singer” what are the 3 things that they need to know to both get the job *and* make the University of Illinois proud to have this graduate working in this field? By focussing on the core ideas of the course, I widdled away the extraneous details that basically served to separate the A+++ students from the A++ students, but largely fell on deaf ears on the rest of the class.Students need to understand what a mathematical model for a signal is, what happens when it is sampled, understand the concept of analog and digital frequency and how they are related, understand what happens when the digital signal is processed (in time and frequency) and what happens when this signal is then reintroduced to the analog world, through a digital-to-analog converter. This set of core ideas can be visualized in a picture, where the signals that touch the world—say a musical recording—are sampled and become a digital file, this digital file is manipulated, and then the file is played out through a D/A converter. By showing this to the class at the beginning of the term and referring back to this example, I found I could keep the class on track to the core messages I wanted them to learn. I also focussed on this core message when deciding what material to keep in the course and what should be left out. This was all before reading M2S, and now I see that I had successfully managed to get chapter 1 on my own, with a little of the notion of stories and concrete examples.

Post M2S: The night I finished reading M2S, I literally put down the book, went over to my lecture notes for the next day’s lecture and asked: “What is the core message of this lecture?” Where is it? Why am I burying this message so deeply in mathematics? I wrote a single page with the core message for the day on it together with a catchy diagram that illustrated these key concepts. Then, I focussed on creating a set of increasingly challenging concrete examples that illustrated this key concept and developed the supporting concepts one by one. Each example that I wrote, I looked at and decided were not yet concrete enough. For example, in one case I had a signal of the form “a^n u[n]” to express a one-sided complex exponential sequence. I thought, “Why am I introducing this extraneous variable ‘a’ ” in my supposedly “concrete” example?” I replaced this with the number “1/2” instead. Additionally, I provided a story to go with each concrete example. “Suppose the number of album sales for a particular record fell off geometrically, with half as many sold each day—that is, the sales took the form 1000(1/2)^n for the nth day of sales, beginning with 1000 sales the first day, 500 the next, and so on…”

Basically, I grounded each signal in as concrete an example as I could. Then, when I wanted to describe properties of the signals or how I would manipulate them, I gave the corresponding meaning (as close as I could) in the story of the album sales. The lecture went flawlessly, and I kept them in class past the bell at the end of the hour. Since then, I’ve added “mysteries” to be solved, introduced early in lecture, with the answer only revealed at the end. I’ve included such “riddles” in homework and laboratory exercises, to tease out the student’s interest in understanding the concepts sufficiently well that they *want* to find the answer.

I don’t know what the end result will be at this point, however I know that the course text that I write will be much more inviting, more concrete and focussed after reading M2S than it would have otherwise been, and, whenever I stand up in front of the students, I am constantly going through the “SUCCESS” list, where, in my case, the last “S” is for Student.

The Screaming Man in the Four Stroke Engine

Here’s one of our favorite stories so far from the “100 books for 100 stories” contest. There are still plenty of books to giveaway, so make sure to tell your teacher friends: Email us — heaths@fastcompany.com — a story of a lesson that stuck and we’ll ship you a free signed copy of our book. (Must be a U.S. resident and a current teacher.)

Check out this tale from Saleem Reshamwala (a few comments below the story):

When I was a middle school student in Apex, North Carolina, I took a class called “Small Engines” with a guy named Mr. Trueblood. It was basically a class in how to repair lawnmowers, and a stepping-stone class for learning how to fix cars.

Here’s the four steps in making a four-stroke engine (the one in most cars) go:

1) Piston goes down, gas and air mixture gets sucked into the cylinder
2) Piston goes up, compresses gas and air (makes gas and air mix more explosive)
3) gas explodes piston is forced down (this is the explosion that makes your car go)
4) Piston goes up (exhaust is pushed out)

I don’t think a single one of us understood that about cars before we started the class. So, Mr. Trueblood tells us, a group of middle-school boys in rural North Carolina, that he’s going to teach us the basic science of how a four-stroke engine works. We’re expecting him to go to the blackboard with the chalk. He walks out of the room.

1) He then walks back in giving a monologue as if he were a mix of gas and air that had been sucked into a car engine. “Woah, got sucked in here, it’s not so bad lots of space to move around” and he’s kind of moving around the class a bit, acting as if he’s talking to various particles around the room. It’s a little weird, and some of the boys are laughing.

2) Then he starts acting as if the back wall of the class is moving toward him. He gets really into it. Laughing nervously at first, talking about how the piston is making things get really crowded for him and the other particles. Then he briefly looks genuinely scared. He’s talking about how being this crowded in, all he wants to do is anything he can to get out.

At this point, a few of us were like, ‘Uh, what the hell is going on here’

3) He yells something about a fire coming in the side of the class, and then SCREAMS and SPRINTS toward the back of the room, yelling that he’s burning. I was kind of terrified at this point. He looked crazy. And, like I said, he’s yelling about having come into contact with flame.

4) He slams himself into the back wall, stops acting crazy, and just acts like he’s exhausted, mentions how shocked he is at the force that he was able to push the piston away with, acts like it’s coming back towards him, and then walks out the classroom door.

I can’t remember if we clapped or not, but I know we all laughed. Nervously. And it sure as hell taught the concept.

There’s a lot to love about this: Note how the teacher is trying to turn a complex process into a concrete story. He is trying to get students to experience the four-stroke engine. And the fact that he freaks them out a little is just gravy. Also note that the initial student reaction to the, er, performance is not particularly positive. Sticky ideas won’t always get instant acclaim, and yet it wins in the end — here’s a guy who still remembers the details of a class from middle school!

Oceanography, amplified

I conducted a workshop recently for high school science and math teachers. We were working together to find ways to make their lesson plans stickier. My favorite example came from a couple of teachers who were trying to revamp the oceanography unit. Below is my own paraphrasing of what they said:

“We weren’t happy with how our unit on oceanography went last year. So we’ve put a lot of energy into how to make it better. Here’s what we’ve come up with.

In the first class in the unit, we start with a mystery: Let’s say you put a message in a bottle, drive out to the coast, and throw it as far as you can into the ocean. Where will the bottle end up? We let students make their guesses. (‘The waves will bring it right back to shore.’ ‘It’ll end up in Antarctica.’ ‘It’ll sink.’ Etc.) But we don’t give an answer (since there isn’t a clear answer).

Then we began to explore this same mystery in a more dramatic form. We’ll have students read a wonderful article from Harper’s magazine. What happened is this: In January 1992, somewhere in the Pacific Ocean, a cargo ship hit a severe storm lost a container overboard which held 7,200 packages of plastic toys, including thousands of rubber duckies. Years later, we know where many of these rubber duckies ended up. In fact, many of them ended up on the same beach! By tracing the paths that these duckies swam, we learn a lot about the way ocean currents work.

Next, we let the kids do some hands-on experimentation. We’ll set up tanks of water with different salinities and different temperatures, and let them see how those variables change the water current. In essence, we are letting them create their own ocean currents.

Finally, we’ll pivot to the critical role that oceans play with global climate. We’ll start by asking them: What determines the weather of a city, like New York City? Inevitably, students say it depends on the latitude of the city ‘ the closer to the equator the city is, the warmer it is, and the closer to the poles it is, the colder it is. There is much truth to that, but there are huge discrepancies: For instance, New York City and Madrid are at roughly the same latitude. Yet it snows every winter in NYC and doesn’t snow in Madrid. What’s the difference? That paves our way to talk about the way that ocean currents influence climate.

We will be trying this ‘new & improved’ sequence this fall, and we’re hopeful it will make the unit much more vivid for students!”

An ob/gyn on lectures that work

Chip and I love this post by an ob/gyn, which is titled “Teaching medicine to residents and students.” Lots of concrete examples of good versus bad teaching techniques. In particular scroll down and read the author’s 4 different options for presenting the “differential diagnosis of amenorrhea” (from the “right way” to the “disaster”). Here’s a quote:

I refuse to introduce topics with “this disease is veeery important because it is veeery expensive and xxx billions are spent annually on blablabla….” This is such a horrible introduction. Boring. Xxx billions means nothing to me, absolutely nothing. I can’t even imagine a billion dollars, I stop thinking after 20 million, since I would retire and sail around the Caribbean if I had them. And what do the billions matter to your practice? Nothing, nada, zilch, zero. It might matter to federal policy makers. Are those people seeing your power points?

What matters to me is “what percentage of patients that walk through my office door have this” because that determines if I am going to do something about it, how seriously I am going to take it and what I am going to do…

And finally, topics should be taught in a clinically relevant way and not in a pathologically / systematic way. It is depressing when students or residents are shown long lists of differential diagnoses with weighing them according to clinical importance. It is absolutely impossible to remember the 22 causes of amenorrhea when they are presented as a long systematic list. It is an insult to the learner! Presenting a list without weighing the differential diagnoses by frequency of occurrence means that the teacher really does not care about the student and just slaps something on the slide in who-cares-what-you-can-learn-from-it style.