[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) âfinding the coreâ 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 worldâsay a musical recordingâare 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?â 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 dayâthat 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.