One of the most interesting things I’ve noticed in educating thousands of engineering students, that has directly led to evidence for my thinking on memetics, is the inability of my students to grasp the significance of all forms of data.
Just so you realize, this belies their education, as well as the constant, chronic chattering of STEM education reformers about kids needing more math classes. My students have HAD those classes. They’ve often gotten ‘As’ in those classes. They’re not stupid kids either, so don’t go down that route.
And it’s not like classes in calculus, statistics, and such don’t help. They can indeed. But there’s more going on under the hood that is extremely poorly understood in how people think about numbers. And frankly, while it may have something to do with the numbers a bit, that’s really not the deep problem.
The deep problem is a lack of ability to reason with numbers. That requires a number of things — the ability to make connections, as well as the ability to frame things consequentially, and project into the future. Add on to that the ability to read something like a graph, and then connect that graph to a physical instantiation of action. Now we’re talking.
That’s a lot of verbiage that makes sense to me, but likely doesn’t make sense to most of the readership. Here’s an example.
One of the things we beat kids in engineering education over the head with is the idea of a mass-spring-damper. Mass-spring-damper (MSD) systems make up a ton of mechanical systems — they’re a simple oscillator, a car suspension system, a building swaying in the wind. Anything that vibrates can be approximated with an MSD system. Here’s the basic block diagram.
The mass is, well, a mass, the spring is a spring, and a damper is something that takes energy out of the system as it goes up and down in the direction ‘x’.
Let’s say you pull this thing up, let it go, and watch it wobble. If you plot ‘x’ over time — the vertical displacement, you get a curve that looks like this:
There is math involved in getting these results, of course — the graph above can be predicted using things most folks would find “fancy” — differential equations — but you don’t need to know all that to think about what I’ll say next.
I put up the picture of the MSD system. Then I tell them — the decaying oscillation (a sine function) is what happens when you displace the mass. NOW everyone stand up (I’ll often ask for volunteers) and physically demonstrate WITH THEIR BODIES how the graph says you should move. This is a deep, intrinsic understanding — reading the graph, and then actually demonstrating that you can translate the numbers on the graph into a motion your body executes.
Virtually none of them can do it! Occasionally, I’ll have a more evolved student who will get it. But most will either a.) have no idea whatsoever, or b.) think there’s a catch in all this and I’m trying to humiliate them.
Of course, I immediately start jumping up and down appropriately, and it’s fascinating to watch the concept slowly seep into their brain. I put up numerous graphs, with different types of behavior, and repeat the exercise.
That’s innumeracy — the deep variety. The inability to take numbers and have them make sense to yourself. It has nothing to do with practicing algorithmic thinking, which these students have done in their differential equations class, a form of calculus. ALL the students that sit in front of me have had the math I haven’t discussed in this piece drilled in their heads over the course of the semester. It’s just that none of it “made deep sense” to almost all of them. And if it doesn’t make deep sense, it’s meaningless.
The real problem (if you’re here on purpose, you know likely what I’ll say next) is agency development, and that’s hooked to empathy. They have little ability to have complex, consequential thoughts that they construct. So the idea that they would pull a graph a professor writes on the board and embody it within their own experience is something that they can’t do. They have to be TOLD what it is — and then that opens the doors for more problems. Without embodiment/internalization, and appropriate agency development, it becomes one more semi-useless fact that floats around in their brain, and is soon forgotten. Reasoning with the concept? Are you kidding? Think Charlie Brown in the classroom, with the teacher’s voice going “BLAH BLAH BLAH”.
In my advanced “capstone” design class — the last class they will take as an undergraduate — I work directly on this problem. How? Through having students do estimation of physical systems with equivalents. That’s a fancy way of saying I have them take something they have a “feel” for — like how hot a lightbulb might get — and then reason through some estimate for a physical system they might be designing. I started doing this after noticing students studying thermodynamics would invariably do a calculation where they would estimate the heat in a lighted match of being something like 1M BTUS. A BTU is the amount of heat required to raise 16 oz. of water 1 degree F. Students would invariably make a mistake somewhere in the calculation, then write down a preposterous answer. Their own fact-checking circuit in their brains was disabled.
I give the example I like to use — “how many table saws would it take to drive this large machine?” I am fond of table saws, or power drills, or angle grinders, because I use them all the time. Students often have drills or grinders themselves, and most folks do know the factoid that 120VAC comes out of the wall, and can look up the amperage on Amazon for a given tool. By forcing them to find meaningful ways to reason with numbers, they make far fewer mistakes.
Understanding equivalences matters much in fighting innumeracy, because once one can do that, one can scale one’s reasoning appropriately — as well as ask, when given an inappropriate equivalence, what the hell that has to do with anything.
And the problem is this kind of innumeracy has been coming fast and furious with the COVID crisis. How many people have heard the equivalence “We’ve lost more people to COVID than we did during all of WWII”? This factoid is actually true — we did lose something like 250K troops in fighting in both the European and Pacific Theaters. But it is a meaningless, manipulative equivalence. Approximately 7.7K people die every day in the US under normal circumstances (more than 2 9/11s! if I wanted to be histrionic) — but it’s a meaningless statistic. It counts on the preying on the fear, and distorting the response of the person subject to it. In all things that matter — national sacrifice, governing mood of the populace — comparing COVID to WWII is a psychopathic manipulation, whether intentional or not.
And we have a media culture that is fond of this — on both sides of the aisle. What it does is makes any statistic a weapon to advance a worldview, instead of triggering a thoughtful approach to understanding where and how a number might be related to meaningful policy. I was on Twitter the other day, and a person, a respected leadership consultant, was informing us that they couldn’t leave their house because the death rate in their community was 3%, and they were certain that their 2 young children and themselves would be infected and likely die.
I immediately went to the COVID deaths page — that person had taken the population in their town, and divided it into the total number of COVID deaths in their county of over 3M people.
COVID deaths in the entire county/Actual population in their town ( the actual population of the town was ~ 1/60 the actual population of the entire county) — this would have been a national news story if true!
The actual COVID death rate for their county was around .05%, which is typical for a healthy population at this point in the pandemic
One might think this as an innocent mistake, save for the fact this person had been stuck inside the house with young children, not daring to venture out, for eight months. The deeper truth was that numbers had no real meaning — they were a tool for reinforcing fears, and no questioning was possible for their fears — they only thing they felt they had agency over.
It’s easy to go to the fallback from Mark Twain — “lies, damn lies, and statistics” but once again, the problem is different. More illustrative is considering how a person interprets numbers will directly link to how they ground their own knowing — through using numbers and correlating, or using causal reasoning — to establish validity — how true something can actually be. Or to listen to an authority and just take whatever they say carte blanche. And that involves empathetic development.
The real problem is not just the techniques of learning.
Don’t take this the wrong way, folks. Math classes CAN help. One of the amazing things about math, once you get into it, is that it delivers a range of mental models and cognitive concepts that you can use in your own reasoning. Mathematical concepts like nonlinear systems, chaos, and fractals permeate the very fiber of this blog. My whole system of complexity understanding is based on understanding canonical sets. They are valuable scaffolding for some of the not-so-simple ideas I explore in other posts.
But they do one no good without empathetic development and appropriate agency. The innumeracy we see is really just the tip of the iceberg of a lack of personal growth. And until we fix that, teaching our students advanced logic and statistics will not get us to where we need to be. Instead, we’ll see the raw exercise of manipulation from those conscious, or semi-conscious individuals looking to control how we think. They will be acting out of their lesser natures — according to the v-Meme stack in their social structure. And considering we’ve set up most of those in low-empathy hierarchies, don’t expect the results to be pretty.