The importance of math for the trades

There’s a cynical joke that goes “School never taught me how to go about buying a car or a house or paying taxes. But boy am I glad I know … the pythagorean theorem!” I always disliked the joke, but I think it’s fair to point out that school doesn’t do enough to teach life skills. I also used to think that people generally never really used math after school, so putting such an emphasis on math in school was not worthwhile, except for people who go into STEM fields. This was because I underestimated how crucial basic math knowledge can be.

If you asked me two years ago whether it was a reasonable scenario that someone was too bad at math to be a good welder, I would have said: no. I no longer think that, and not just because I’ve seen some people who are really, really bad at math. That’s not even the primary reason.

Instead, I learned a little bit about welding. (Not a lot, unfortunately. Seriously, I am so bad at welding. It hurts).

For instance: welders need to calculate material usage. That requires using fractions, maybe some elementary algebra. They need to know how to run their machines for what process and what material, and that requires reading charts and graphs.

practical-problems-in-mathematics-for-welders-applied-mathematics-5th-edition-93aba35c2759dbb0298c443bc8660e97Welders need to read blueprints. That requires the ability to convert between 3D and 2D representations. To go between these blueprints and real objects, they sometimes need to calculate areas and volumes. To read dimensions off blueprints, they need good mental arithmetic involving fractions. And they need a basic understanding of Euclidean geometry, including angles.

Then there’s also the math you need to run a business, or to not get screwed over by someone else. How many people can understand the mathematical arrangement of doing piecework? It turns out, not everyone, not by a long shot.

You may say that all of these skills — reading blueprints, planning material use, figuring out rudimentary finances — are tangential to welding itself. Maybe so, but they are required in order to be a welder worth hiring. They won’t help you put down a bead. But, surprise, they already have robots that can put down a bead like nobody’s business. You can only dream of welding as consistently as a robot. If you’re going to be a welder, you need to succeed at what the welding robot doesn’t do. Part of that is dealing with non-repetitive situations. And part of that is all the peripheral aspects of the job.

And yet, there are people who can’t do it. And yes, some of it has to do with not being able to do the math to figure out the material you need, or to read a blueprint*.

There are also specific mental blocks around multiplying fractions, and about using algebra with letters instead of numbers. And calculating things in 2D or 3D. And the people that have problems with this kind of math are going to have trouble being successful welders, automotive technicians, machinists…

What is someone who can’t get a welding job going to do for steady, secure, dignified work? There’s a sort of triumphant Tom Friedman-esque idea that the loss of low-skilled work doesn’t matter, because workers can be retrained into at least slightly-below-average coders, and get work. But you need more math than many people have in order to be a good welder. And you’re saying they’re going to be coders? I really, really don’t think that’s true.

*Interestingly, the way some people are bad at math isn’t the way I expected. Most people I’ve seen are actually pretty good at “mental math” up to a point. But they don’t perform the mental math in a conscious step-based way. Instead, it’s like a black box that spits out an answer. So if it gets past the point where they can intuitively guess the correct procedure, they are totally lost. For example, there are many people who can easily answer “If 2/3 of a number is 6, what is the number?” but can’t say how they got that answer. And that means that they can’t — even with using a calculator — answer “If 5/12 of a number is 40, what is the number?”

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