It's absolutely useful to tell 4th-graders that x(t) = vt + x₀ (assuming no acceleration) since they're probably not on top of exponents yet.

It's also absolutely useful to tell 8th-graders that x(t) = at² + v₀t + x₀ since now they can handle exponents.

And it's useful to tell 12th-graders how to do the calculus to get x(t) for variable acceleration.

But that's also inaccurate for very large values of v (or a) due to relativistic effects. However, it's a very convenient simplification ("lie") for the vast majority of people in the vast majority of cases. It's probably possible to explain the relativity math to most 4th-graders, but for most of them it's a terrible use of teaching time and the old "rate times time equals distance" that was drilled into my head at a young age is much more practical.

> It's absolutely useful to tell 4th-graders that x(t) = vt + x₀

Why is this useful? Where and when are they going to use this equation until they learn the correct one?

In 4th grade I was writing very simple animations in basic on an Atari 400 and I absolutely would’ve used and understood this. I think this is a perfect example of perfect being the enemy of good. (And I think I’m mangling that phrase)

Fair enough.

Anything moving horizontally, I guess?

(admittedly that's not what tsm's post implied, but still...)

I have a working mental model for how electricity works that is useful enough to let me do (some) electrical work, figure out simple electronics circuits, have some sort of understanding of how electrical devices like light switches, light dimmers (of the mechanical and the electronic kinds), motors, batteries etc work, ... All of these are useful skills.

Yet I know for sure I do not understand electricity, as I do not even understand most of the answers given to me when I ask about whether electricity has mass. And, apparently, many people who claim to know about physics don't either, because I get all sorts of answers that contradict each other.

Should I not know what I do know about electricity because my mental model is a simplification? I think your position is needlessly absolutist. I don't think my teachers ever taught me 'junk', just a (useful) simplification/model of reality.

I remember learning that electrons actually move in the opposite direction that current is marked on diagrams because when they started drawing them they couldn’t tell which way it flowed and ended up being wrong, but it doesn’t actually matter as long as you are consistent about it so they kept it “wrong”.

According to Accelerated Expertise, it is even actively harmful, depending on goals. A lie-to-children can later be used by the student as a "knowledge shield" to reject evidence that their understanding is wrong.

Of course, if one does not expect any further learning in the field, a lie to children may be acceptable.

Well forgive me if I'm misunderstanding but it seems that all human knowledge being approximate it all comes under this heading. They are simply saying is that it may not be best to start with the most complex approximation.

It would be better to think how to appropriately simplify the state-of-the-art knowledge instead of going through consecutive confusingly wrong historical theories as often happens now.

I'm in the same boat. I always wondered whether the thing they are teaching next is really the way things are supposed to be or if it's once again simplified mumbo-jumbo..

The article says it's all simplified mumbo-jumbo. It's just a question of how simplified it is.

My wife already explained my kids I tend to complicate things, so I always start by saying, "in simple terms, yes [whatever whatever was asked]".