I disagree. The biggest thing that can help you learn something complex is by introducing it as it was discovered, and making someone feel like they could have come up with it on their own.
I don’t see why the history of discovery of something should be a particularly good way to rediscover it.
As a concrete example, if someone asks “how do we know the Earth is round” or “how do we know the planets orbit the sun”, one could go through ways to figure this out with math and minimal technology. But one could also point out that we have spaceships and probes and have actual pictures! You can see the Earth from a satellite or the ISS or the moon, and you can see the planets from space!
I agree that a process of rediscovery can be a useful teaching technique, but that doesn’t mean that rediscovering something the way it was first known to have been discovered is the right approach.
Another concrete example of the conflict is classical vs quantum physics which is nearly exclusively taught as the historical story of the quantum revolution or whatever you call it around 1900.
It would be trivial to skip the historical story and just "yo here's a FET transistor, a solar cell, and a vacuum tube, and the math just works, so get used to it" but nobody is ever taught that way.
Would be interesting for someone to attempt to write a non-historical physics textbook.
On the other hand, in IT, this style of learning is considered normal. "This is how the kool kids do things today. The past does not matter and probably didn't exist anyway. The end."
>On the other hand, in IT, this style of learning is considered normal. "This is how the kool kids do things today. The past does not matter and probably didn't exist anyway. The end."
And yet nand2tetris is one of the most common suggestions for people who actually want to figure out how computers work. Because you actually are posed with problems that real world engineers used to struggle with, and are allowed to play with the problem before finding out the answer. It builds a much deeper understanding than "it works like this because it is"
A downside to the modern approach is that “plug the equations into a computer and let it churn for a bit” plays a big role I think. This is seems a bit annoying from a teaching point of view
* “here’s what the computer came up with” doesn’t really build as much intuition as doing the equations out by hand
* there’s enough material in “how to plug it into a computer and make it run quickly” for a whole degree
> Would be interesting for someone to attempt to write a non-historical physics textbook.
I recall some prominent physicist saying they've never read Einstein's original papers on relativity; and they don't have any real desire to, since we understand it much better now, and have better examples, notations, etc.
Most physicists have never read them, fwiw, as interesting as they may be for their historical role. Most classic papers go unread, and it’s not a bad thing pedagogically. How things get sorted out is usually a huge mess and following the real history can be an enormous distraction (and can confuse and misdirect students).
While that is true, I would highly encourage everyone to read the original EPR (Einstein Podolski Rosen) it is so amazingly clear in its writing and can be understood even by laymen.
I've been interested for awhile in a distinction between math and philosophy here. Just descriptively speaking, we don't tend to teach math from original source (at least, not well-established math like you'd see in high school and early college). We don't teach calculus out of Newton/Leibniz/Cauchy/etc, we don't teach Fourier analysis out of Fourier, etc. Maybe geometry students will work from the Elements, but I certainly didn't.
But in philosophy, students do read everyone from Plato to Rawls in the original. There are (lots of) supplementary texts, of course, but they're companions.
I think that shows an interesting divide that the way we actually think about philosophy is not just a catalogue of arguments and positions one could take, but that the famous works are things worth reading unto themselves. There are a few math papers like that ("God Created the Integers" tries to anthologize them) but they are the exception rather than the rule.
“How do we know the world is round” is an interesting example to use. Eratosthenes got an estimate for the radius of the Earth that was pretty close using, I dunno, sticks and his eyeball or whatever ancient Greeks had.
The history is useful there, I think. First off, it is motivating — that’s a pretty big question, really shows what math can accomplish without much hardware. Second, it provides some sort of useful constraints if you are trying to work out the computation yourself. In a textbook the problems are always a bit artificial, some info will be given, some hidden. “Anything an Ancient Greek would have” is a bit more real-world, you can see where the constraints come from.
Erastosthenes did it by comparing the angle of the shadow cast by a stick on the summer solstice at noon in two cities, Alexandria and Syene (now Aswan), which are about 800 km apart. What was special about Syene was that it is so close to the Tropic of Cancer line that the sun would hit the bottoms of wells on the solstice, meaning that he only needed one stick, in Alexandria, and the distance between the cities, to do his estimate. His error was about 2%.
He's also famous for the sieve of Erastosthenes for finding prime numbers and figuring out the earth's axial tilt.
Darn, at some point I started imagining he had a protocol for synchronizing clocks over a distance. assuming the difference was in longitude. (E.g. Symmetric NTP over carrier pidgeon.)
Yea, recalling the book of that name might have contributed to my drift of recollection. Solvable earlier on land (but not sea) on terms of clock synchronization.
You can get a vaguely credible estimate by standing on a (small!) hill and measuring the distance to the horizon. Works better if you have a body of water handy, because bodies of water are nice and flat.
I think it can depend on the particular discovery whether we should teach "here's how the first person figured it out" or skip right to "here's how a later person found a much better, easier to understand approach".
Things were usually discovered in a confusing way that kind of made sense at the time, but had false starts and conceptual limitations driven by people still being in an older mindset when they were trying to discover it. A good teacher sands off those edges, leading to an oversimplified history, but not starting from the firm conceptual footing we only got later on still makes things overly difficult to grasp. Good teaching builds on concepts, even if history took a messier route.
>> Things were usually discovered in a confusing way that kind of made sense at the time, but had false starts and conceptual limitations driven by people still being in an older mindset when they were trying to discover it
To know this gives us some perspective on our own biases/limitations and not take things as gospel.
The way calculus was discovered was via highly geometric methods that are beyond the comprehension of people today. So the historical development of calculus needs to be modernized into modern notation and concepts, which at that point basically becomes examples.
While calculus is actually easy to develop and motivate, the way we "discover" it today is nowhere close to how it was originally discovered.
In my opinion, calculus is most easily motivated via physical examples. Here is a curve, it represents some information, and what are some things we'd like to know about this curve and thus the information it represents? What are some things we can do with that information? Such motivation can be more abstract and not rely on physical examples, but I think the physical examples help tie it to the so-called real world and somewhat mirrors, in spirit, how and why calculus was originally developed.
That's not the biggest thing that can help you learn something complex. Practice is the biggest thing. And there are many variations of what motivates people to practice.
