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> Just as you don't really understand how a CPU works until you've programmed in assembly, you don't really understand math if you haven't done hand-computation
by AndrewMoffat 15y ago
> Just as you don't really understand how a CPU works until you've programmed in assembly, you don't really understand math if you haven't done hand-computation, at least up to a point.
Conrad Wolfram addresses this very point in the video (11:30). He says that the most valid point that hand-calculating helps understanding is that teaching processes themselves helps understanding, but that there's a better way to do that: programming. In other words, programming a math solution is better for teaching math understanding that hand solving it.
In the end, I think the idea he's trying to impart is that the core of math is not calculation at all, it just seems that way because they've been intertwined for so long. But now that we have computers to do the tedious calculations, we can work on defining and exploring what math really is: how different conceptual intuitions are related
- alextp 15y agoAgreed, but only up to a point. To program it is fundamental to have a strong intuition as to what should happen, why, and how to get there. Doing that without some amount of manual computation is temerary.
- DanWaterworth 15y agoActually, I disagree. Programming is about building and using abstractions. It is not strictly necessary to understand how the abstractions are built. Case and point, how many web developers do you know who could outline the TCP/IP protocols in great detail?
- Aloisius 15y agoSpeaking as someone who's primary problem with math in school was poor handwriting, I would have much preferred to learn via programming.
- vidiviciveni 15y ago> In other words, programming a math solution is better for teaching math understanding than hand solving it. I completely agree. But couldn't this be said about education in general? Public schools seem to be stagnated in archaic methods of teaching.