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What the Next Generation Needs Is Math, Not Programming

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Re: What the Next Generation Needs Is Math, Not Programming

#41
Of course, mathematics education in public schools is notoriously awful, though quality obviously varies across jurisdictions.

I can't see programming education faring better, especially considering that the emphasis is on "code". This is a horrible thing to put at the forefront, because it limits your view to the particular set of language constructs you use as opposed to broader properties of computer systems and computation. It is best to start by a rundown of high-level computer architecture (von Neumann and Harvard) so as to understand basic machine instructions and types, progressing into OS fundamentals (something like The Design and Implementation of the FreeBSD Operating System, though condensed), then briefly into compiler construction and language VMs, onto practical usage of a CLI shell, the various ways of representing resources and IPC, data structures and how to use them in forming basic services (like a message/event broker bus or publish-subscribe with named pipes and the file system under a standard interface/toolkit), build systems and so forth. Ideas and concepts with code on the side.

Obviously these are rushed examples, but the point is that code-centric computing education in public schools will probably backfire by creating people with just enough knowledge to have extremely warped views of software. Unless your goal is to turn kids into ALGOL monkeys who can't see beyond the mnemonics, I suppose.

You might say this would be too complex for public schools to implement. I agree, which is why it should stay out. Do it right or don't at all. Bashing out Java code alone is nowhere near as relevant as some people seem to think it is.

Re: What the Next Generation Needs Is Math, Not Programming

#42
post #37

> Today, we can get away with ‘knowing’ how Google works without understanding what a ‘principal eigenvector’ is. Tomorrow, we need to absolutely know that. Part of the advancement of technology is that fewer and fewer people actually understand how stuff works. What percentage of the population has any notion of how a computer works under the hood? How many people understand how our national power grid works? Our se…

Agreed. Its an old story - warriors say we all need to think like warriors; merchants say we all should think like merchants; engineers are getting on that bandwagon.

Re: What the Next Generation Needs Is Math, Not Programming

#43

What the next generation really needs lessons in: - Humility - Empathy - Patience - Self restraint and control - Mindfulness/Awareness - Disappointment - Resilience - Communication - Listening - Learning - Financial independence and literacy - Critical thinking - Problem solving - Self acceptance Then we can focus on what area the person can best contribute in. Not everyone is going to suited for a job in programming…

I don't think you can teach useful levels of Critical Thinking without a solid understanding of Math, Science, and Human behavior. But, programming can also help people think more deeply about problems.

There is this huge realization that computers and by extension reality does not care about what's in your head only what is. You can argue that Math has similar levels of precision, but once people start getting partial credit some of that harshness is lost.

That said, I don't think school should overly focus on directly useful skills or even what people studied in the past. How many lifetimes of highschool sudents where wasted learning how to identify and name Regular Polyhedra?

Re: What the Next Generation Needs Is Math, Not Programming

#44
According to the Curry-Howard correspondence, all mathematical proofs are actually programs. This is normal. A proof is a series of steps, and if you unambiguously describe these steps, a computer will obviously be able to execute them. Furthermore, since Alonso Church successfully proposed a Turing-complete axiomatization based on just functions (even numbers are just functions), a computer program is clearly a mathematical object. An alternative axiomatization, Zermelo-Fraenkel, is based on sets. There is probably no better playground for sets than using a relational database. SQL is pretty much Zermelo-Fraenkel on steroids. In other words, large areas in math go into supporting the discipline of computer programming already. I do not believe that everybody would have to spend more time with areas in math for which no useful applications exist and that we are therefore unlikely to use in programs.

Re: What the Next Generation Needs Is Math, Not Programming

#45

What the next generation really needs lessons in: - Humility - Empathy - Patience - Self restraint and control - Mindfulness/Awareness - Disappointment - Resilience - Communication - Listening - Learning - Financial independence and literacy - Critical thinking - Problem solving - Self acceptance Then we can focus on what area the person can best contribute in. Not everyone is going to suited for a job in programming…

What the next generation really needs is an economy where everyone can make a decent living with a modest effort, without having to desperately "outcompete" other job seekers. The US had that kind of economy at some point. Since we haven't lost any arcane secrets since then, it must be still achievable today.

Re: What the Next Generation Needs Is Math, Not Programming

#46
post #43

What the next generation really needs lessons in: - Humility - Empathy - Patience - Self restraint and control - Mindfulness/Awareness - Disappointment - Resilience - Communication - Listening - Learning - Financial independence and literacy - Critical thinking - Problem solving - Self acceptance Then we can focus on what area the person can best contribute in. Not everyone is going to suited for a job in programming…

I don't think you can teach useful levels of Critical Thinking without a solid understanding of Math, Science, and Human behavior. But, programming can also help people think more deeply about problems. There is this huge realization that computers and by extension reality does not care about what's in your head only what is. You can argue that Math has similar levels of precision, but once people start getting parti…

Partial credit on a math problem is pretty analogous to still getting paid even though your code has bugs.

Re: What the Next Generation Needs Is Math, Not Programming

#47
post #37

> Today, we can get away with ‘knowing’ how Google works without understanding what a ‘principal eigenvector’ is. Tomorrow, we need to absolutely know that. Part of the advancement of technology is that fewer and fewer people actually understand how stuff works. What percentage of the population has any notion of how a computer works under the hood? How many people understand how our national power grid works? Our se…

I agree to an extent but it's also very scary that some knowledge can become so rare it's more diluted than homeopathic medicine.

In a world where very few know how some ubiquitous technology works, it's easy and cheap for some corp or govt to get a monopoly on that knowledge (just hire everyone). And with a monopoly on it, you can modify it to your liking and suddenly we're in a dystopian novel and nobody knows about it.

Yes, yes, tinfoil and all that. It's theoretical, but is it really that far off?

Re: What the Next Generation Needs Is Math, Not Programming

#48
post #46
post #43

Earlier quoted context omitted.

I don't think you can teach useful levels of Critical Thinking without a solid understanding of Math, Science, and Human behavior. But, programming can also help people think more deeply about problems. There is this huge realization that computers and by extension reality does not care about what's in your head only what is. You can argue that Math has similar levels of precision, but once people start getting parti…

Partial credit on a math problem is pretty analogous to still getting paid even though your code has bugs.

... or designing a bridge that looks nice, but falls down in the wind.

Don't get me wrong I think we could just teach LOGO or other pure educational language for a few months. The goal IMO should be critical thought not jobs. https://en.wikipedia.org/wiki/Logo_(programming_language)

Re: What the Next Generation Needs Is Math, Not Programming

#49
post #37

> Today, we can get away with ‘knowing’ how Google works without understanding what a ‘principal eigenvector’ is. Tomorrow, we need to absolutely know that. Part of the advancement of technology is that fewer and fewer people actually understand how stuff works. What percentage of the population has any notion of how a computer works under the hood? How many people understand how our national power grid works? Our se…

Agreed. Its an old story - warriors say we all need to think like warriors; merchants say we all should think like merchants; engineers are getting on that bandwagon.

It is rare that a population has a long term sustainable soldier/war economy. Merchants have always needed supporting trades (farmer's for food and raw material, sailors for shipping, for example).

Today we have enough technology that an engineer can build a soldier or a merchant (or a farmer or a sailor). We are all familiar with drones and vending machines.

It is important that an engineer not constrain his thinking though. Neither of these replacements does everything a human can do. Sometimes a soldier takes a bullet for a civilian and sometimes a merchant haggles and gives discounts to needy.

Even though these replacements are not perfect they still compete with humans for jobs. We are still a long way from creating a robot engineer. If you want a job that won't be replaced quickly think like an engineer.

We are also closer than ever but still a long way from having a robot doctor or lawyer and will likely be requiring humans for anything resembling a bedside manner or sympathy. Hopefully there will be jobs alongside these artificial replacements for human experts for some time.

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