Teach kids basic arithmetic WELL, teach them logic in a fun way, find a way to get them to like reading and think critically about what they read. That's fine for me. I'd do away with all the rest of math (algebra, trig, etc) and have it as optional in high school. Really, if you got the stuff above right as a kid, you don't need to learn trigonometry if you don't want to at the time.
What the Next Generation Needs Is Math, Not Programming
61–70 of 152 posts
Re: What the Next Generation Needs Is Math, Not Programming
#62According 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 math…
All things that exist are mathematical objects and programs. Algorithmic information theory asserts that my cup of coffee is actually a program. While mathematics is important to computer programming, for most practical purposes it is of limited utility unless you are inventing new computer science. Knowing how to use a relational databases correctly requires no formal set theory. Understanding how to build a massive…
Mathematicians need to be more open to accepting computer programs as results. It's one of the reasons we need better programming languages.
Re: What the Next Generation Needs Is Math, Not Programming
#63According 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 math…
All things that exist are mathematical objects and programs. Algorithmic information theory asserts that my cup of coffee is actually a program. While mathematics is important to computer programming, for most practical purposes it is of limited utility unless you are inventing new computer science. Knowing how to use a relational databases correctly requires no formal set theory. Understanding how to build a massive…
> Knowing how to use a relational databases correctly requires no formal set theory.
Very true, I guess. But the other way around, someone who has used relational databases, will immediately understand formal set theory and find it absolutely trivial. Another example would be regular expressions. Anybody who has ever used them will immediately recognize what Kleene's closure is about and effortlessly deal with it. I think that this is generally the case. If you first solve problems with tools that embody a particular theorem, and if later on you read up on that theorem, you will find that theorem trivially simple. In other words, math and computer science are only hard, when you have never used them. Since formal education does things systematically in the wrong order, students tend to consider math and computer science to be hard.
Re: What the Next Generation Needs Is Math, Not Programming
#64Not everybody needs to know how to do math beyond arithmetic (though the opportunity should be provided). The focus should be making sure everybody can understand the math, and especially statistics, they are presented with everyday.
You can't understand statistics with arithmetic. At least, not any more than you can understand quantum mechanics or tensor algebra.
Re: What the Next Generation Needs Is Math, Not Programming
#65Here's the challenge faced by strong students. At a recent science fair, a strong 8th grader presented a simulation where you could fly a rocket around a plant, with the ability to change gravity, thrust, etc. I asked if he had explored the math (since this was a soluble problem.) The answer "The math is too difficult - I do it numerically, much easier that way." There is great advantage in re-using the work of other…
There are whole subfields of mathematicians who would agree in spirit with "I do it numerically, much easier that way" :-)
Absolutely - numerically is they way to go in some fields, but without a deep understanding of the underlying limitations there will be no expansion understanding/knowledge. It's the old academic vs. practitioner argument.
Re: What the Next Generation Needs Is Math, Not Programming
#66What 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…
I think you're employing an extremely narrow definition of critical thinking.
The ability to question everything you read, hear and learn in search of the truth (what is), or, most likely, of more accurate or useful representations of it, is not dependent of your math or even science knowledge.
At the end of the day, intellectual curiosity and a willingness to understand things are what you need to get ahead.
Re: What the Next Generation Needs Is Math, Not Programming
#67What 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.
The "decent living" of past generations is still available today, but past generations were poorer than you think they were, particularly for those who don't come from white and privileged backgrounds.
Re: What the Next Generation Needs Is Math, Not Programming
#68What 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.
What's a "modest effort"? And when did we have an economy based on a "modest effort"?
Work has never been easier in the US than it currently is. Record number of office workers, minimal number of farmers, factory workers, and manual labor in general.
Re: What the Next Generation Needs Is Math, Not Programming
#69What 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…
Not exactly related , but my grandmother often tells my parents :
Pray to god that you and your children have long lives. Whatever comes afterwards , we can endure.
Re: What the Next Generation Needs Is Math, Not Programming
#70Earlier quoted context omitted.
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.
The "decent living" of past generations is still available today, but past generations were poorer than you think they were, particularly for those who don't come from white and privileged backgrounds.
Exactly. My father was dirt poor. Grew up sharing his bedroom with his 4 brothers. Never had a new piece of clothing except underwear. And that was just normal for everyone he knew. Being a farmer in the 50s and 60s meant you were frequently very poor.