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In other words it can't happen, unless everyone's parents know math

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Just discovered this: http://www.maa.org/devlin/lockhartslament.pdf

So, /sci/, how should math and science be taught ideally in schools?

So, /sci/, how should math and science be taught ideally in schools?

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In other words it can't happen, unless everyone's parents know math

In other words it can't happen, unless everyone's parents know math

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Same curriculum, just fucking explain what's going on. Explain what pi is, a constant, and how it relates to the area, rather than saying "plug in r and multiply". The standards are fine, but the big idea needs to be explained.

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>>5556437

Furthermore, Lockheart states that teaching students methods and formulas to solve problems but not giving them real problems that require a great level of though is a "sad" thing, but we can't expect kids to figure out how to find the area of a triangle given the area of a square; it's trivial to us, but that kind of stuff takes brilliant minds to figure out. The way many of my math classes have been taught is we're given some methods to solve problems, then perhaps on the test and the homework there will be a problem that employs these methods to solve, but perhaps it requires some more creativity. That's a fine way to teach mathematics. As a society, we have to teach the masses, and we have to teach them centuries of advances in maths; that's not something we can take our sweet time on.

Furthermore, Lockheart states that teaching students methods and formulas to solve problems but not giving them real problems that require a great level of though is a "sad" thing, but we can't expect kids to figure out how to find the area of a triangle given the area of a square; it's trivial to us, but that kind of stuff takes brilliant minds to figure out. The way many of my math classes have been taught is we're given some methods to solve problems, then perhaps on the test and the homework there will be a problem that employs these methods to solve, but perhaps it requires some more creativity. That's a fine way to teach mathematics. As a society, we have to teach the masses, and we have to teach them centuries of advances in maths; that's not something we can take our sweet time on.

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>>5556441

It's the same reason real analysis books exist, because it's not efficent(even if possible) to develop theory over again.

I believe proofs from base principles should be provided along with intuition on all subjects but it's not possible to develop theory again, to do so goes directly against the history of human advancement:using what someone else used as a basis and improving upon it.

It's the same reason real analysis books exist, because it's not efficent(even if possible) to develop theory over again.

I believe proofs from base principles should be provided along with intuition on all subjects but it's not possible to develop theory again, to do so goes directly against the history of human advancement:using what someone else used as a basis and improving upon it.

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>>5556436

Technically incorrect. What you want is *at least* one teacher per student. You can still have specialists, as long as they coordinate properly, and there is attention to the progress (or perhaps even the mind) of the student at all times.

This may some day be feasible with AI, or with extreme longevity and post-scarcity boredom. To a limited extent, I expect AI to come first; digital learning environments are receiving plenty of attention in didactics, voice recognition is getting better and better, etc. etc.

captcha: but sizzings

Technically incorrect. What you want is *at least* one teacher per student. You can still have specialists, as long as they coordinate properly, and there is attention to the progress (or perhaps even the mind) of the student at all times.

This may some day be feasible with AI, or with extreme longevity and post-scarcity boredom. To a limited extent, I expect AI to come first; digital learning environments are receiving plenty of attention in didactics, voice recognition is getting better and better, etc. etc.

captcha: but sizzings

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>>5556444

What's incorrect?

What's incorrect?

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Why can't everyone just learn maths and science on their own from reading books and doing their own experiments?

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>>5556449

Largely because of time constraints, enormous variability in interest levels in different subjects, and the law.

Largely because of time constraints, enormous variability in interest levels in different subjects, and the law.

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It's simple, we kill the Batman

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>>5556441

I think if possible, teachers should guide students into facts and formulas rather than just telling them.

Example with the triangle areas, have an activity where kids draw a triangle on a rectangular sheet of paper. Show them that for any of their triangles, you can cut it out and get another equal triangle with the leftover paper. The area of the two triangles must be the same as the original rectangle, so the area of one must be half the area of the rectangle. Done, do similar activities with cutting trapezoids and parallelograms and shit. Takes longer than just saying "Hey kid, memorize this shit," but anybody remembers things better when they're active and when they understand why.

Contrasting with Lockhart, I think memorization does have some place. Embedding multiplication early on would save them from counting on their fingers to figure out what 4! is.

And why for the love of fuck do we teach algebra 2, pre-cal, and linear algebra to the general public of kids? Those should be reserved for students actually planning to go into qualitative science. Regular required math should be more geared toward logic or basic combinatorics. Nobody outside of scientists just goes around cubing binomials or multiplying matrices, but people would benefit from actually knowing how to think logically or knowing about grouping and counting things.

I think if possible, teachers should guide students into facts and formulas rather than just telling them.

Example with the triangle areas, have an activity where kids draw a triangle on a rectangular sheet of paper. Show them that for any of their triangles, you can cut it out and get another equal triangle with the leftover paper. The area of the two triangles must be the same as the original rectangle, so the area of one must be half the area of the rectangle. Done, do similar activities with cutting trapezoids and parallelograms and shit. Takes longer than just saying "Hey kid, memorize this shit," but anybody remembers things better when they're active and when they understand why.

Contrasting with Lockhart, I think memorization does have some place. Embedding multiplication early on would save them from counting on their fingers to figure out what 4! is.

And why for the love of fuck do we teach algebra 2, pre-cal, and linear algebra to the general public of kids? Those should be reserved for students actually planning to go into qualitative science. Regular required math should be more geared toward logic or basic combinatorics. Nobody outside of scientists just goes around cubing binomials or multiplying matrices, but people would benefit from actually knowing how to think logically or knowing about grouping and counting things.

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I think there should be more options in the math classes kids take. My high school used to have several options of English courses we could take in 11th and 12th grade, and I think it would be cool if they offered something like that for math. I'd say combine algebra and geometry (one semester each) 9th grade, and then precalc with some algebra 2 type stuff in 10th grade.

Then in 11th and 12th grade, you can choose your classes. Basic number theory, proofs, logic, probability, stats, calculus, linear algebra, that sort of thing. Some of that sounds more advanced but I think the average high schooler could handle it if presented correctly.

And obviously in general put more emphasis on intuition and understanding.

And teachers who care about math a bit more would REALLY help.

Then in 11th and 12th grade, you can choose your classes. Basic number theory, proofs, logic, probability, stats, calculus, linear algebra, that sort of thing. Some of that sounds more advanced but I think the average high schooler could handle it if presented correctly.

And obviously in general put more emphasis on intuition and understanding.

And teachers who care about math a bit more would REALLY help.

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>>5556465

Pre-cal and algebra II topics are necessary for calculus, which is a requirement for many, many majors. I definitely see what you're saying, though.

Pre-cal and algebra II topics are necessary for calculus, which is a requirement for many, many majors. I definitely see what you're saying, though.

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I'm a second year in uni, and I honestly can't remember a single thing I learned in middle/high school math. I got through algebra and geometry in 7th and 8th grade, and I couldn't name one thing I learned. I got through algebra 2 in 9th grade by cheating and doing trial and error on the poorly written tests. In pre calc and calc I learned a bit, but it's pretty hazy and didn't help me much for math in uni.

I took calc 1 last year, and I pretty much taught myself all the trig, geometry, and algebra I needed as I went along (sometimes it's a bit of a problem since I can't remember any trig identities).

This made me see that we could teach kids a lot more in the time we have. I am definitely not good at math, and I didn't even know I liked it until I retook calc in university. As long as the focus is getting kids to pass standardized tests, math education will always be inefficient and boring.

I took calc 1 last year, and I pretty much taught myself all the trig, geometry, and algebra I needed as I went along (sometimes it's a bit of a problem since I can't remember any trig identities).

This made me see that we could teach kids a lot more in the time we have. I am definitely not good at math, and I didn't even know I liked it until I retook calc in university. As long as the focus is getting kids to pass standardized tests, math education will always be inefficient and boring.

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all male schools, where hand picked youngsters will be introduced to the art of mathematics, rhetorics, philosophy, poetry, fencing, and gentle male lovemaking.

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>>5556494

>engineer who wishes he was a mathematician

>engineer who wishes he was a mathematician

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>>5556451

Are you saying that math and science is uninteresting to most people?

Are you saying that math and science is uninteresting to most people?

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>>5556531

demos and pretty pictures are interesting to most people.

But a lot of people can't be bothered to actually do the work needed to understand those pretty things.

To them reasing a page of a text book to understand something cool their teacher just showed them isn't worth it.

demos and pretty pictures are interesting to most people.

But a lot of people can't be bothered to actually do the work needed to understand those pretty things.

To them reasing a page of a text book to understand something cool their teacher just showed them isn't worth it.

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I am a student teacher. A lot of the content is good, but we just teach tricks or formulas and gone them little explanation.

For example, when graphing rational functions in a pre calculus class, the students are asked to identify the vertical and horizontal asymptotes, x and y intercepts, and holes, then to use this to graph.

The problem is that they are asked to do this without knowing why the graph will behave the way it does at an asymptote or a hole. Therefore, they are memorizing a ton of specific cases. ...I'll continue

For example, when graphing rational functions in a pre calculus class, the students are asked to identify the vertical and horizontal asymptotes, x and y intercepts, and holes, then to use this to graph.

The problem is that they are asked to do this without knowing why the graph will behave the way it does at an asymptote or a hole. Therefore, they are memorizing a ton of specific cases. ...I'll continue

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>>5556559

>isn't worth it.

How is it not worth it?

>isn't worth it.

How is it not worth it?

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Continued,

I personally am excellent at math, but if I were asked to memorize a ton of cases, eventually I would run out of space.

Apart from this, it also makes no sense that we move past units without ever allowing students to try and understand material that was already covered. Even if a kid gets a 90 on a test, he still might be missing something, but if a kid gets a 60 on a test, there is no way in Hell we can expect to build off of that knowledge. So rather than just say that it sucks for them and their grade, we should let them continue to battle through the subject until they understand and reward them when they do.

Those ideas could go a long way I believe.

I personally am excellent at math, but if I were asked to memorize a ton of cases, eventually I would run out of space.

Apart from this, it also makes no sense that we move past units without ever allowing students to try and understand material that was already covered. Even if a kid gets a 90 on a test, he still might be missing something, but if a kid gets a 60 on a test, there is no way in Hell we can expect to build off of that knowledge. So rather than just say that it sucks for them and their grade, we should let them continue to battle through the subject until they understand and reward them when they do.

Those ideas could go a long way I believe.