Paul Lockhart said it better than I ever could: https://worrydream.com/refs/Lockhart_2002_-_A_Mathematician's_Lament.pdf
A Mathematician's Lament
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8
24 days later
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@Math_Enthusiast
Alright, read it.
I get the gist, and it makes fair points, but I lean towards basic utility for math myself,
Though I don't think it's bad to include fun math methods, art, history.
69 days later
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@Lemming
Sorry this response is so unbelievably late. I haven't really been active on this site for a while. I think Lockhart actually addressed the point of basic utility quite well. His thoughts on this can be found at the end of page 11 on to the start of page 12. Regardless, I think I'll make my own similar but not identical commentary on this point: No one is using algebra and trigonometry in their day-to-day lives any more than they're using the skills they learned in art class. Why are we even teaching these subjects if we can't teach them in a way that actually develops creativity and critical thinking? For those who will need subjects like algebra, trigonometry, calculus, and beyond for their careers, it is only more important that they learn math in a way that they will actually retain and that teaches them to problem solve in a mathematical context. Every high-school student I have spoken to can only solve problems laid out in exactly the way that they were taught. Not one of them can solve an actual problem that isn't just applying a prememorized formula, and there is no reason for this. Lockhart's example of the area of a triangle is a great one: The level of reasoning here is certainly accessible to your average high-school student, and yet they just chant "one-half base times height" to themselves over and over so that they'll be able to find the area of a triangle on their next test. It should be reasonable to ask them why this is the formula, given that if they are to ever actually use this math it would be incredibly useful for them to understand where area formulas come from, and yet I can only imagine the number of angry parents a teacher would have on their hands for putting such an "unreasonable" question that "the students were never told they needed to study for" on the test. To quote a math teacher I knew who understood the disaster of math education: "[Kids] remember, regurgitate, and forget."
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@Math_Enthusiast
Why are we even teaching these subjects if we can't teach them in a way that actually develops creativity and critical thinking?
Good point raised.
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@Math_Enthusiast
Fair point that in ordinary life 'most people won't use advanced math.
One 'could argue it's a 'long aptitude test of sorts, that people with a greater ability in math are able to identify and slightly grow said ability in themselves.
'Some jobs involve a fair degree of math,
Medical for example, had math for dose amounts and times.
Pretty simple, but such is what I meant by 'basic utility.
Lot of people still do their own taxes, math there.
. . .
Still, aptitude test,
If I hadn't learned math is far from my best subject, I might have tried becoming a nuke tech.
. . .
While I think it is 'better for people to be able to be more freeform and understand 'why they use various formulas,
I'm not sure it's 'necessary for people using advanced formula in their jobs,
They just need to use the formulas relevant to their jobs and show their work in a standard method that everyone uses and can check their work.
To me,
Nonstandard methods seem more useful in people advancing math 'itself.
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@Lemming
To me,Nonstandard methods seem more useful in people advancing math 'itself.
As of 2022, the U.S. was below average in math but above average in science compared with other member countries in the Organization for Economic Cooperation and Development (OECD), a group of mostly highly developed, democratic nations: U.S. students ranked 28th out of 37 OECD member countries in math.
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@Lemming
@Math_Enthusiast
1 + 1 = 2 linear 1D math
One 2D triangle { closed shape } + one 2D triangle { closed } = four 2D triangles as a 3D tetra{4}hedral volume aka geometric synergetics.
When this latter occurs, then, 3 nodal points { events of the 2D triangle } + 3 nodal points { events of the 2D triangle } = 12 vertexial { 3 line conjunction of events } as the 3D tetra{4}hedron
If subdivided the three 3D tetrahedron with four lines, going to nuclear center point of the tetrahedron, get a vertex with a 4 line conjunction subdividing the tetrahedron into four internal tetra{4}hedra and 3 new 2D triangles of a lesser square area than the four surface triangles of the tet, ergo, a total of 4 surface triangles area { Q4-equal areas }, and four internal triangles of lesser area { Q4-equal areas, Sh-Equal, + Q3-Is-equal-lesser-area, } and total triangles 8.
Q = value of area question
Sh-ape { Sc-alene, Is-osceles, and Eq-uilateral
Angle = Ac-ute, Ri-ght, Ob-tuse }
Curved triangle shapes = Euclidean triangle, Spherical excess { Riemann } and Angular defect { spherically concave triangle }, Lobaveskian { planar hyber-bolic aka angular defect }
}
AI..." Based on their side lengths and angles, there are three main types of triangle shapes: scalene, isosceles, and equilateral; however, when considering the measure of their angles, you can also classify triangles as acute, right, or obtuse, making a total of six different types of triangles ".
We see how complexity can arise greatly when going from a rather simple, in one directional set of linear set of considerations, when going too 2D considerations.
Going negative on the same linear line can also increase complexity considerations, tho perhaps less than those that arise shape
Wave is a mathematical pattern { 2D open shape } only, composed of changing angles of linear set.
Complexity also becomes obvious when trying to use concepts { via words } to define this or that or the other. Welcome to world of Meta-space mind/intellect/concepts and sometimes ego in complex humans.
Therefore one plus one seemingly equals four according to the link.