When are we going to adjust our educational system to produce thinking adults rather than trying to stuff students heads with things they'll never use. I am currently tutoring a young lady in calculus three, which seems to be more semi advanced linear algebra than calculus.
She has to learn how to find equations for lines and curves, how to find norms for five dimensional surfaces and tangent planes, equations for intersecting planes, and much more, ...and this is just 3 weeks into the course. I spent 40 years as an engineer and applied physicist and never needed to find equations of plane intersections or tangents to level surfaces.
I have no objection to asking students to gain understanding of complex
topics, but instead of focusing on underlying concepts the course(s)
devolve into learning procedures and tricks ( like looking for all the
ways one can arrange trig functions to come up with sin square plus cos
square terms) to get answers to examples that will never be encountered
outside the course.
Learning fewer procedures and doing fewer examples, but gaining insight into the true meaning of gradients and why level surfaces are important would be so much more rewarding and stimulating of intellectual growth.
Learning fewer procedures and doing fewer examples, but gaining insight into the true meaning of gradients and why level surfaces are important would be so much more rewarding and stimulating of intellectual growth.