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Technology Review is running an unusual book review -- books about learning math, pure math, not applied math, https://www.technologyreview.com/2023/04/24/1071371/book-reviews-math-education/
The author admits to being adrift,
As a graduate student in physics, I have seen the work that goes into conducting delicate experiments, but the daily grind of mathematical discovery is a ritual altogether foreign to me. And this feeling is only reinforced by popular books on math, which often take the tone of a pastor dispensing sermons to the faithful.
An initial attempt led to a MasterClass by a "living legend of contemporary math", but the master is seated in a white armchair with no blackboards, pens or paper and does not enlighten.
A side story covers a writer for the New Yorker who plans a year to go back and learn the high school algebra/geometry/calculus that escaped him, but mostly fails. For backup he has a niece who is a math professor...but after months without getting it, he complains. Her answer?
"For a moment, think of it as a monastic discipline. You have to take on faith what I tell you." Where his niece and others see patterns and order, he perceives only "incoherence, obfuscation, and chaos"; he feels like a monk who sees lesser angels than everybody around him.
I won't spoil the end, but the author does make some progress with books by mathematician and concert pianist Eugenia Cheng, starting with "Cakes, Custard and Category Theory", where each chapter starts with an analogy to baking.
Unfortunately, for the SN audience, the article does not include any car analogies...
(Score: 4, Interesting) by RamiK on Sunday June 11, @05:18PM (4 children)
A professor in uni forced me to retake a test over using (yet to be taught) Laplace transforms to solve a test in ordinary (surely it wasn't complex ones as that would have been unavoidable? can't recall...) differential equations. So, in the redo, I developed the transforms I needed from the axioms that were on the material and they were forced to accept the answer.
I don't know how your teacher would have responded to that but I'm guessing they wouldn't have objected too fiercely...
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(Score: 3, Interesting) by JoeMerchant on Sunday June 11, @05:42PM (2 children)
I took every (Calculus II and up) math class offered in my uni math department, then I took one more from the physics department that taught three subjects: Green's functions (a way to solve some differential equations) something about closed path integrals around singularities, and something else about differential equations. The final exam counted as 60% of the final grade, and was pre-announced to be: select 5 of 11 questions. I never did learn how to use Green's functions, but probability told me that the likelihood of 6/11 questions being on Green's functions was slim. The prof also handed us sample previous exams to study, which I did.
Exam day arrives and 5/11 questions explicitly stated "using Green's functions..." and one of the remaining questions was a "solve this differential equation" which could have used Green's functions. However, I recognized the equation as being a simple transform of a question from a previous exam, so I proved my "solution by inspection/recognition" and flew through the other four questions. 5/5 perfect answers, and yet I still received a B...
Seems that the prof saw through my shortcut and, having failed to demonstrate knowledge of Green's functions 100% earns a B.
Україна досі не є частиною Росії Слава Україні🌻 https://www.pravda.com.ua/eng/news/2023/06/24/7408365/
(Score: 2) by RamiK on Sunday June 11, @05:52PM (1 child)
I think you sorta vindicated your high-school teacher there... :D
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(Score: 3, Funny) by JoeMerchant on Sunday June 11, @06:34PM
By the time I was taking Mathematics for Physics 517, I had learned how little the difference between an A grade and a B matters - to me, to my future, etc. I certainly enjoyed waterskiing on Tuesdays and Thursdays much more than mastering Green's functions could ever have done for me.
Україна досі не є частиною Росії Слава Україні🌻 https://www.pravda.com.ua/eng/news/2023/06/24/7408365/
(Score: 2) by bzipitidoo on Monday June 12, @03:14PM
I found the approach of deriving things took too long for tests. The timed format forces the student to memorize a lot more and consequently understand less, in order to be fast enough to finish the tests.
Math is one of my favorite subjects, because it is objective. The right answer is the right answer. Teachers who hate smart students have much less room for subjective bull excuses to justify giving a good student a bad grade. They can still do some crap ("you didn't show your work!") but as your anecdote shows, that's harder.