I love all the topics you present here. I especially liked that you would have the students evolve the ideas themselves in probability. For example, examining the debate between the frequentists and the conditional probabilists would be one. How Poisson incorporated the idea of time into the binomial distribution. In my experience these ideas are given as static truths at point blank range, without any background or explanation. Eventually, this needs to be re-incorporated into the usual teaching methods. I believe for instance, that we need to minimize memorization and increase understanding; especially in areas that were presented as static truths. It may take longer, and call for extracurricular activities, or possible sacrifice of some material for saving time. Why are the proofs of Euclid given in the order that they are given, and how does this extend logical thinking. Another instance, why were the ideas of Galois and Abel ignored by the existing establishment (this is true for other topics as well). One person could pose as Cauchy, holding to his already established standing and the other could be Galois, trying to get him to accept an even more advanced understanding of the meaning of algebra. Critical thinking needs to be revved up; especially in a day and age where we are going to need a lot better thinkers, and the nature of work has changed. If students come up with truly original ideas, possibly they could be incorporated into a body of work that would extend understanding, answer many unanswered questions, and extend respect for the subject matter itself.
+1
Great ideas well explained!
I love all the topics you present here. I especially liked that you would have the students evolve the ideas themselves in probability. For example, examining the debate between the frequentists and the conditional probabilists would be one. How Poisson incorporated the idea of time into the binomial distribution. In my experience these ideas are given as static truths at point blank range, without any background or explanation. Eventually, this needs to be re-incorporated into the usual teaching methods. I believe for instance, that we need to minimize memorization and increase understanding; especially in areas that were presented as static truths. It may take longer, and call for extracurricular activities, or possible sacrifice of some material for saving time. Why are the proofs of Euclid given in the order that they are given, and how does this extend logical thinking. Another instance, why were the ideas of Galois and Abel ignored by the existing establishment (this is true for other topics as well). One person could pose as Cauchy, holding to his already established standing and the other could be Galois, trying to get him to accept an even more advanced understanding of the meaning of algebra. Critical thinking needs to be revved up; especially in a day and age where we are going to need a lot better thinkers, and the nature of work has changed. If students come up with truly original ideas, possibly they could be incorporated into a body of work that would extend understanding, answer many unanswered questions, and extend respect for the subject matter itself.
Yaayy, here comes my evening entertainment 🫶 thank you for sharing these!