chat

You're missing the bit in the middle and being reactionary, comrade. This is done automatically, I did not consciously decide to do these, I noticed and am describing them.

You are correct that they are surface level and therefore appear superficial. The depth of understanding does not come with off-the-cuff dismissal. To quote Mao, "No investigation, no right to speak." Have you asked yourself, and engaged dialectically with your reactionary take, to say "If what this brainwormed Bateman comrade says is true, then how could it be true?" or "If 60% of what Bateman comrade said are good points, to my judgement and evaluation, could it be the other 40% are also good points? Or perhaps 30% of the remaining 40%?"

I likewise did not investigate your claims. You did not give much to investigate in your immediate comment. Obviously there are things which can be investigated. Your comment history, the historical context of your comments, the social structure and culture of this forum, etc.

You were dismissive, which is fine. You did not explain to me and I do not understand. I would appreciate critical comments as that would be most helpful for me, if you are so inclined.

A note, to quote a notable piece in mathematics education, Lockhart's Lament, he states the decrepit state of mathematics education in Amerika has to do with the introduction of concepts. He mentioned, unlike a painter who has an idea and assortment of tools and a challenge to make what they wish. Who struggles in their own manner and gets a result which they have an intimate knowledge of due to their experience. He says the mathematics student is given the finished piece of art and told what the meaning is.

Rather than give a problem and have students attempt to work it out on their own, they are given the entirety of the explanation and the sense of wonder, of learning, is lost. It is no surprise route memorization is practiced.

In my examples I did not strive for the utmost quality of examples as 1. the issues can be worked out by the reader and a novel solution which is most amenable to them can be found, and 2. there is limited knowledge on my part of the audience, or the reader, which for myself and in my experience makes communication difficult as my 'general style' without knowing the specific audience has been called 'incomprehensible' or 'incoherent'. Then I try to do my best to explain or communicate to the audience I believe there to be (to my and obviously others' dismay).