1) Every year I fret and fume in private abt my undergrad maths students previous years "algebra" prep which basically thwarts what I need to get them to do. But I think its precisely the "engagement/application/utility" route Gates is advocating that has worsened the situation.
https://twitter.com/BillGates/status/1473727212629209096
2) Forcing the mind to think abstractly right from the beginning, through the algebraic structures - opens up the simple relationships between the structures and their properties - which "examples" route diverts frm and blocks developing the ability to think abstractly.
3) what I see is a dumb "AI" style pattern matching from "examples/applications" and not the simpler and more direct abstract thinking. If the "examples" dont match the issue at hand, "nearest neighbour" need not help - as the thinking needed to use it is not there.
4) or a blind application (again the "AI/machine learning" mind) of the "nearest neighbour" can trip up badly - as there is failure to recognize the fundamental aspects that might be different between the "closest match" and the issue at hand.
5) the serious consequence of this is a lack in developing logical skills, esp pursuing through a chain of logic and ability to unwind and restart from an earlier node once we can foresee an obvious dead-end. The manic avoidance of "proofs" is simply a reflection of this problem.
6) the power and beauty in algebra is uncovered once the abstract is grasped. and learning to approach it abstractly develops the human capacity for abstraction, and logic. Its a pity that we are going for the apparently more "engaging" but ultimately disabling route.
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