I have been meaning to focus on this aspect of mathematics for some time. It is a topic I elaborated in my “Angular Momentum” post. But I also think it has something to do with the difficulties that normal folks have with elementary math, in particular, numbers. I thought I would dub it the Cheshire Cat Paradigm, involving the Cheshire Cat’s grin.
See the Cheshire Cat Paradigm.
(Update 6/7/2025) Contra Concrete Algebra
A recent posting has prompted me to address yet again my concerns about tying the learning of algebra so tightly to concrete objects and manipulations.