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That Morris Kline quote reminds me of a book that I had enjoyed some years ago, "Arithmetic for Parents" by Ron Aharoni. The author goes from teaching college-level mathematics to introducing arithmetic to elementary school children. [1of4]

Throughout most of the book, he notes the physical meanings behind basic operations (e.g.: "subtraction" as either a separation of one amount from another, or a comparison, a "difference" betweeen two things without removal). [2of4]

It is very basic, but it renewed my love for applied mathematics and is a nice example of how tightly our abstractions can correspond to more familiar life experiences. Becoming aware of those relationships seems like a good way to develop a strong "mathematical intuition". [3of4]

Another really good example of this is the work of Saunders MacLane: https://en.wikipedia.org/wiki/Mathematics,_Form_and_Function#Mathematics_and_human_activities I would love to read the book that this table is derived from someday. [4of4]

Thanks for bringing up Aharoni's book - I'll have to give it a read. And that table from Mac Lane looks fascinating, I think it ties in surprisingly well to Morris Kline's overarching claim, that the origins and even the present motivation of mathematics were/are anything but abstract.