“All teachers through grade school at least should study your book (Teaching to Intuition). It would make a huge difference in how students could learn and enjoy math. Have you managed to get this book used in college math education classes?”
I received this comment from Fred Krogh who also put a link to my book on his website, Mathalacarte.com that said::
“We recommend Edric Cane’s book, Teaching to Intuition, as an excellent source for how mathematics should be learned. This is mainly for elementary mathematics, but the principles hold for all levels!”
Now Fred Krogh has no business reading Teaching to Intuition. Mathematically speaking, he is at the other end of the spectrum. He is a professional mathematician, not just someone who knows a lot of Math and applies it to new problems, but one who creates new Mathematics that others may learn and use. He worked for 30 years at NASA’s Jet Propulsion Laboratory where he was part of the team that designed and sent into space planetary probes, including the Viking probe, now the first man-made object to have left our solar system. Within a large team of engineer and physicists, he was Principal Mathematician, the pure mathematician that others could consult and rely upon.
In contrast, all the Math included in Teaching to Intuition is taken from the Elementary and Middle School curriculum, what everyone should know. I deleted from an early draft everything that might go beyond the most elementary pre-algebra topics. I took out an excursion into Trigonometry as possibly leading readers back to some long forgotten, no longer familiar territory. So Fred Krogh has no business reading my book. But his wife bought a copy, and he laid his hands on it. From his detailed comments, it is clear he ended up reading much more of it than could be expected. He e-mailed me: “I am very impressed… I could make a list of all that I like in your book, but then this email would probably be too long to send.”
Fred is the gatekeeper to much of the pioneering mathematics that was done at JPL, often by himself, during those years of active planetary exploration. His website Mathalacarte.com makes the topics available to other researchers and practitioners. Reading the list of mathematical algorithms and software available on the site is like trying to read a foreign language (Sample: Eigenvalues and Eigenvector values of a Hermitian complex matrix.) But he felt strongly enough about the kind of perspective described in Teaching to Intuition, and the need for it at all levels of mathematical endeavors, that he put a link to it on the home page of his site, the only outside link on it.
I am sorry that I cannot reciprocate and recommend ‘Hermitian complex matrices’ to readers of Teaching to Intuition. Like most of us ordinary humans, I just don’t have a clue.