> Jonathan, > > I found your book description very interesting. I > have ideas and some scribbling on some parts of what > you want to cover. Would you have any interest in > working together, maybe on a paper or article, or > maybe even on the or a book? > > Bill > firstname.lastname@example.org
That sounds interesting. I can't say "yes" for sure at this point, but I'm definitely considering it.
I'm still debating as to what my arithmetic book ought to cover and what is still okay to include ("okay" in the sense that the stuff is not essential for an arithmetic course but may do some good to include it in the book for those students who might be interested or might need it).
Alain Schremmer notices that one problem with the book's organization is that it makes him wonder what the "story behind the mathematics" is, that is what the point of the development of this math is, where it leads, what it allows us to do. He has noted that I still appear trapped in the usual mode of presenting math as a series of disconnected topics rather than as a unified whole but that he can also tell that I'm trying to escape that mindset. That is, I believe he is thinking that, if I continue the book with this organization, I may make much further progress in escaping this mindset than most do but that I still won't escape that entirely.
I wonder where he gets that idea when he hasn't seen the text of the book. But maybe he can see something in that organization that tells him this fact whereas I don't see it.
Others can be found in that same discussion thread on Mathedcc. Actually, this post you are referring to was one that I had intended only for Mathedcc but then got accidentally copied here to Math-Teach. But since the question is of mutual interest to these lists, I suspect that perhaps it would have been a good idea for me to post this message here anyway! So let it stay here as well, I say.
One of those messages in this thread (it is not one of the two I had cited above), written by Alain Schremmer, makes a good point that perhaps we beat fractions to death. As he said, "Are fractions really necessary--other than code for division? If so, for what? (Aside from appeasing ignorant administrations.)" However, I don't think it hurts to include the development of fractions in my book that I had planned to develop anyway. Though fraction arithmetic might not have the needs today that it had in the past, fractions are still of mathematical interest. The same can be said of logarithms: Though they are not used as computational aids anymore, logarithms are still of mathematical interest.