> On Sep 14, 2010, at 7:03 AM, Jonathan Groves wrote: > > > Alain, > > > > Thanks for the insightful comments since I believe > these comments > > apply to virtually all of us. They do apply to me > far more > > than I would like to admit. > > So, how about a table of contents for Arithmetic? > > Hopeful regards > --schremmer
That's a good question. I had originally decided to write my book for my students as a supplement to a remedial course on arithmetic in case whatever schools I teach for still insist on using the standard, commerical textbooks--especially when I can tell that my book is not likely to appeal to others enough to use them for classes as replacements for the standard commerical textbooks. So I had planned to discuss whatever such courses normally discuss so that students can find a (hopefully!) good explanation of those concepts. The explanations of those concepts will, of course, be different, but the concepts themselves that I had planned to discuss are pretty much the same.
Here is what I have so far:
Chapter 1 is an introduction that gives my reason for writing this book and the goals I hope to accomplish with my book. I haven't written a draft of the introduction yet.
Chapter 2 is whole number arithmetic. Meanings of whole numbers, comparing whole numbers, and the four operations on whole numbers.
Chapter 3 is decimal number arithmetic. Meanings of decimal numbers, comparing decimal numbers, and the four operations on decimal numbers. I motivate decimal numbers via the need to make measurements. I also discuss the problem with decimal number division: The quotient of two terminating decimal numbers is not always a terminating decimal number. I briefly mention that we do not have such problems with fractions in that a fraction divided by a nonzero fraction is always a fraction.
Chapter 4 is fraction arithmetic. Meanings of fractions, comparing fractions, equivalent fractions, and the four operations on fractions. I mention connections between decimal numbers and fractions, which decimal number divisions and fractions do not have terminating decimal expansions and which do. In the section on multiplying fractions, I do mention that the fraction A/B is the same as A divided by B because multiplying A/B by B gives A. If the quotient is indeed A/B and if B is indeed the divisor, then multiplication should give us the dividend.
I had originally planned to create Chapter 5 on ratios and proportions, Chapter 6 on percents, and Chapter 7 on signed numbers. None of these chapters have been drafted thus far. Chapters 2-4 have been drafted but are only rough drafts thus far. I'm not sure if I want to move Chapter 7 on signed numbers to Chapter 5 or not. I'm not sure if I want to include the chapters on ratio and proportion and percents. Probably so. I'm not sure if I want to include anything else.
I had based on what is covered in a remedial arithmetic course by basing it on Argosy's course. I'm glad that the recent revision of the course had put decimal numbers before fractions rather than after fractions. What was especially silly is that the old course had discussed signed number arithmetic in Week 1 and then spent Weeks 2-4 discussing fractions and decimal numbers, but they have now moved signed numbers after decimal numbers and fractions and in fact after ratios and proportions and percents. I do want to go a bit further with ratios by not sticking with just binary ratios A:B. I don't remember where I had read this recently, but I do recall someone saying that one problem with ratios in school is that we stick with just binary ratios when, in fact, we can form ratios of any number of quantities such as 1:2:4:6 as a ratio of the number of cans of Coke and Sprite and Pepsi and Mountain Dew on sale at a store, for instance (I'm not sure if he called them "binary ratios" or "bivariate ratios").
However, one problem I had run into for test driving my book with my courses and with using it as a supplement is that Argosy's contract appears to say that they then would own my book if I use it in their classes:
"You acknowledge and agree that (1) the course(s) and all materials relating thereto, in whatever form, that you are being engaged to teach under this Agreement are and shall remain the sole and exclusive property of The Art Institute of Pittsburgh/Online (Argosy University); and (2) all models, curricula, programs, materials and systems designed or developed by you under this Agreement in connection with the teaching of such course(s) shall be and remain the sole and exclusive property of Argosy University. You also hereby grant to Argosy University an unlimited license to use any content that you create as part of teaching this course, such content to be provided in a form satisfactory to Argosy University that can be archived and that may be used by Argosy University in any future Argosy University courses. You certify that all materials you create in connection with teaching a course are original works and are not copies or derivatives of copyrighted works you explicitly instruct Argosy University otherwise and you have obtained written permission for using such works. You shall indemnify and hold Argosy University harmless for any penalty, claim, liability, deficiency or damages arising as a result of your use of copyrighted work or other violation of copyright laws."
Another problem is that different remedial arithmetic courses are organized differently, so the book as a supplement works best if the course is organized in much the same way, especially given--for example--that my chapter on fractions builds on the chapter on decimal numbers.
But now I'm wondering if I should write a book for the purpose of changing such courses and for the purpose of being used as the primary book for the course. Or perhaps I can find a way to write the book so that it can be used either way.