For people who want to learn or teach mathematics on the basis of reason …
Downloads of "Reasonable Decimal Arithmetic"
By the end of January 2012 I came to accept that the way I had been going was not going to work the way I want RDA to work and I completely redid the first four chapters---which took quite a bit of painful "reassessing". The results are available immediately below the following Notes.
June 25, 2012:
For a text to make sense to our students, there are two things that are necessary (Whether or not they are sufficient is another story):
On both counts, I have finally arrived at something I am not overly happy with but that I think I can live with without reaching for the delete key. More precisely, I hope that necessary local changes---by myself or by others---will not force global changes---which is what had been happening for the last several months.
- "Globally", there has to be a very clear "story line".
- "Locally", the language has to be very consistent because, at the stage they are at, the students will not take a chance by deciding that some language variation was accidental and they will automatically imbue any such linguistic variation with some hidden meaning and they will stall.
- Another thing which I think is important is giving background. For instance, the Roman System is an example of a system that didn't allow for computations and, from its shortcomings, one could see the way to go. Unfortunately, this sort of background was taking too much space and I think was mostly distracting. So, here I have tried to compress background matters to the absolute minimum. To compensate a little bit, I have inserted a number of links to Wikipedia.
What should follow now will be dealing with "comparing numbers" and "operating with numbers" and both should not be too hard to do inasmuch as the first chapters will support that.
June 29, 2012:
I have not uploaded the source because it would probably become obsolete in a very short time but I am of course more than willing to send it to anyone interested.
I am keeping the "2011 version" further down as a "witness" to see how, after Chapter 1, things started to crumble but also to give an idea of what will be "covered".
The latest version is immediately below this line.
Here is the current state of RDAv3.0 (It is fully linked and clicking on any line in any table of content will get you there.):
And, for those who prefer one thing at a time, here are the individual chapters in their current state:
PART ONE: THE LANGUAGE OF ARITHMETIC
Chapter 1 - Symbolic Systems This has in fact been stable since late 2011 and this 2013-09-23 edition is only the result of the nitpicking I have being doing each time I had been warming up for something else.
Chapter 1 - Symbolic Systems This 2014-07-22 edition is the result of the nitpicking I just did as I tried to read it as a beginner---with good will---would.
Chapter 2 - The Basic Ideas Stable as of June 25, 2012.
Chapter 2 - The Basic Ideas This 2014-07-27 edition is just the result of some nitpicking with the intent of makeing the text a bit smoother to read.
Chapter 2 - The Basic Ideas This 2014-07-28 edition corrects what I consider to be a serious structural mistake as well as some bad terminology. Compare 2.3 Lists, 2.4 Representing Large Collections in the 2014-07-27 edition with 2.3 Bunch Lists, 2.4 Splitting Large Collections, 2.5 Representing Large Collections in this edition.
Chapter 2 - The Core Ideas This 2014-07-31 edition corrects a few more structural defects.
Chapter 2 - Symbolic Systems This 2014-08-15 edition corrects a few more structural defects.
Chapter 2 - Symbolic Systems This 2014-08-22 edition introduces zero, restructures list-phrases and edits "Amounts of Stuff". Hopefully it's done.
Chapter 3 - The Decimal System Stable as of June 25, 2012.
Chapter 3 - Decimal System 1-Representing Numbers This 2014-08-15 edition tries to regroup things in a "more logical way".
Chapter 4 - The International System Of Units Stable as of June 25, 2012.
Chapter 4 - Decimal System 2-Representing Amounts This 2014-08-15 edition is to bring things in line with the "more logical way".
The "2011 VERSION" as a "witness". A couple of chapters are still empty and most are "in progress".
PART ONE: THE LANGUAGE OF ARITHMETIC
Chapter 2 - Tally Mark Systems
Chapter 3 - Base TEN Place System
Chapter 4 - Metric-Exponential System
Chapter 5 - Counting
Chapter 6 - Comparing Collections
Chapter 6 - Basic Problems
PART TWO: THE ARITHMETIC OF PLAIN NUMBERS
Chapter 7 - Comparisons
Chapter 8 - Translations
Chapter 9 - Subtraction
Chapter 10 - Multiplication
Chapter 11 - Division
Chapter 12 - Decimal Approximations.
PART THREE: THE ARITHMETIC OF SIGNED NUMBERS
Chapter 13 - Signed Number-Phrases
Chapter 14 - SignedComparisons
Chapter 15 - Signed Addition And Subtraction
Chapter 16 - Signed Multiplication And Division
Chapter 17 - Powers
Chapter 18 - Large Medium And Small