Contents of RDA



While it may or may not be reasonable to teach Arithmetic to young children the way it is usually done in elementary schools, in the case of adults, particularly "developmental" students, it is certainly not reasonable to reduce it to a set of recipes . This for a variety of reasons:
For a more detailed discussion, see Chapter Thirteen.


Reasonable Decimal Arithmetic (RDA) is based on the following premises:
The reverse engineering used to specify the most economical prequel to Lagrange Differential Calculus so as to get an A2DC sequence first led to the following algebra 
and, then to the following arithmetic:

1. Decimal-Metric Number-phrases. RDA starts from the necessity to represent real-world collections of items which requires the notion of number-phrases, that is both a denominator to record the kind of items and a numerator to record the number of items. However, if the real-world processes are based on the cardinal aspect, one-to-one correspondances, the paper procedures are based on the ordinal aspect, counting. Also, signed numerators are introduced almost from the start. There are then two issues: The first issue is with large collections which force us to bunch the items and then count the bunches. This gives us decimal number-phrases and is best seen in the context of the metric system with money as its embodiment.

2. Approximation. The second issue comes up when we deal with amounts of stuff as opposed to collections of items, for instance water as opposed to rocks. This forces us to introduce the idea of approximation. While this is usually done almost as an afterthought, here, inasmuch as arithmetic is to represent real-world situations, the idea of approximation is totally natural and, as a prequel to Lagrange Differential Calculus, an absolute must.

3. Arithmetic Functions. They occur quite naturally once the distinction has been made between states and actions. Strictly speaking, this may not be necessary to a "profound understanding of fundamental arithmetic". However, it certainly facilitates matters and of course helps considerably the flow in the framework of A2DC.

4. Comparisons and Operations. This is probably the more conventional part of RDA except that it turns out that the four operations are seen here as unary operations, in other words as functions

Even though the above contents are strictly what is being implemented, the contents architecture is another story and it is in fact the table of contents which is the most difficult to develop and, in fact cannot be ascertained independently of the actual implementation. To see what the current state of the contents architecture, please look at the list of downloadable chapters.
So called "Standard" topics such as percentages, ratios and proportions, etc usually found in current Arithmetic textbooks are absent because of: