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:

- It is almost impossible to keep all these recipes in memory and almost all students will agree to this—at least privately.
- The recipes need to
*fit*exactly the situation at hand or else they cannot be used. And they seldom do fit. - Memorization of recipes is a
*bad investment*as there is no way that anything further can be based on just memorization. - This creates a vast
*misunderstanding*in the mind of the students who equate learning with memorizing. - Children learn arithmetic over a period of years while adults must learn it over a period of weeks

Reasonable Decimal Arithmetic (RDA) is based on the following premises:

- The only way to
*learn*Arithmetic is to realize the*logic*of the way it is working. - Adults don't have all the time in the world and any
*realistic*course has to be minimal. - The study of arithmetic in college should be such as to facilitate the study of further mathematics.

and, then to the following

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.

2. Approximation. The second issue comes up when we deal with

3. Arithmetic Functions. They occur quite naturally once the distinction has been made between

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

So called "Standard" topics such as percentages, ratios and proportions, etc usually found in current Arithmetic textbooks are absent because of:

- The standard time constraints
- The desire to avoid a "mile wide, inch thick" coverage.
- The fact that these topics are historic remnants totally unnecessary to a smooth and mathematically correct development of arithmetic