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Why are different words 算数 and 数学 used for mathematics at and after elementary
school? I understand that the quality is different in that, in the former, the
method of solving an equation is usually not allowed, and special calculation
methods that developed within the 和算 tradition are used, but is that different
enough to be considered as different academic fields? I don't see any more
difference between these two methods than the difference between number
theory, algebra, geometry, calculus, combinatorics, etc. which are all
subsumed under 数学.
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2012-05-31T02:00:37.313
5702
2012-06-01T15:07:26.860
question
words
Why are there two words 算数 and 数学 representing different fields?
I thought `算数` was just arithmetic (addition, subtraction, multiplication,
division) and `数学` was the whole scope of mathematics.

According to this dictionary definition, arithmetic is "the branch of
mathematics dealing with the properties and manipulation of numbers." But we
all know that math is way more than just numbers. And the definition says it
right there: the **branch** of mathematics. So `算数` would have to be a (likely
small) subset of all `数学`.
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2012-05-31T15:04:52.147
5708
2012-05-31T15:04:52.147
78
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answer
To preface, I think that this question involves something more than just the
structure of mathematics in Japan. It might be related to how mathematics are
organized generally.

The two fields should be characterized for clarification:

> 算数 can be characterized by: 現実的、日常的、具体的.
>
> 数学 can be characterized by: 空想的、非日常的、抽象的.

If 算数 refers to the branch of mathematics taught in elementary school which is
arithmetic, then that should be referred to specifically as "elementary
arithmetic". This is a subset of number theory, but with more constraints.

算数 allows for only the operations add, subtract, multiply, and divide
(足す引く掛け割る) which are specific algorithms. 算数 also usually imposes the
constraint of using only natural numbers with a standard log scale.
Considering this, the operations in 算数 traditionally allow for memorized
expected results with possible aid of tools (such as multiplication tables).

When being taught 算数, the goal or purpose in mind is accuracy (正確性). Whether
or not an individual is able to use the given numbers and operations
appropriately is what defines this field.

However, 数学 deals with the process of arriving to a mathematical answer
(論理の正確性). It is irrelevant whether the numerical accuracy is correct or not
because that is not the goal of what is being taught. (I'm not sure for Japan,
but in America teachers give points only whether the logical thought process
was correct in solving the problem regardless of the arithmetic)

As for why these two are treated like two independent fields, I would make a
guess that in the daily use of arithmetic (日常的) such a strong emphasis is
placed on whether the numerical operations are handled correctly. If you are a
cashier, your thought process regarding theories of mathematics are irrelevant
compared to whether you can perform basic operations with accuracy.

For this reason, 算数 (which I would refer to as elementary arithmetic) seems to
be a separate taught field due to the intended goals in mind.

EDIT: It might be useful to note that while arithmetic can be a field of
study, "the practical use of elementary arithmetic" probably does not have
enough merit to be a field of study. It has also been stated that elementary
arithmetic is a "calculation / computational discipline"

EDIT2: I'm not sure, but I found the term 暗算 (doing calculations mentally)
when reading about abacus' or 算盤. I'm not certain, but if 算盤 was used in
elementary school, it would allude to doing 暗算 being the focus of the course.

EDIT3: If 算数 as a course includes geometrical aspects (幾何学), then the a
similar distinction can be made with analytical geometry (解析幾何学).
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2012-05-31T16:46:07.450
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2012-06-01T15:07:26.860
2020-06-17T08:18:27.500
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answer