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I'm reading a certain set of kindergarten/lower primary maths textbooks that
is written by North American authors for an Asian company.

Whenever students are asked to identify the number of rectangles in a given
picture, the answer booklet gives the number of oblongs instead of the number
of rectangles.

While the topic may be too advanced for kindergarten students, the maths
textbooks indeed explicitly say at the bottom of the first page of a textbook
at the very first level to tell students that squares are special types of
rectangles, where levels 1-4 are for kindergarten students.

Additionally, the accompany guide for teachers devotes a whole page of
discussion as to how to teach that squares are special types of rectangles.
There's even a paragraph about teaching to kindergarten students. The
authors/some of the co-authors of the teacher guides are also authors/co-
authors of the textbooks. They have also said that if students are taught that
squares are not rectangles, then they will have misconceptions later.

Perhaps, the ones who wrote the answer booklets were not fluent in English
while the ones who wrote the textbooks were.

For example

> [picture with 4 circles, 2 triangles, 3 square rectangles, 2 oblong
> rectangles for a total of 5 rectangles]
>
> Circle ___
>
> Triangle ___
>
> Square ___
>
> Rectangle ___

The answer key would give only the numbers:

> 4
>
> 2
>
> 3
>
> 2

So, the last line is wrong since it should be 5.

Could this happen in Japanese? Or a Japanese dialect? I mean, is there
something specific about the translations of any of the following words
'rectangle, square, oblong, quadrilateral, quadrangle, parallelogram,
trapezoid/trapezium, rhombus' that would cause such confusion? I guess the
translator/s thought that when English speakers say 'rectangle', it means
'oblong in their language/dialect, but I don't see that as specifically a
problem for this particular language.

By the way, are squares considered rectangles in Japan? Apparently, these
things can vary by state, curricula, culture, time, etc. Please provide a
document from the education department of your government or something.

P.S. I'm a monolinguist.

Related:

[In Korea, are squares considered
rectangles?](https://korean.stackexchange.com/questions/3394/in-korea-are-
squares-considered-rectangles)

[Are kindergartners supposed to be steered from squares being
rectangles?](https://matheducators.stackexchange.com/questions/13831/)

[In what curricula are “rectangles” defined so as to exclude
squares?](https://matheducators.stackexchange.com/questions/13700/in-what-
curricula-are-rectangles-defined-so-as-to-exclude-squares)

[Why do we have circles for ellipses, squares for rectangles but nothing for
triangles?](https://math.stackexchange.com/questions/2249741/why-do-we-have-
circles-for-ellipses-squares-for-rectangles-but-nothing-for-tria)

[What are/should kids (be) taught about the colour of the
sun?](https://physics.stackexchange.com/questions/394471)
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translation word-choice nuances terminology mathematics
Could a translation error lead to squares to not be considered as rectangles?
A "square" is a specific case of a "rectangle." This is a geometric problem,
not a linguistic one. Geometry has no language--a square is always a
rectangle, no matter what.

If they do not include squares in the count of rectangles, they need to
mention that the count of rectangles should not include squares. But you said
this was for kindergarten-level readers, so maybe they don't think that
children know that squares are also rectangles? If that is the case, then it's
yet another problem entirely of "when do we teach children the specifics of
geometry." TL;DR We adults might consider squares rectangles, but perhaps
small children do not.
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The situation is a bit different in Japanese. In the first place, _rectangle_
in Japanese math jargon is 長方形 (lit. "oblong square") so that it's even less
intuitive than English, but for better or worse, it's not so basic a word that
kindergarteners would learn.

The most basic, vernacular word in Japanese to refer to square-like shape is
四角 (lit. "quadrangle"). Though I personally have been thinking it be somewhat
synonymous to _rectangle_ , [a
study](https://www.jstage.jst.go.jp/article/jjep1953/30/2/30_147/_article/-char/ja/)
reports that most young children only refer to _square_ by that word. (Even
though we actually have a basic word exactly for _square_ : 真四角 (lit. "true
square").)

>
> 周知のように幼児は「さんかく」「しかく」という名称を知ってはいるが，これらを正三角形や正方形に対してのみ（若干名は二等辺三角形や長方形に対しても）使用可能で，不等辺三角形や不等辺四角形に対しては「三角でも四角でもない」「わからない」と判断することが非常に多い  
>  _As we already know, that while preschoolers know such terms "triangle" and
> "quadrangle", in most cases they judge them to be only applicable to
> equilateral triangles and squares (for a few also isosceles triangles and
> rectangles), and not to scalene triangles and irregular quadrilaterals *,
> towards which they answer "neither of them" or "not sure"._

* * *

* I mean the shape known as [_trapezium_ in NAm and _trapezoid_ elsewhere](https://english.stackexchange.com/q/65259/157006) in English. Translation error :)
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In Japanese, there are two sets of words we learn to describe various kinds of
quadrilaterals.

**Mathematical terms** are 四角形【しかっけい】 _quadrilaterals_ , 台形【だいけい】 _trapezoid_
, 平行四辺形【へいこうしへんけい】 _parallelogram_ , 菱形【ひしがた】 _rhombus_ , 長方形【ちょうほうけい】
_rectangle_ and 正方形【せいほうけい】 _square_. Some are specialized forms of others, as
shown below:

[![enter image description
here](https://i.stack.imgur.com/tC2hA.png)](https://i.stack.imgur.com/tC2hA.png)

If I remember correctly, Japanese people learn these terms in the 4th or 5th
grade. Technically speaking, all 正方形 are also 台形, too. People say yes if
someone asked "Is all 正方形 also 平行四辺形?" in math classes.

However, in reality, people usually use the most specific term when possible,
and unspecific versions are used when they really need them. 菱形のハンカチ normally
refers to a diamond-shaped handkerchief even though a 正方形 is technically a 菱形,
too. In most cases, this is not a _confusion_ but an _optimization_ ;
obviously, it's too bothersome to say 正方形ではない菱形の形をしたハンカチ or 角が90度ではない菱形のハンカチ
in daily life. Likewise, when I hear someone say 長方形 in everyday situation, I
usually assume it's an oblong rectangle.

That said, if I saw "the number of 長方形 is 2" in your example, I would still
argue that it's technically incorrect, too, because they call it a _math
textbook_! So it purely depends on the situation; the more the situation is
closer to math, the stricter you should be.

There is also "easier" or "elementary" set of words suitable for
kindergartners:

  * 四角【しかく】
  * 真四角【ましかく】
  * 長四角【ながしかく】 or 細長い四角

Adults also use them in non-math situations. 四角 (without 形) [usually refers to
squares](https://japanese.stackexchange.com/a/38517/5010) but sometimes
includes rectangles. We should not be too strict on 四角, and we should not use
these words if mathematical strictness is important. 真四角 specifically refers
to squares, and 長四角 specifically refers to oblong rectangles like envelopes.
After all, for kindergartners, people can easily avoid this problem by using
ましかく and ながしかく.
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