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:





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.


In Korea, are squares considered rectangles?

Are kindergartners supposed to be steered from squares being rectangles?

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?

What are/should kids (be) taught about the colour of the sun?

3 Answers 3


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

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 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.

  • If the visual were about convex quadrilaterals, it would be missing a kite (凧形) (and I guess strictly speaking isosceles trapezium/trapezoid).
    – Earthliŋ
    Aug 16, 2018 at 22:13
  • @Earthliŋ Yes, but a kite is not something Japanese kids learn at elementary school.
    – naruto
    Aug 17, 2018 at 8:20
  • 1
    @BCLC 四角形 is a math term (quadrilaterals) which includes everything in my picture. 四角 is not a math jargon. It's used even by kindergarteners just as broken laptop describes. (BTW, which paper?)
    – naruto
    Feb 4, 2021 at 23:33
  • 1
    @BCLC Ah, I see. But both he and I are basically saying "四角 (without 形) usually refers to squares and sometimes rectangles", so I'm not sure where he thinks the contradiction lies.
    – naruto
    Feb 5, 2021 at 2:29
  • 1
    @BCLC If you read my answer, you know naruto-san and me basically hold the same belief, until I found a paper that young children actually only recognize しかく as "square", so if that study is correct, our belief will be wrong, much to my surprise too. Feb 5, 2021 at 2:43

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 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").)

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 in English. Translation error :)

  • so what's the verdict: do you agree with naruto?
    – BCLC
    Feb 4, 2021 at 10:17
  • 2
    @BCLC Almost, except for his last paragraph, because it seems contradictory to the paper I cited. Feb 4, 2021 at 10:32
  • thanks for the clarification. (P.S.: his/her just in case)
    – BCLC
    Feb 4, 2021 at 23:00
  • @BCLC I mean, his in this case. At least according to themself. Feb 5, 2021 at 2:03
  • naruto is asking 'which paper?'
    – BCLC
    Feb 5, 2021 at 2:11

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.

  • I would argue that, in colloquial English usage, a rectangle is specifically a quadrilateral with right-angled corners, wherein two sides are longer than the other two. I.e., a rectangle in common usage is what the sample text describes as an oblong rectangle (a term I've personally never encountered), and thus is specifically not a square. So this is partially a linguistic problem, as it depends on contextual meanings of terms. In the vernacular: a square is not a rectangle. In geometry: a square is a specific kind of rectangle. Mar 21, 2018 at 22:00
  • 1
    I agree with you completely that when people say the word "rectangle," they almost never actually mean "square," even though a square is a rectangle. However, this is only in casual conversation; in the practice of specifically qualifying shapes, it no longer becomes acceptable to use casual meanings of words.
    – Kurausukun
    Mar 21, 2018 at 22:03
  • Kurausukun, thanks! I'll reread later but for right now: the very first level of the textbooks (levels 1-4 are for kindergarten students) introduces the concept that squares are special types of rectangles
    – BCLC
    Mar 22, 2018 at 4:36
  • If the book specifically mentions that squares are rectangles, then it's even worse that they don't count them. At the very least, if they have introduced the concept, they should at least explicitly state it one way or the other in their listing.
    – Kurausukun
    Mar 23, 2018 at 5:56
  • 2
    so where's the japanese here?
    – BCLC
    Feb 4, 2021 at 22:58

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