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 Korean? Or a Korean 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 Korea?


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?

  • squares are a special case of rectangles I suppose
    – user17915
    Mar 22, 2018 at 0:13
  • @user17915 Do you have a Korean Education Department of the Government document to support your claim please?
    – BCLC
    Mar 22, 2018 at 5:21
  • @user17915 Oklahoma is in the u.s. this is Korean s.e....
    – BCLC
    Mar 22, 2018 at 9:35
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    As you say these books were written by American authors, I'm a bit unclear where translation to or from Korean took place here? Mar 23, 2018 at 8:37

2 Answers 2


Could this happen in Korean? Or a Korean dialect?

Nah, not at all. This is just an obvious geometric concept. Korean language does not have a single word for a non-square rectangle, which might have caused such a translation problem if it existed; so it has nothing to do with Korean language.

The Korean terms have the same definitions with the English ones:

  • A quadrangle is a 사각형 (四角形), where means four, means angle, and means shape: a four-sided plane figure, especially a square or rectangle.
  • A rectangle is a 직사각형 (直四角形), where means perpendicular, and 四角形 means a quadrangle: a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides.
  • A square is a 정사각형 (正四角形), where means right and neat, and 四角形 means a quadrangle: a plane figure with four equal straight sides and four right angles.

  • 사각형 (quadrangle) ⊃ 직사각형 (rectangle) ⊃ 정사각형 (square).

It's just that they misused the term rectangle.

The thing is that they just used rectangle to mean one with unequal adjacent sides, which might not be a good practice, and it has nothing to do with linguistic inter-language terminology confusion.

  • Thanks K._! If I understand right, your opinion is that Korean doesn't have a word for non-square rectangle and hence this is probably not a Korean thing? So, to generalise, if we were dealing with a language without a word for non-square rectangle then the issue is probably not with the language? (I'm not as confident as you, so I include the word 'probably'! Haha)
    – BCLC
    Mar 22, 2018 at 10:09
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    @BCLC Maybe. Since they used rectangle to mean oblong rectangles, to assume this issue to be a wrong translation, there should be a word for an oblong rectangle in the original language, which might be the cause for the wrong translation. Mar 22, 2018 at 16:36
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    @BCLC Please feel free to accept my answer if you find it's helpful. :) Mar 25, 2018 at 16:49
  • 1
    waiting for bounty to end. During bounty period I hope to attract to attention to my question . Hopefully some of that attention will also be toward your answer. Thus, your answer will have further support, have review, be proven outright wrong or any combination of the aforementioned.
    – BCLC
    Mar 25, 2018 at 17:37


rectangle =직사각형 (quadrangle with four right angles)

regular tetragon=square=정사각형 (which is included in rectangle)

oblong rectangle (In the context, this is a rectangle which is not a square. But in Korea, I never heard a specific word. We do not use frequently. If we are in the situation, then we say 정사각형이 아닌 직사각형)

parallelogram =평행사변형 (quadrangle such that any side is parallel to the side in facing position)

trapezoid/trapezium=사다리꼴 (quadrangle such that there is a side parallel to the side in facing position)

rhombus=마름모 (quadrangle with four sides of equal lengths)

  • HK Lee, thanks. So, what exactly is your answer? Could this probably be a Korean-language/Korean-culture thing? Or probably not?
    – BCLC
    Mar 22, 2018 at 10:07
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    In general, 4, 2, 3, 5. But if your book answers 4,2,3,2, then it may be correct. I believe that the book distinguish rectangle and square.
    – HK Lee
    Mar 22, 2018 at 11:02
  • HK Lee, I mean, what is your answer to whether or not this may be a Korean-language/Korean-culture issue instead of a regular common geometric misconception issue? Also, edited question
    – BCLC
    Mar 23, 2018 at 3:05
  • Frankly, I do not catch your question exactly : (1) This may be Korean language issue ? Here what is this ? (2) To the last question in OP, I answer that the square is an example of rectangle in Korea (Yes, it is considered rectangle).
    – HK Lee
    Mar 23, 2018 at 3:56
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    HK Lee, I'm not asking about Korean children or adults. I'm asking about the Korean language. The thing is the answer booklets do not treat squares as rectangles even if the teacher guides and level 1 of the textbooks says squares are rectangle. My question: is it possible that the reason why this is so is due to some translation error related to the Korean language?
    – BCLC
    Mar 24, 2018 at 10:17

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