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I'm reading a certain set of kindergarten/lower primary maths textbooks that is written by 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 Chinese? Or a Chinese 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 China? Apparently, these things can vary by state, curricula, culture, time, etc. Please provide a document from the education department of your government or something.

Related:

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?

  • rectangle 长方形,square 正方形,we have equilateral/等边 triangles 三角形(isosceles/等腰 ones having only one axis of symmetry只有一轴对称) – user6065 Mar 21 '18 at 19:48
  • @user6065 oblong? – BCLC Mar 21 '18 at 19:51
  • see dictionaries, e.g. iciba (also Chinese editions of Wikipedia, or also search web using e.g. "中文 English word") – user6065 Mar 21 '18 at 19:51
  • @user6065 Anyhoo, what's the point? I know how to look up dictionaries and google translate, I guess. My question is how a translation error could result in mathematical confusion – BCLC Mar 21 '18 at 19:57
  • evidently everywhere mathematics (mathematicians) uses a more precise language, resulting in special cases subsumed in general ones, which may disagree with everyday language habits – user6065 Mar 21 '18 at 20:06
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My guess is it depends if rectangle is translated as:

  1. Oblong
  2. Quadrilateral

Could be the case that the teaching is for young children, where the word / concept of rectangle vs Oblong vs Quadrilateral might be difficult to understand, but it is essential for them to differentiate between square and Oblong

Others (parallelogram, trapezoid/trapezium, rhombus) does have a specific name and are not confused with rectangle.

  • But Alex what specifically about the chinese language is or isn't relevant here? Is this a geometric issue rather than a chinese language issue? why/why not? – BCLC Mar 22 '18 at 10:23
  • @BCLC as it's not mentioned i'm not sure if the origin content was Chinese or it's translated to Chinese. Either way if the word "Rectangle" is translated to/from Quadrilateral, then it make sense to include both "square" and "Oblong", and vice visa. – Alex Mar 22 '18 at 14:16
  • Alex about the origin content: I'm not sure myself. It could be 1. textbooks english originally then read by non-fluent english 2. textbooks non-english originally then translated then read by non-fluent english 3. non-english textbooks read (either by fluent or non-fluent of that language) though that's not the one i came across 4. in any case, it could be that the ones who wrote the answer booklets were not the ones who wrote the textbooks 5. any valid combination of the previous – BCLC Mar 23 '18 at 15:08
  • Alex in re 'Either way if the word "Rectangle" is translated to/from Quadrilateral': Thanks for your effort. What specifically are the mandarin words, and why? – BCLC Mar 23 '18 at 15:09
  • @BCLC Rectangle - 矩形 / 长方形. Quardilateral - 四边形. I've seen all these word used for describing an Oblong, and they are indeed differ from each other. – Alex Mar 23 '18 at 15:29
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Your question does not make it very clear, but since you are posing this question on the Chinese Language site, I am assuming the kindergarten books you are referring to are in Chinese, by American writers.

When you say "square rectangle", I assume you are referring to a shape with 4 equal sides and 4 right angles? And "oblong rectangle" is one with 2 pairs of equal sides and 4 right angles? To many people, the first shape is called a "square" and the second a "rectangle". Note that I am not trying to correct the usage of your English words. I am simply wanting to make sure we are talking about the same things.

In Chinese, a square is 正方形, rectangle is 長方形, and a shape that has four right angles without specifying the lengths of the sides is simply 方形. I am guessing the writers are trying to teach young children basic shapes with 3 angles 三角形 versus 4 angles 方形 versus no angle 圓形.

If they are asking for the number of 方形, then 5 is the correct answer, as both squares and rectangles fall under the more general shape 方形.

  • monalisa, yes to both your questions. Thanks! Please cite a source for your statement 'In Chinese, a square is 正方形, rectangle is 長方形, and a shape that has four right angles without specifying the lengths of the sides is simply 方形.' (Btw, I assume your 'rectangle' actually means 'oblong') – BCLC Mar 22 '18 at 10:21
  • A source for my statement is any English/Chinese bilingual dictionary. If you look up "rectangle", it will give you 長方形, meaning a shape that has 4 right angles and two pairs of equal-length sides. "Oblong" is defined as an elongated shape, such as a rectangle or an oval. So, no, my rectangle does not mean oblong; it means "elongated rectangle", which is a bit redundant, since "rectangle" is already an elongated shape. – monalisa Mar 22 '18 at 22:16
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I think I've found the confusion.

ABC English to Chinese's definition of oblong is

长方形(的)

but then their Chinese to English definition of 长方形 is

Rectangle


Back to what you said:

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.

It seems that oblong rectangles and rectangles are not specifically distinct in many Chinese dictionaries.

  • Thanks user3306356! Lemme clarify, so it is plausible that a chinese person read the text in english (whether it was 1. originally english or 2. originally chinese but then translated to english), saw the english word 'rectangle', looked up the dictionary and saw the chinese word for what they understood to be 'oblong' ? – BCLC Mar 22 '18 at 10:12
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    There's a couple ways this could have gone down. But, in Chinese it seems that 长方形 is an acceptable term for both oblong and rectangle (although it is strictly rectangle and oblong should be further classified). Some attention to detail was obviously lost along the way. – user3306356 Mar 22 '18 at 10:20
  • Re your post: Wait I looked up ABC. 长方形的 is oblong while 长方形 is rectangle. So, what's the problem here? The person confused appeal and appal? Also, what's up with the 的? that's supposed to be like apostophe-s or the Japanese の right? – BCLC Mar 22 '18 at 10:28
  • Re your last comment: user3306356, by 'in Chinese' I guess you mean in colloquial Chinese usage? Or Chinese culture/society or something? So, your answer is affirmative (related to the Chinese language)? Negative (not related to the Chinese language but eg 1. related to Chinese culture 2. related to regular common geometric misconceptions)? – BCLC Mar 22 '18 at 10:31
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    @BCLC Yeah you're right oblong is 长方形(的) while rectangle is 长方形. A good translation of 的 here is the English suffix -lar. Making 长方形的 something like rectangular. If you check out Oxford English to Chinese they just simply state oblong as 长方形. – user3306356 Mar 22 '18 at 10:32
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i think the question is not good enough. a principle of multiple choices question is: the choices are mutually exclusive, that they do not overlap.

though the question is asked about the number of each choice, there's strong tendency that answerer would think choices are mutually exclusive in the question.

that's why they said 3 square & 2 rectangle.

a better approach would be asking the number of e.g.: square, circle, triangle and pentagon. in which all are mutually exclusive here.

  • Thanks 水巷孑蠻! Sorry for the confusion. I edited the example. – BCLC Mar 22 '18 at 10:15

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