I'm reading a certain set of kindergarten/lower primary maths textbooks that is written by North American authors for a European 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 Italian? Or a Italian 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 Italy? 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.


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?

  • 2
    I'm not sure this is on topic as it the question about squares being rectangles is more on the mathematics teaching side rather than the linguistic side. – egreg Mar 23 '18 at 8:14
  • @egreg How was it on topic for all the other language SE sites I've posted this question in? – BCLC Mar 23 '18 at 8:14
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    You only cite the post in the Korean language site and the answer says “it has nothing to do with Korean language”. – egreg Mar 23 '18 at 8:19
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    What is an “oblong” in English? – DaG Mar 23 '18 at 8:52
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    @DaG 'Rectangle' refers to either 'oblong' (rectangle that is not a square) or 'square' (rectangle with equal sides) – BCLC Mar 23 '18 at 8:54

In Italian, a rettangolo is any quadrangle with four right angles (including squares), a quadrato is any quadrangle with four right angles and all sides the same length.

For the sake of completeness, a rombo is a quadrangle with all sides of the same length (so it includes quadrati); a parallelogramma is a quadrangle with the sides pairwise parallel (so it includes rombi, rettangoli and quadrati), and a trapezio is a quadrangle with (at least) two parallel side, so it includes all of the above.

How this translates to any given variety of English, is out of this site's scope.

  • DaG, thanks! 1. Is there any Italian word for quadrangle with four right angles excluding squares? 2. To clarify, 'rectangle' and 'square' translate to, respectively, 'rettangolo' and 'quadrato' ? – BCLC Mar 23 '18 at 9:01
  • Not officially, @BCLC. Then again, probably the mental image of a rettangolo might be given for many people by something with unequal sides, but that is not in its definition, nor there is a specific term for rettangoli with unequal sides. See here a Venn-like inclusion diagram of the different quadrangles in Italian. – DaG Mar 23 '18 at 9:17
  • Thanks so much DaG! Finally, for completeness, would you say it's unlikely that this issue is with language instead of simple geometric misconception because Italian, like Spanish and Korean, doesn't have a word for inclusive rectangle? – BCLC Mar 23 '18 at 9:21
  • @BCLC: It might well be that an Italian not too conversant with mathematical terminology assumed that a rettangolo has to have two pairs of side of different length, and transferred this to “rectangle”: if you do a Google search for rettangolo, you'll be shown almost only oblongs, since every page explaining stuff about rectangles tends to show a “generic” one, which may breed this misconception, since Italian doesn't have a specific word for oblongs. (You'll be also shown right triangles, which in Italian are triangoli rettangoli.) – DaG Mar 23 '18 at 14:41
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    @DaG: At least the definition of "rettangolo" in the main Italian dictionaries (except for De Mauro) is correct. I was shocked when I read the wrong definition of "rectángulo" in the "Real Academia Española" dictionary linked in the answer to the same question on Spanish.SE. I'm afraid this shows the lack of mathematical and in general scientific culture of my country. :( – Charo Mar 23 '18 at 15:59

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