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What math textbooks for kids do you know that use Logo or similar languages with visual robots like Turtle (in "The Turtle Geometry") that demonstrate space motions, transformations of all sorts and stuff, and their matrix descriptions? Residue arithmetic, rational numbers, and symmetries of shapes and motions with a visual demonstration using a programming language with a compact enough syntax that you don't have to spend time explaining the structure of the language, and spend more time learning basic math concepts.

UPDATE: The main objective is to demonstrate motion, composition, reflection, etc. in mathematics using computer science.

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How a school math course in middle school grades is usually structured:

  1. Numeracy and everything related to it.
  2. Measurements.
  3. Description of motion.
  4. Objects of mathematics that describe other objects of mathematics.

If you look at the regular school program, the modern one, there's a gap along this pattern. First very long 1, then very little 2 and immediately 4, and 3 only in physics and very little at the end of geometry in the 9th grade.

Very little 2 is in 7th grade.

But there is a quick transition to 4, the so-called functional line.

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  • $\begingroup$ The language doesn't really matter, but it must be compact enough in order not to concentrate kids too much on the syntax and API, and focus them on concepts itself. It may be Logo, Scheme, C, Boxer, KuMIR, whatever. $\endgroup$
    – paus
    Commented Apr 2 at 6:48
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    $\begingroup$ Updated the question. $\endgroup$
    – paus
    Commented Apr 2 at 10:11
  • $\begingroup$ You might have better luck with this question on matheducators. Would you like me to transfer it? $\endgroup$
    – Ben I.
    Commented Apr 3 at 15:43
  • $\begingroup$ @BenI. yes, it would be helpful. $\endgroup$
    – paus
    Commented Apr 3 at 17:59

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I don't know much about math textbooks, but turtle logo is still around from the Python Foundation. Python is often used as a first language because it allows students to start programming with little syntax getting in the way, so if sounds like this is roughly what you're looking for.

The library in question is called turtle.py, and you should be able to use any logo- oriented textbook that you like with very little adaptation.

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  • $\begingroup$ The question is not about the programming language, the question is about the textbook teaching MATH (and the specific section of math I mentioned above) through the programming language. Such a language must have decent graphical library support and tools, work in REPL (like in Dr.Racket), easy enough to teach it in class with 30 kids in a row. $\endgroup$
    – paus
    Commented Apr 3 at 5:02
  • $\begingroup$ @paus Yeah, I don't have a real answer because I teach computer science. I was just adding a bit of side information in case it was helpful to you or future visitors. $\endgroup$
    – Ben I.
    Commented Apr 3 at 15:42

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