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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 a programming language with a good graphical library, working in REPL.

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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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    $\begingroup$ This version of the question should be closed, because it was first asked on cseducators and then transferred. (It should not have been asked on two sites.) $\endgroup$
    – Ben I.
    Commented Apr 4 at 11:44
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    $\begingroup$ Does this answer your question? Math textbook for secondary school using Logo like syntax $\endgroup$
    – Ben I.
    Commented Apr 4 at 11:45
  • $\begingroup$ @BenI. no. Take a look at "Turtle Geometry" by Abelson and diSessa. We're looking for something more contemporary covering arithmetics (from Peano axioms), basic algebra, and geometry. $\endgroup$
    – paus
    Commented Apr 4 at 12:08
  • $\begingroup$ Weird, I never made that comment. I was just trying to flag this one for closure (and redirect traffic that accidentally came here towards the one that should remain open) -- I thought I was flagging for the mods to come and clean it up, but apparently it also auto-generated a comment from me. $\endgroup$
    – Ben I.
    Commented Apr 4 at 14:46
  • $\begingroup$ Btw, I found another example of what I need: "Elementary functions: an algorithmic treatment" by Kenneth E. Iverson, author of APL. But it's more about adaptive courses for Calculus, not basic math. $\endgroup$
    – paus
    Commented Apr 4 at 19:40

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