Why should kids learn how to use a compass and straightedge, and not rely on a drawing program?

The main point of the composition of the compass and the ruler is to give students an empirical inference about the axiom system. The accuracy of the actual drawing is basically irrelevant (unless it is sloppy to prevent visualization) - the important thing is to prove the accuracy of the ideal structure.

This axiomatic construction method was originally studied for historical reasons and is not a more general "analysis" of modern times but the current one related to "synthesis" axiomatic geometry being used by ancient Greeks It does not matter. "Style. Mathematics (such as Cartesian coordinates) But geometry is still a useful aid because it is a simple axiomatic system that can be a good way to learn to relate geometric instincts to accurate reasoning with close attention. It can be used for educational purposes.

For example, a student who learned how to make a half angle once, may be asked to try the triangle and use it to introduce the concept of proof of impossibility. This can also be used to show how subtle changes in axioms can influence provable / configurable things (for example, doubling cubes with compass and rulers It is impossible). Possible)

These are just some of the concrete ideas I think - a general idea is to use geometric reasoning and structure as a tool to teach logic.

A case study on how to not teach geometry - this may highlight some pitfalls to avoid - "Good teachings lead to bad results:" good "mathematics curriculum disaster"

The opposition to the assertion that "students do not need to use compasses and rulers, all shapes need to be created using a drawing program" is not everyone's access to the computer, so most If it depends on the classic. In some cases more practical drawing method

Students are not required to use compasses or rulers, and all shapes must be created using a drawing program. The primary reason for this argument is that since 2017, students do not need compasses and rulers, and there is enough drawing program to create perfect circles, squares, and other shapes with one click is. If technology took over and older fashions disappeared, how about learning new technology and using it? Technology is expensive and worth purchasing a drawing program. Your work is much faster than actually drawing squares or circles. Students also do not need to remember how these numbers are set.

Do you need to be able to understand and build geometry using compasses and rulers?

To configure rational numbers and Euclidean numbers, you can use ruler and compass configurations. In general, the number of terms that can be constructed using compass and rulers is a configurable number. You can construct several irrational numbers, but there is no overrun. You can use a compass and a ruler to complete all possible configurations as long as you are considering configuring the lines when placing the ends. Jacob Steiner shows that all structures that can be done with rulers and compasses can only be done with rulers unless there are no centers on the ruler and its compass (or two intersecting circles, or three non-circles) . The x mark is drawn in advance. Steiner structure