zlacker

>>lewisf+(OP)
From my experience, calculators in classrooms have had a few interesting and odd effects on intuition and expectation. For years, classes were separated and had "theoretical" components without calculator use and "computational" components with calculator use. The computational parts would involve gross numbers with real-ish answers --- things don't work out so nicely. But the theory parts would always have very nice answers (if some sort of computation had to be done).

It turns out that I came to expect theoretical aspects to always work out nicely; similarly, I often failed to see the light through the hairy parts of the computational parts.

This came to the fore when I took an Ordinary Differential Equations / Calculus of Variations course. There were no calculators now --- when we needed computational power, we used various CAS. I remember being very confused the first time we showed a solution existed to some ODE, and then "found it" to any degree of precision we wanted. This was partly theory, but it was very imperfect! My mathematical intuition ended up sharpening strongly during that semester.

Now I'm a number theorist. When I teach, I don't use calculators. I'm acutely aware, however, that early elementary number theory ends up being presented as a delightful and pure little topic. I think there is some need for continued computational aspects in math courses, but I haven't quite seen it done just right yet. (When I do incorporate computational aspects, it's either attached to a basic programming course or attached to an introductory sagemath CAS course).

>>mixedm+2o
The computation of early (primary school) math courses could be done with a counting board, which is a type of general-purpose computer with memory consisting of buttons/coins and a human for a CPU.

Later (high school / undergraduate coursework), it would be good to use a programming language like Python or Julia or Swift ....

I also think students should spend at least a few weeks or months using a slide rule and printed tables for basic arithmetic, but more to learn about logarithms and mathematical history than to learn about computational mathematics per se.