My job keeps me math practiced. You are totally correct about basic math
mechanics. When my son was young and learning adding, subtracting
positives and negatives, I asked him if the he ever was shown a number
line. Nope, never. So, I drew one, he got the concept of negatives and
positives right away. When I grew up, everyone knew what a number line
was, and understood it. They need to put that back in the early math
courses.
I am not even sure the current batch of teachers understand it. We are
old. They grew up with a calculator in their hand. (anyone younger
than 45 or so).
In 1971 my Bomar "4 banger" cost about $100.
A few years later you could get one free with a "fill up" at a gas
station.
Number lines were on the walls of all the middle school math teachers when I was teaching. I can't
imagine a decent teacher not having one when introducing kids to negative numbers.
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