Binary arithmetic is both an educational basis for elementary logic and an pervasive tool for practical mechanics in managing computer systems (at a very particular level). That is the state of affairs. And the history of it is well known: Leibniz introduced it (in 1703), Claude Shannon introduced it as the mathematics behind circuit design in the 1937 (yes, neither invented the concepts, but instead introduced or popularized the notions).
Except I don't know how individuals are presented the material, if at all, in the modern school and university curricula.
In my (very possibly dated) experience, often in late elementary school (in the US system, 4th or 5th grade), a section is taught on alternate number systems (Mayan, Babylonian, binary, maybe even Roman). Basically all that is presented are some different ways of writing digits, and you learn how to write a number and that's about as far as it goes, no binary addition.
It is fairly common practice now to have computer classes in high school, but only to the extent of teaching the simplest of programming.
In the university setting, it is assumed as a matter of course that binary, and even hexadecimal, manipulation is understood, with no mention of the basics. The students deal with it with no problem at all (as far as I can tell).
My questions are:
- Does the above description match others (in detail, or in the general observation that binary is never explicitly taught)? That is, in the US secondary/tertiary system, is binary arithmetic taught at a particular stage? If not, is it considered so elementary?
- Is it taught in the school system in other countries, and if so at what stage, and with what extent?
- Additional question: Is it taught at all in university classes? (in my experience not in Discrete Math or in elementary computer engineering)
As a teacher and tutor who's often introduced binary to students with good results, I found this question intriguing, so I did a little research on the US (I can't speak for other countries).
The closest thing to a nationwide US mathematics K-12 curriculum is the common core state standard for mathematics (also see the Wikipedia article for background)
Guess what -- neither "binary" nor "base two" appears in the standard at any grade level!
So I looked at the ACM Model Curriculum for K-12 Computer Science (The ACM is the major professional and academic society for Computer Science, roughly equivalent to the AMA for Mathematics). In that curriculum, binary is introduced in Level II, which is grades 9-10.
Despite all this, it does appear that binary is taught in many state and local mathematics school curricula. As I said, I have found that students pick up the concepts of binary nicely even at early grade levels, and it helps them gain perspective on a number of conceptual issues in school mathematics. I also use it as an entry point to simple digital logic (gates, adders, etc) and I find many students absolutely love that material, especially brighter ones with a bent toward math -- makes the abstract stuff come alive.
That said, there is a ton of crucial topics that is typically covered in school mathematics curricula, and I can understand why binary is farther down the list. It is too bad, though.