Richard Feynman was critical of teaching children how to convert between number bases.
I'll give you an example: They would talk about different bases of
numbers — five, six, and so on — to show the possibilities. That
would be interesting for a kid who could understand base ten —
something to entertain his mind. But what they turned it into, in
these books, was that every child had to learn another base!
And then the usual horror would come: "Translate these numbers,
which are written in base seven, to base five." Translating from
one base to another is an utterly useless thing. If you
can do it, maybe it's entertaining; if you can't do
it, forget it. There's no point to it. (Surely You're Joking, Mr. Feynman!)
Are there good reasons for teaching children this skill?
Best Answer
I am of the opinion that if you cannot add and subtract in a base other than ten, then you haven't really understood arithmetic.
A $9 \times 9$ table of addition facts is not too hard to memorize over the course of years in elementary school. When children see the symbols "5 + 7" in that order, they can recall that the appropriate response is to write down the symbols "12" in that order. All this can be done with no understanding of the fact that the answer is meant to represent a group of ten and two "singles".
Suppose instead a child has some understanding of alternate bases and sits down to evaluate "5 + 7 (base eight)". It is unlikely she has committed all the various addition tables to memory. She is forced to visualize (maybe using manipulatives) five singles and seven singles and regroup them into a group of eight and four singles. Thus, the answer is 14 (base eight).
In summary, I do not think understanding an alternate number base is useful in itself, but is useful as a means to deeply understand base ten.