The point has been made that there is a lot more to maths than "mere" algebraic manipulations.
Real mathematicians write sentences (albeit with lots of symbols in them) not lists of equations. Provided that he's making rigorous arguments that he completely understands and that other mathematicians accept, I'd say it's fine - I'd expect him to be able to adapt to a required format as and when required, if it's straight in his head.
And there's a cautionary tale about being good at equations, but struggling with the higher math.
I can only tell my own experience. At a younger age, I had trouble showing my work, I could look at a problem (word problem or otherwise) and know the answer but it took me a while for showing my work to click, but then I became very good at equations. Then, while in grad school working on an Engineering PhD, I had to take a course from the Math department where we had to write proofs. I was horrible. It was a shock to my system because the proofs were not equations and algorithms. They were sentence explanations. I barely got through it with a lot of help from a friend and I frankly still get headaches thinking about it. However, I am now trying to figure out the best way to train my DDs for that type of thinking because I do see the value in it.
But that said, I agree with the OP
Quantum2003, that this "step-by-step math equations as a method of showing your work" is nevertheless a necessary developmental stage in mathematics, and
Quantum2003 is right to want her DS to do this properly. I'm just starting to get our DS to do this (with reluctance).
One thing to realize is that while many people can make a fairly competent "step-by-step math equations as a method of showing your work" argument of the form
blah=blah
blah=blah
blah=blah
blah=blah
blah=blah
they may not have it clear that
(1) equations are statements that are true for some values of the variables, and false for others, and that
(2) they should be connected by logical words such as "if and only if" or "implies" or "is implied by", as appropriate, and even if you omit the words, you'd better know how the equations are related.
For example someone may write
ab=ac
b=c (cancel the a)
without being clear that the 1st equation is merely implied by (but does not imply) the 2nd equation (soultions have been lost). They may not really think about the logic at all (since, after all, it's algebra, not logic, right?). They should write
ab=ac
if and only ifb=c
or a=0.
[Mathematicians will know there are extra caveats to add here but nevermind that.]
I guess my point is that some people can be quite adept at algebraic manipulations, but still be quite fuzzy on the logic. Nevertheless, fluency in algebraic manipulation is a necessary skill (just as basic arithmetic is a developmentally earlier necessary skill), but it has to be placed in the larger mathematical picture.
So OP
Quantum2003, yes I agree, your DS does need to learn how to write out this algebra properly.
