Its not IT Specific
I don't believe Programming means 'Computing'.
Many people will argue the "problem solving" facet which is so commonly tied to IT, but its not distinctly correct.
There are many ways to solve problems without computers.
'Programming is the practice of implementing algorithms.'
Isn't accurate either, you can implement algorithms without programming. ( Get out a Rubicks cube ;) )
To me, programming is:
the act of specifying a sequence of instructions, that can be recorded and performed at a latter time by an entity.
This is why I consider "DNA" as a form of "Programming", and there is also "Social Programming" and all sorts of programming contexts that exist outside IT.
Although, its important to note, that while you are programming, you are also practising other skills from other schools, such as math, problem solving, and logic.
The only part of these which is the "programming" phase is the serialisation of your ideas and logic and reasoning into instructions for an entity ( in this case, a computer ) to perform.