That seems to imply that the pleasure and beauty of mathematics is in the way one perceives symbolic manipulation. I actually think the pleasure and beauty of mathematics is in the stage before one gets to manipulating symbols; the stage where you have an idea about something and are thinking about ways to communicate it or prove it. People should be given problems ('how much of this box does this triangle take up?' to paraphrase Lockhart's example) and allowed to drum up their own solutions/syntax.
The pleasure and beauty is in your perception of it, the concepts you develop to give intuitive substance to the abstract rules.