A while ago we had cause to meet with a school principal. The principal happened to have a PhD in mathematics education, and it was on that basis that they began the conversation: “As a fellow mathematician …”. It will come as no great surprise that our association with the principal ended soon after.
The principal was doubly wrong: no, of course they are not remotely a mathematician; but, neither are we. Once upon a time, yes, but not now. We are no longer seriously engaged in mathematical research, in trying to discover the facts and the nature of mathematical truth.
But, to the principal and the principle. Of course it doesn’t matter whatsoever if a principal is not a mathematician. What matters a great deal, however, is if a principal falsely imagines that they are. If a school principal does not understand what it means to be a mathematician then they cannot possibly understand what a mathematician might offer to their school, or to education in general.
Such a lack of understanding, an ignorance of what it means to think deeply about mathematics, is now endemic in Australian mathematics education. The consequence is that mathematicians are treated as inferior teachers and education academics, merely as weirdos with relevant training a proper subset of that of the education pros. The consequence is that clear and informed and deep mathematical thought is marginalised to the point of non-existence. The consequence is a pointless mathematics curriculum taught using painfully bad textbooks by poorly trained teachers and administered by organisations with no respect for or understanding of the nature of mathematical thought.
Mathematicians can be arrogant and annoying, and wrong. But mathematics education without the deep and continued involvement of good and serious mathematicians is pure insanity.