Pedagogy and mathematics
It is undeniably important that mathematics teachers have mastered the topics they need to teach. The new Australian national curriculum is misguidedly increasing the amount of “statistics” of the school mathematics curriculum from less that 10% to as much as 40%. Many teachers are far from ready for the change.
But more often than not, the problem is not the mathematical expertise of the teachers. Pedagogical narrowness is a greater problem. Telling that there is a correct idea in a wrong solution to a problem on fractions requires unpacking of elementary concepts in a way that even an expert mathematician is not usually trained to do.
One of us – Jon – learned this only too well when he first taught future elementary school teachers their final university mathematics course.
Australian teachers at an elite private school could not understand one of Jon’s daughter’s Canadian long-division method nor her solution techniques for many advanced school topics. She got mediocre marks during the year because of this.