Is anyone really evaluating the efficacy of math instruction either qualitatively or quantitatively?
I know of no agreed upon instrument for evaluating instruction in any area independent of student achievement in that area. We depend on assessments of what students learn in mathematics to judge the effectiveness of math instruction—using tests at various grade levels that assess an understanding and use of the mathematics taught by a grade level. That is why PISA isn’t a useful test for understanding national issues in K-12 Curriculum and Instruction. It uses a low level of math content in its assessments, I’ve been told by mathematicians. One of the major functions of the K-12 curriculum in any country is to prepare a substantial number of students for intellectually demanding professional or occupational work as adults, much of which requires an understanding and application of higher levels of mathematics. No one knows in advance who those students may be, but in a democracy we should assume that it could be anyone. So we must prepare all students for algebra so that they all have
