https://archive.ph/5xwq3 >New Mathematics or New Math was a dramatic but temporary change in the way mathematics was taught in American grade schools These curricula were quite different from one another, yet shared the idea that children's learning of arithmetic algorithms would last past the exam only if memorization and practice were paired with teaching for understanding. >More specifically, elementary school arithmetic beyond single digits makes sense only on the basis of understanding place value. This goal was the reason for teaching arithmetic in bases other than ten in the New Math, despite critics' derision: In that unfamiliar context, students couldn't just mindlessly follow an algorithm, but had to think why the place value of the "hundreds" digit in base seven is 49. Keeping track of non-decimal notation also explains the need to distinguish numbers (values) from the numerals that represent them, a distinction some critics considered fetishistic. >Topics introduced in the New Math include set theory, modular arithmetic, algebraic inequalities, bases other than 10, matrices, symbolic logic, Boolean algebra, and abstract algebra. All of the New Math projects emphasized some form of discovery learning. Students worked in groups to invent theories about problems posed in the textbooks. Materials for teachers described the classroom as "noisy." Part of the job of the teacher was to move from table to table assessing the theory that each group of students had developed and "torpedoing" wrong theories by providing counterexamples. For that style of teaching to be tolerable for students, they had to experience the teacher as a colleague rather than as an adversary or as someone concerned mainly with grading. New Math workshops for teachers, therefore, spent as much effort on the pedagogy as on the mathematics. It's totally different than common core from what I've read though.