Even in Mason’s day, testing drove much of educational policy, but we must not allow ourselves to fall into the trap of teaching for a test. Just as we do not study history in order to win a trivia contest, so we do not study math merely to produce answers on an exam.
“Arithmetic, Mathematics, are exceedingly easy to examine upon and so long as education is regulated by examinations so long shall we have teaching, directed not to awaken a sense of awe in contemplating a self-existing science, but rather to secure exactness and ingenuity in the treatment of problems.”
— Charlotte Mason, Towards a Philosophy of Education
Remember Mason’s twin goals of rightness and reason. Even if you use a math book that focuses on memorizing rules and cranking out answers, you and your child can look for the ideas behind the rules: “Why does this work? How can we know for sure?”
Not just because the book says so, but because you search out and discover the innate sense of it. That is the essence of mathematics.