I began working with both girls, and each one progressed. But while both of them brought similar aptitudes and difficulties to the subject, and each one was affable and engaged in our sessions, they differed sharply in attitude and approach. Anna retreated from the difficulties, relying on the teacher's performance or my explanations. She merely went through the motions, never pushing past her own confusion. It was more difficult for her than for any student I have ever taught, and yet when she left for her final exam I observed that of all my students in that subject, most with aptitudes far greater than hers, she knew it best of all.
Few parents can.
But in the messages they sent, the responsibility they encouraged, the support they offered, and the absence of excuses, they created a learner. We can do the same. And parents can unclench their teeth, for math success does not rely on aptitude or luck or our ability to explain it to them, but on things we can do in the normal course of raising our children. Too often in math, parents send a message that the struggle is sign of a problem. But we seldom respond similarly to struggle in mathematics.