The saying “practice makes perfect” requires some qualification: “Perfect practice makes perfect.” It is not mere mindless repetition that improves skill, but deliberate practice with the aim of improvement. Deliberate practice, the kind that requires “careful reflection on what worked and what didn’t work,” is the subject of this Freakonomics article by math professor Sanjoy Mahajan, particularly as it relates to math and science education. In it, he proposes the question, “What would an educational system look like that took seriously the principles of deliberate practice?”
This is another one of the ways that the role of a tutor is invaluable for creating true expertise. In math, students typically get graded on their results only, with little, if any, attention given to the process of arriving at the results. But math is not just about arriving at the right answer; that’s something a computer can do. For a human, it is also about arriving at the result in the most artful and efficient way possible. As a tutor, I have the opportunity to directly observe and shape the student’s thought process in the way that a teacher rarely does. This way, the student not only gets feedback about whether their answer is correct, but also about how to improve their thought process. A good tutor can make the difference between struggling for hours to come up with an answer and being able to arrive effortlessly and artfully at a result. A teacher can teach, but a tutor can make the learning process fun, changing the work from a grind into a delight.