Its the mistakes and not right answers that lead to more learning

I am teaching again; through tutoring. As Algebra, Geometry and Pre-Calculus and Calculus flood my evenings I am amazed by how much math learning is driven by the impetus to get to the right answer. Concept explanation, problem sets, quizzes and tests, its all about getting to the answer. As students learn how to get to answers and work so hard to shy away from “getting it wrong” we all miss out on rich learning.

Math, of all academic subjects, seems naturally geared towards getting the right answer. And, it is exactly this method of answer-based learning that makes math an enigmatic,

dry and intimidating subject. I postulate that there is much more to be learned from the mistakes made in solving a math problem than there is to be learned from getting the right answer. Computers and calculators can produce right answers to mathematical problems. This will be even more true in the future. So, the only thing left for students to learn is the process, the messy, mucky, discovery-based process of learning math.

When a student gets an answer wrong, it is instinctive to jump into correcting the mistake; to identify the step where the calculation went wrong, where the data was misread and to course correct from there. If instead, we can pause and ask why the student got the answer she got, we can learn about how she thinks and what she has really understood about the topic. As she explains her thinking, she explains it to herself and often she discovers for herself why she got the answer wrong. 

But that’s not all. As she explains her thinking, we can take her false assumption and play with it, try to apply it and prove to ourselves why the misconcept doesn’t work. We discover why the concept is the way it is, what lead it to being defined the way it is defined. 

Looking at mistakes with curiosity leads to fuller learning. And, I don’t think this applies just to mathematics. I think it applies to all subjects, doesn’t it?