In an earlier post I wrote about the mantra for my precalc class. The general idea is that the process of learning begins with a surface level understanding, followed by some confusion, and finally a deeper level understanding. Calcdave used a great illustration of the idea in his Diary of Infinity. I think I stumbled upon another application this weekend.
I’m currently reading a book called Mindset by Dr. Carol Dweck. In the book, Dr. Dweck (I love that name by the way) distinguishes between two different mindsets – the idea that ability is an unchangeable vs the idea that people can improve with practice. According to her, “In one world – the world of fixed traits – success is about proving you’re smart and talented. Validating yourself. In the other – the world of changing qualities – its about stretching yourself to learn something new. Developing yourself.” In other words, people with a fixed mindset approach every challenge as a test of their innate abilities, while people with a growth mindset approach challenges as an opportunity to improve oneself. I believe that this ties in very well with the precalc mantra in my classroom.
For example. Suppose a student scores a 20% on a test. I used to struggle with what to say to that student. My canned response now goes something like this:
Just because you failed this test does not mean it’s the end of the world. What it means is that you are in the confusion stage when it comes to understanding this concept. In a way, that is a good thing, as it means you’re well on your way to a deeper understanding. We now have some very valuable information as to how we can proceed in this class and help you emerge from your confusion with a mastery of this concept.
I feel as though this viewpoint is advantageous in a few ways. It doesn’t place the blame on the student or imply that the student is somehow defined by his 20%. Instead, it takes a perspective that the 20% is a launching pad for improvement and a natural part of understanding mathematics. The fact that a student is confused does not mean that he or she is a failure – a score on a test proves nothing about the student. It means he/she has an opportunity to learn something new and a lot of room to grow.
(I also feel as though the growth mindset ties in very well with standards based grading, but thats a whole other story.)