EDUC115N How to Learn Math

I am thrilled to be a part of Jo Boaler's open course at Stanford (EDUC 115N). I am on the third session and wanted to pass on some of the wonderful material she is sharing.

This session focuses on the value of making mistakes in math class, which is something that speaks to my core philosophy as a teacher.

Here is what I wrote for one of the session prompts:


I am so thrilled to see the emphasis on the importance of making mistakes in learning. I have spoken about this to my classes in the past and have created structures to encourage this "mistake and recover cycle" (quiz corrections for example) but now I actually have some research and data to back this up.

My main take aways are the following:

1) Boaler echoed my fear in math, that "we are raising a generation who are terrified of
blundering, of failing, of even sitting with the discomfort of not knowing
something for a few minutes."

I can't stress how important it is that we move away from the high stakes testing model and move away from an education system that punishes error. 

2) Boaler was kind enough to share some of the science behind why this is so important, "when they (students) make a mistake about an idea in math, two sparks happen. First when they make the mistake, and then again when they think about the mistake. And that brain growth that comes from those sparks in the brain doesn't happen when people get work correct, so this was stunning to me. And the reason is it turns out that making mistakes its the most useful thing to be doing."

So not only do mistakes seem to help the brain grow, but they help us more than getting an answer right. This makes sense to me, since the process of learning through error and challenge, not simple repetition, has helped me learn and understand mathematics.

3) The final piece in this puzzle is that the student mindsets sets the stage for learning from mistakes. Boaler stated that researchers "also found that the brain growth that happens was greater in growth-mindset individuals than in fixed-mindset individuals. So again, the greater response of the growth mindset people and the brain growth they've showed, they were more aware of mistakes with greater reaction and a greater accuracy afterwards."

The growth mindset sees mistakes as opportunity for growth where as the fixed mindset sees mistakes as a reflection of their intelligence. A growth mindset might make a mistake and think, "I can work through this and figure this out. Perhaps my mistake will give me some insight." A fixed mindset might think or say "I am smart so I can solve it," or "I am dumb so I can't solve it." Which are both equally dangerous.

This has got me thinking that if mistakes are necessary for learning and if students benefit more from their mistakes when they adopt the growth mindset, then it is imperative that we share the growth mindset with students and set them up to make valuable mistakes and jump in to help them analyze their errors.


Here are some of the resources she posted:

An article by Peter Sims in the NYT: http://www.nytimes.com/2011/08/07/jobs/07pre.html?_r=0

Tugend, A. (2011). Better By Mistake. The Unexpected Benefits of Being Wrong. Riverhead Books: New York.

Moser, J.S., Schroder, H.S., Heeter, C., Moran, T.P., Lee, Y.-H., 2011. Mind your errors: evidence for a neural mechanism linking growth mindset to adaptive post-error adjustments. Psychological Science 22, 1484 – 1489.