Another term, another round of productive failure (or #PF) implemented in my classes. Last term I used #PF in Calculus 1 with freshman. Previously I included it in a course taken by math majors in the teaching option (i.e. preservice secondary math teachers). This term (Winter Quarter 2016), productive failure was implemented in a course for future elementary teachers.
This term, students were asked to share two instances where they learned from being stuck or making a mistake. Sharing would be done via short presentations to the whole class. Learning is what is emphasized in productive failure presentations, and students were asked to share what they were stuck on and more importantly what they gained from it.
The purpose of highlighting productive failure is to de-stigmatize mistakes. Most all students in the class commented in their reflective writing assignments that they were taught that mistakes were bad. Mistakes were to be avoided. The goal was to be "perfect." The problems with this type of mindset is clear. Students who are afraid to make mistakes are not fully engaged in their learning process. They experiment less, are reluctant to try something new, and focus on getting right answers instead of primarily focusing on why things work the way they do. This is all the more important for future elementary school teachers. If young children are taught at an early age that memorizing (and only memorizing) is the key to success in math, then they will learn far less than they are capable of. It's a crippled way of doing mathematics really.
Productive failure ties in with Dweck's notion of a growth mindset. Early in the term, I share a short video of Carol Dweck interviewed by the Khan Academy to help set the stage.
Additionally students are given reading assignments (outside of class) based on Jo Boaler's book, What's Math Got to Do With It? This book is about major issues in K-12 math education in the U.S., what doesn't work, and some research-based claims of what works. Boaler's book adds another layer of support for #PF, offering more reasons why productive failure is an important aspect in successful learning.
As the course progressed, more students shared their experiences of being stuck, and after each presentation, they earned a sticker. Stickers are not necessary, but they add a fun way for students to keep track of how many #PFs they have presented. Stickers also served as a model for how they could implement #PF in elementary school classes.
Productive failure is fundamentally about unlocking a robust learning process. When math classes, especially in K-12, are overly concerned about answer-getting, then students (children) learn to focus almost exclusively on memorizing steps and worrying about not being wrong. And that's when seeds of math anxiety are planted! Education is about learning to become a powerful learner. Far beyond memorized algorithms or basic facts lies a much more valuable and useful education. Society needs independent, critical thinkers, who are filled with curiosity, creativity, and tenacity. You can't develop these traits, if the predominant concern is not making a mistake.