In every mistake there is a potential for growth!

I personally am a big believer in productive failure. Don’t get me wrong, I think it’s very important to co-construct learning goals and success criteria with our students.  They need a framework in order to show them where they are going academically. Goals and criteria paint a clear picture for the students of the teacher’s intended outcome.  They provide them with clear directions and examples (or rubrics) of what is expected, thus enabling students to feel more successful in their tasks and allows them to feel more in control.

BUT…don’t most of us learn by DOING?  Everybody makes mistakes and most successful people learn from those mistakes.  When all of the criteria are laid out for students, some of them may achieve the intended outcomes but many of them may not know how they got there.  In allowing for productive failure, students may not necessarily achieve the set learning goal initially but they do gain knowledge and understanding that may allow for them to reach that goal on their next try.

I read the following article which solidifies by point exactly.

http://ww2.kqed.org/mindshift/2016/04/19/how-productive-failure-for-students-can-help-lessons-stick/

We must help our students change their mathematical mindsets. Manu Kapur, a professor of psychological studies in Hong Kong has studied productive failure for years.  He says as teachers, we must provide students with tasks they won’t be able to solve but aren’t too difficult that they give up.  During and after their struggles is where the real teaching/learning occurs.  (His lesson design is outlined in the article)

I love Kapur’s quote “No matter how engaging, entertaining or logically structured the new information is, the novice by definition is not going to see the same thing as the expert in the presentation.” In letting the students explore, question and converse with each other on mathematical problems, not only does everyone have an opportunity to participate irrespective of their mathematical ability, but the students increase their knowledge and understanding as a whole. In every mistake there is the potential for growth!