Embracing Wrong Answers

As I shared in a previous blog post, my goal is to be more present in the classroom this year.  One area I am growing in, in regards to presence, is to be present with students when I call on them.  I am uncomfortable when I call on a student and they answer incorrectly, and I believe students also tend to be uncomfortable when they give an incorrect answer.  My habit has been to brush past the incorrect answer and move on to another student, looking for the correct answer.  But that isn't a very present practice.  When a students answers incorrectly, I want to stay with them and help them understand their misconception.  I have been trying a new practice where I continue to ask the student who answered incorrectly questions until they understand the problem.

In the fall, I asked my Algebra 2 students the following question:

Students were able to get two equations fairly easily by writing equations with each coordinate as the vertex.  The challenge was coming up with a third equation that contained both points.  While students were working, I encouraged them to perverse in problem solving.  Students kept trying new approaches to the problem.  I began the class discussion by asking "What made this question challenging?"  For the most part, students were able to verbalize how they got stuck on the third equation.  I then called on students at random to ask for their equations.  It was neat to see students have different equations that worked, and have different explanations for how they solved this problem.  When I called on one student, he said he didn't have a third equation (one where the vertex wasn't (-1,2) or (-3,-6)).  I was about to move on to another student, then I realized by asking him a few questions, we could model "persevere through problem solving" for all of the students.  I asked him a series of questions that I knew he could answer, leading him without telling him, until he figured out how to write the third equation.
Many students were raising their hands in order to "rescue" the student in the hot seat.  I want everyone one of my students to know that they don't need a rescue.  They have the background knowledge and skills to be able to get to the final answer.  They might need some scaffolding and smaller steps along the way, and that's okay because it's part of the learning process.
In Make It Stick:  The Science of Successful Learning by Peter Brown, Brown says "What you tell yourself about your ability plays a part in shaping the ways you learn and perform – how hard you apply yourself, for example, or your tolerance for risk-taking and your willingness to persevere in the face of difficulty."  I don't want students answering questions incorrectly and telling themselves that they are not capable of solving hard problems.  I want to call on them, and help them have success in answering a challenging problem.  I want each of my students to believe that they can solve hard problems.  
I can see that students are uncomfortable when they don't know the answer and I don't rush past the incorrect answer to get to the right answer.  Learning happens in the discomfort.  I'm not looking for an answer, I'm looking for a discussion leading to learning.  By not shying away from a student who answered incorrectly, I am communicating to that student, and the whole class, that each students' understanding is important to me.  As I continue this practice, both me and my students are becoming more comfortable with wrong answers.  Chances are that if one student answers incorrectly, then others have a misconception too.  Getting the answer is an immediate goal, but building the problem solving process is more helpful to the class in the long run.  This practice not only benefits students, it has also made me more present during my lessons.  When I listen to students' answers, and think about how to help them get to the correct solution themselves, I am engaged with the student and curriculum in a way that I haven't been before.  Despite the discomfort and challenge of the process, I believe that it is worth it.