Students are presented with three possible ways to begin solving the problem, “Solve for x: 2x2-14x+20=0,” and asked to decide together which way(s) of starting the problem are correct.

I put examples of common mistakes in front of students so that they can confront them when they are not part of the work the student has created him or herself. I find that the distance created when students analyze another person’s work – especially when that person is not immediately present – allows students to be more analytical. In this case, it also presents the challenge for students of trying to make sense of someone else’s work when that person is not present to answer questions about it. In pushing students to take a stand or make a choice about who is correct, I am trying to get them invested in either confirming their answer or understanding why someone disagrees with it so that they are less passive listeners. In this case students were reluctant to do so, leaving me unsure whether they had been able to understand the students’ work or were not sharing their opinions for other reasons. It was helpful to hear how students were interpreting factoring as a tool that is used to rewrite an expression when the rewritten expression is the goal, rather than as a tool that can help you work toward a solution to an equation. Through the discussion I recognized that students did have confusion about what question they were answering, and what the answers meant. I was faced with decisions about how much more to explore in a class discussion and what to leave for them to discuss in pairs and teams, and I opted to move students to work in pairs rather than continuing to pursue the discussion whole class, so that more students would have the chance to participate in articulating questions and trying to answer them.

I put examples of common mistakes in front of students so that they can confront them when they are not part of the work the student has created him or herself. I find that the distance created when students analyze another person’s work – especially when that person is not immediately present – allows students to be more analytical. In this case, it also presents the challenge for students of trying to make sense of someone else’s work when that person is not present to answer questions about it. In pushing students to take a stand or make a choice about who is correct, I am trying to get them invested in either confirming their answer or understanding why someone disagrees with it so that they are less passive listeners. In this case students were reluctant to do so, leaving me unsure whether they had been able to understand the students’ work or were not sharing their opinions for other reasons. It was helpful to hear how students were interpreting factoring as a tool that is used to rewrite an expression when the rewritten expression is the goal, rather than as a tool that can help you work toward a solution to an equation. Through the discussion I recognized that students did have confusion about what question they were answering, and what the answers meant. I was faced with decisions about how much more to explore in a class discussion and what to leave for them to discuss in pairs and teams, and I opted to move students to work in pairs rather than continuing to pursue the discussion whole class, so that more students would have the chance to participate in articulating questions and trying to answer them.