Anticipating Student Thinking.
A key part of planning an effective math lesson is to do the problems (both those in the lesson and the Review & Preview problems) yourself as a teacher or with a team of teachers. As you work through the problems in a lesson think about all the possible ways a student may approach the problem. Think through each of the mathematical representations (see chart below Principles to Actions NCTM 2014) that may be used. Not all will apply for every problem but most will work for any problem and allow for more entry points for students to make sense of a problem. Recording some of the anticipated methods and misconceptions on a lesson plan document can help you focus on these methods during class as you select and sequence the students/teams who will share during whole class discussion or closure. When you have gone through the work of anticipating student thinking the actual teaching process becomes more fluid and powerful. Your students will learn more than ever because you are prepared to support them to make connections between the different ways of thinking. A lesson plan format for recording anticipated student thinking can be found at this link.