When learners enter my class the first day of the semester, they typically see the following projected on the front board:

In this series of posts, I want to share an approach we use with student teachers to support their development as reflective practitioners. The first post introduced the idea of using an action plan as a way for teachers to identify an area of challenge and seek out support. In subsequent posts, I plan to share examples of this approach in action.

My problem is that I tend to teach as I was taught. I know that research shows that I am not alone in this, but I thought I had gotten over this hurdle. Since 1990, I have been teaching math differently - and I have the student comments and parent phone calls to prove it. The changes I made as a math teacher were one of the reasons I became interested in mathematics education. Unfortunately, these changes did not transfer to all aspects of my teaching.

This was the question guest host, Susan Page, asked author, Eric Greitens, on an episode of The Diane Rehm Show. Greitens responded:

So far in this series I have discussed the need to empower learners by getting them to ask and explore their own "Now what?" questions (here), considered possible answers to a messy learner-generated word problem (here), and identified implicit conditions associated with the different answers (here). In this final post of the series, I share my preservice teachers' efforts to extend our understanding of one of the possible answers to this word problem:

Thus far we have considered ways middle school learners can extend their learning by generating their own problems based on young adult literature (here) and how preservice teachers  can extend their understanding by considering alternative solutions (here). Given the four different answers they usually come up with (1/15, 1/30, 1/21, and 1/36), the preservice teachers attempt to revise the original problem to match each answer.

In the prior post, I introduced a problem written by a seventh-grader as both an example of what middle school students could do when deciding what comes next and an opportunity for preservice teachers to develop and explore their own "Now what?" questions. This was the student-generated problem: