Both on October 22 at Germantown Academy in Fort Washington, PA and most recently on October 27 in Rochester, NY, I presented sessions about problem solving and the CCSS Mathematical Practices. In both venues we agreed that one of the more difficult challenges is to slow things down so that students have opportunities to:
1. Make sense of problems and persevere in solving them.
3. Construct viable arguments and critique the reasoning of others.
Neither of those practices can be done well in a rushed atmosphere where the goal is to check off the “skills” that a student has mastered. Recent years have had this “quicker is better” tone. Teachers have been encouraged to cover everything that might possibly be on the standardized test. They have had long checklists of what the students must learn. Now, with the Common Core there is a return to a focus on process but how do we help make that happen? A change in classroom culture takes time and effort. Approaching problem solving as a process over time is one idea that might help.
I provided some ideas to focus on the process of problem solving and the communication that accompanies it:
* start a problem by reading it as a “story” and then ask students “What did you hear?”
* don’t plan to finish a problem in one class period — work on parts over time
* use our Noticing/Wondering activity with students working in pairs or groups
* use technology to approach a problem with virtual manipulatives when you’ve first introduced it with concrete manipulatives or vice versa
* start a problem at the end of the period, wait to re-engage until a day or two, and continue to do a little each day
* encourage students to read their solution drafts out loud to a partner and then discuss what the listener might still be wondering
* take time to give feedback to each student — it could be as short as “I notice … (one thing).” and “I wonder … (one thing).” If the teacher values the process and provides feedback, it models to the student that their initial draft is worth reflection and revision.
How are you helping your students persevere? How are you thinking that you will help your students persevere? What are you noticing? What are you wondering?