As a way to further develop and incorporate the ideas we've been working on - both the 8 math practices and using more cognitively complex problems with students - each teacher will have their class work on a cognitively complex problem and write up that activity. The problem and write-up are due on Dec. 13th, 2013 as the final requirement of your participation in this PD opportunity.
The activity/problem should target specific math practices in support of preparing students to persist in the face of math problems of Depth of Knowledge levels 3 and higher. Problems should meet the following criteria:
- students are unable to proceed directly towards a solution
- the problem can be solved in different ways
- there is a perplexing situation that the student understands
- the solution requires the use of mathematical ideas
- offer teachers an opportunity to draw out and develop some of the 8 mathematical practices
Part 1: Planning: Answer before you work on the problem/activity with your students
- How does this problem meet our criteria for cognitively challenging math tasks?
- Describe how you solved the problem.
- Create a list of questions you can ask students to help them uncover their methods and/or a solution for solving.
- What are others ways to solve the problem?
- Identify three challenges you think students will have in solving this problem. For each challenge describe what questions you would ask to support the problem-solving efforts of those students without giving too much away.
- Which math practices are you hoping to develop by using this problem? (It might be helpful to consider which practices you used in order to solve the problem)
- What do you want students to get from working on this problem?
- Describe the specific problem-solving strategies of each student. What do you appreciate about each student’s method? How could each student’s method be improved?
- Briefly describe some of the challenges your students had while working on the problem.
- How did it feel doing this problem with your students?
- What did you learn from using this problem with your students (about math, about individual students, about your class, about student thinking in general)?
- Briefly comment on how your class (individual students, or as a whole) benefitted from their work on this problem.
- Did all of your students get what you wanted from the problem? How do you know?
- Describe one highlight from the class discussion of the problem and solution methods.
- What (if anything) would you do differently if you used this problem again? • What advice/message do you have for a teacher who is considering using this problem with their class
- What did you learn from working on this problem?
- What are you still wondering about?
- Describe what was easy and what was difficult for you.
- What is one thing you want to remember?
- What was difficult about this problem? What did you do when you felt challenged/confused by this problem?
In your write-up, please include the prompt you choose and a few excerpts of your students’ responses post your lesson write-up to the blog by December 13th, 2013. You can post it as a new comment or a new post.