Park City Mathematics Institute
Reflection on Practice Class: Day 11
Secondary School Teacher Program
We reported on our discussions from Day 10.
Aki: Just asking a student to create their own problem isn't enough. It is impossible to use all of the student written problems. Problem: How to choose which problem to use with the whole class? We should compare and discuss how many varieties of problems can be done. One missing key point: often each student uses same method over and over. For example: guess and check. It is an important method, but each student needs to use a variety of methods. If we have a variety of solution methods - we have the flexibility. How to facilitate a discussion about different methods? The most important part: Comparing and discussing. How to integrate various methods? How can we use this process to enable benefits?
What might be the benefit of type 3 open ended problems for your students? Here are some of our responses:
- They begin to see connections between ideas - between algebra and geometry.
- Students become empowered when the problems become their own.
- It is much more likely that students will make problems which are appropriate for their classmates.
- Students will be able to generalize ideas - and add structure to the set of problems.
- This can create equity between student and teacher. They can have more control over their own learning.
- It may be that the teacher could become a learner - Maybe students will design a problem that the teacher can't do.
- Students can assess themselves via this process.
Our assignment for Thursday:
Iron chef week 3 - Create your own problem, working in groups of 2 or more.
Answer all four categories: Developing an open-ended problem for your students (end of Thursday)
- Determine if the problem is appropriate
- is the problem rich in mathematical content and valuable mathematically?
- Is the mathematical level of the problem appropriate for the students?
- Does the problem in clued some mathematical features that lead to further mathematical development?
- Anticipating students' responses to design a lesson
- Making the purpose of using the problem clear
- Make the problem as attractive as possible
We spent the rest of the hour working in groups on creating our problems.
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