Problem Solving with PODs and POWs

Laurian Phillips
Jan 04, 2010

An easy change any math teacher can make to increase achievement is to incorporate problem solving into the curriculum. Problem solving is not a skill; it is a process, a way of thinking. Students need to have at their disposal a number of different strategies for solving problems, and then need to practice applying these strategies in problem-solving situations. In Putting It Together, Gary Tsuruda shares how he uses Problems of the Week or POWs to give students an opportunity to solve non-routine problems. He says that he began using POWs as extra credit for students who had finished their regular work or wanted a greater challenge. Near the end of the year, he decided that the experience was too valuable for anyone to miss, so he announced that all students would be required to do the Problems of the Week. Problems are chosen from books of "brain te asers" or other ancillary resources. He uses a minimal amount of class time for them, just a few minutes to present and clarify the problem and then about half a class period a week later for student presentations. The presentations are voluntary but are encouraged if a student has a particularly interesting or elegant solution.

Problems of the Day or PODs are how he teaches students to do longer POWs. These are good problems that don't have the scope or complexity to justify an entire week of problem solving, but are good lead-ins to a particular lesson. These do not happen every single day. Rather, they are smaller versions of the POW. His students call short easy PODs "P-PODs" or "Puny PODs". The main differences between PODs and POWs are the size of the problem, the time allowed, the amount of class time devoted to the solution, and the provision for student interaction.

Here is the POD format:

1) Presentation of the problem. Hand out the problem in written form. Read it clearly once or twice, with emphasis if necessary.

2) Clarification questions. Students ask questions about elements of the problem only. Not about solution methods or the actual answer.

3) Pairs brainstorming. In pairs, students are given a few minutes to clarify their understanding of the problem and discuss possible solution strategies.

4) Large group questions. Students have a final opportunity to ask clarification questions or request additional information if needed.

5) Small-group or Pairs problem solving. Students work in pairs or groups to share strategies and ideas.

6) Individual POD write-ups. Individual students, using the ideas generated in the group problem-solving discussion, complete a four-part write-up about the POD. Although some students are able to begin this part of the process during class time, it is usually completed at home as that night's homework assignment.

7) Large group presentations. Solutions are shared and discussed after the papers are returned.

If a class has a wide range of abilities and limited problem-solving experience, it is best to start the year with only PODs and to only have students write-up their solutions. Do this for the entire first quarter before introducing POWs. The write ups highlight individual parts of the overall POW write up that will be required later in the year. For example, on the first POD, they were asked to write only their process and their answer. Later PODs emphasize their planning and their problem statements. After the first quarter, a POW is done every other week.

For more information on PODs or POWs see Putting It Together: Middle School Math in Transition by Gary Tsuruda.