Recently, I was asked to model learning through problem solving in a school. I will post about that experience in part 6, but I thought I should provide the teachers there with an outline of a learning through problem solving process prior to my visit to their school. With credit to Dan Meyer, who gave me many of these ideas, this is what I gave them. What follows is a step-by-step description of the process I use.
Learning Through Problem Solving Process
1. Present the problem.
- The problem is best presented using a multimedia artifact like an article, video, picture, story, song or any other multimedia artifact.
- It is best if the question the teacher wants the students to explore is not explicitly stated in the artifact.
2. Have students come up with the question they want to answer.
- Ask students what perplexes them in the artifact. What questions do they have? What do they wonder about?
- Let this discussion go on long enough for them to come up with the question that you want them to answer. This is the hook. They feel like the question came from them, rather than their teacher.
3. Ask them to intuitively answer the question by providing a guess, a lowest reasonable answer, and a highest reasonable answer.
- This is one of the most important steps, and is easily overlooked.
- Ask students to make a guess. No mathematics allowed. They can use only their intuition. Allow them to discuss and debate what they think is a reasonable answer.
- By the end of this discussion, the teacher should have recorded on the board a range of reasonable answers.
- Students could be asked to attach their names to guesses within that range of reasonable answers. I like to have them put their name somewhere on a continuum between the two answers.
- This process makes it safe for students to be wrong, and allows them to recognize wrong answers later on if the answer they come up with doesn’t fit in the range.
4. Provide them with clarification and any information they think they require in advance of beginning to work on the problem.
- Ask the students if they need any clarification on the question before they get to work.
- Ask them what further information they require (if applicable)
5. Students work on the problem.
- The teacher’s role here is to circulate and make sure that the groups (or pairs, or individuals) are on task.
- Some groups will require help to get started. Don’t let them opt out.
- Some groups will finish quickly and ask if they are right. If they are wrong, ask them a question to steer them in the right direction. If they have the right answer, don’t tell them because as soon as they know they are right, their thinking will stop. Instead, give them an extension. Extensions are challenging to create. They can’t be the same question with different numbers, because that’s just more of the same work. Instead, extensions must truly extend the student’s thinking.
6. Share student solutions.
- The amount of time required to finish will vary based on the problem. Some will take only a few minutes, and others might take a whole period.
- Do not interrupt the group until they have all gotten an answer. Nothing is more frustrating than being truly engaged in a problem, and having your thinking stopped.
- The teacher should not give the solution or the answer. Have students present their solutions in one of the following ways:
- Use a document camera for students to share with the entire class. (stressful for some)
- Have groups share with another group. (safer)
- Some teachers have students working on boards around the classroom. In this situation, the class can sit down and look at all the solutions simultaneously.
7. Teacher summarizes the learning.
- The teacher should spend a few minutes summarizing what mathematics was learned.
- This is not time for the teacher to show his own method of solving the problem. It is simply time to consolidate the learning.