Note: This post is part 5 of 7. Click here for part: 1 2 3 4 6 7

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.

on May 6, 2011 at 9:15 am |Link: Learning through Problem Solving | A Recursive Process[...] Great post from John Scammell walking through a how-to for “wcydwt” (what can you do with this) or “ltps” (learning through problem solving). Can we just call it great teaching? Learning Through Problem Solving Process [...]

on May 6, 2011 at 9:22 am |Avery“Let this discussion go on long enough for them to come up with the question that you want them to answer.”

I understand the reality of coverage expectations and high stakes test preparation leave little room for tangents, but boy would I love to live in a world where the students didn’t have to come up with the question the teacher wants them to answer, but instead could explore their own questions. In this world, I imagine spending a greater amount of time talking about the aesthetics of what makes for an interesting math problem and much less time cajoling students to ask the “right” question.

on May 6, 2011 at 11:21 am |John ScammellIt’s unfortunate that we are so curriculum driven that we have to trick them into inventing the question we want them to come up with. Part of me thinks that that is the best we can do right now. I’m not sure most students are currently capable of exploring their own questions. It’s not their fault – they are a product of our system. This approach, though, should give them practice at seeing math and asking questions. Maybe it’s a step on the way to the ideal you describe.

on May 6, 2011 at 11:35 am |MaxCould I add something to #5? Sometimes if a group needs help getting started, or it’s seeming like you’ll never get to #6, a “distributed summary” of where we’re at so far can be good. The state of Delaware in the US is moving towards all high-schools adopting LPS curricula and one tool that’s helped keep the whole group well resourced and moving forward is learning to stop small-group problem-solving and strategic times.

At those strategic stops, it’s not helpful to have people share answers, but to harvest new noticings or wonderings, to learn what different strategies people are approaching, to surface and hash out different interpretations of the problem, etc. I’ve seen it work well when one group has veered down a fruitless path, or several groups don’t have a place to get started, or there’s a common sticking point that could use more heads to think through…

It gives the teacher and group more resources during what can be a tricky part of problem solving.

Max

on May 6, 2011 at 3:22 pm |John ScammellThat’s good stuff, Max. I like it. If they’re struggling, a little “share fair” of what various groups have tried so far would be really helpful.

on May 6, 2011 at 4:17 pm |Dan MeyerJohn: “Let this discussion go on long enough for them to come up with the question that you want them to answer.”

Avery: “In this world, I imagine spending a greater amount of time talking about the aesthetics of what makes for an interesting math problem and much less time cajoling students to ask the ‘right’ question.”

John: “It’s unfortunate that we are so curriculum driven that we have to trick them into inventing the question we want them to come up with.”

These descriptions are a lot more heavy-handed than they should be. A problem space needs to be focused enough to be productive and unfocused enough to permit student creativity, exploration, and agency. That’s a tricky spot to nail. I’d prefer to have somewhere around 70% of my class focused on one question (without my cajoling or deceiving anybody — like, they really want to know the answer to the question) and 30% off on tangents we’ll pick up later.

If I show students a photo and a video and they aren’t interested in the question I thought was most interesting, I don’t recur to deception. I don’t play “guess the question the teacher wants you to ask.” I don’t cajole or twist arms. I just ask the question I’d like them to consider. (That’s still within my professional jurisdiction, right?) Then later, I ask myself if there was a more compelling way to frame the problem or if the context of the problem is simply uncompelling to my students.

Can you folks describe your ideal problem space? Something that’s simultaneously unfocused and productive? I mean, the questions over here are all over the place. At least she isn’t cajoling, right?

PS. Fun write-up, John. Obv. lots I agree with, also.

on May 6, 2011 at 5:43 pm |John ScammellI did six of these yesterday (part 6 to come). In all cases, the kids eventually agreed that the question they wanted to explore was the one I would have asked them anyhow. With enough discussion, I suspect 9 times out of 10 they’ll come around to it without me being heavy handed about it. In one of the cases yesterday, the kids wanted to answer a harder question than the one I had thought of, but the one I was thinking of was a necessary step along the way, so I let them go with theirs (which proved to be very difficult for some of them).

I’m with you, though. I wouldn’t be shy about throwing it out if they didn’t get there, and if they came up with something equally interesting or mathematical, I’d let them take it in that direction.

on May 8, 2011 at 10:16 pm |dy/dan » Blog Archive » Dissents Of The Day: Danielson, Pickford, Scammell[...] John Scammell It’s unfortunate that we are so curriculum driven that we have to trick them into inventing the question we want them to come up with. [...]

on May 9, 2011 at 7:54 am |R. WrightAsk them to intuitively answer the question by providing a guess, a lowest reasonable answer, and a highest reasonable answer.Interesting. While I’ve rarely done this during class (because I’ve only recently been getting away from straight-up lecture), I have warned students that if they arrive at a ridiculous answer on a quiz or test and do not acknowledge it, no matter how reasonable their calculations seem, they will receive little or no credit because they have demonstrated no understanding.

Ask students to make a guess. No mathematics allowed. They can use only their intuition… Students work on the problem… Some groups will finish quickly and ask if they are right.The problem I face with this is in teaching college algebra, where most students remember a great deal of the material from high school. Indeed, many of them are taking the course for “easy credit,” which is an issue in itself. I yearn for the privilege of being their first exposure to the concepts of the course, but many of them have been expertly programmed to regurgitate formulas without any real thought.

on July 15, 2011 at 7:54 am |China Wedge – Three Acts « Zero-Knowledge Proofs[...] bit more. I would present it in much the same way I discuss in my learning through problem solving explanation. GA_googleAddAttr("AdOpt", "1"); GA_googleAddAttr("Origin", "other"); [...]