## Learning Through Problem Solving (LTPS) – Defined

April 29, 2011 by John Scammell

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

I recently went back through my posts and tagged many of them “Learning Through Problem Solving”. This post will clarify what I mean by learning through problem solving.

Our Alberta Program of Studies (page 8.) states that “learning through problem should be the focus of mathematics at all grade levels.”

When I was in school, I was taught lessons, and then assigned a set of practice questions which inevitably concluded with the dreaded word problems. The drawback to this approach was that the word problems were nothing more than more practice. For example, after a lesson on adding fractions, we would practice adding fractions, and then get some word problems. The word problems would have two fractions in them, and all I had to do was add the two fractions without reading the problem. Nothing that can be done without reading it and thinking about it is really a problem.

When I began teaching, I approached problem solving the same way. I taught a lesson, let students practice, and then assigned them a set of problems that they could do. Then I patted myself on the back for being such a good teacher because my students could solve problems.

In life, problems require thought. They are missing information. They can’t be answered immediately. Problems in math class are often not like this. We need to present problems to our classes up front, before we have taught our students how to do them. Students will have to struggle, determine which information they are missing, persevere, and ultimately learn from the process.

The following is a list of what I believe to be the components of a good learning through problem solving experience. This list is compiled from a variety of sources including my own experiences, Marilyn Burns, Dan Meyer, Andrew Wiles, Marian Small, John Van de Walle and others.

- The problem should be given at the beginning of the learning, rather than at the end.
- The problem should be non-routine. The students can not solve it immediately, BUT…
- Every student should have an entry into the problem.
- The problem needs to be compelling and engaging enough that students will persevere.
- The problem should invite multiple methods of solution.
- The problem should foster discussion and debate.
- The problem should be at an appropriate level for the audience.
- The best problems allow the students come up with the question to answer.

Thus, I define learning through problem solving as a classroom process in which students are presented a problem prior to being taught exactly how to do it. Through their struggles and conversations with each other, they construct meaning and discover appropriate mathematics.

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on April 29, 2011 at 1:42 pm |Sue VanHattumNice summary. I’ll think about this for a while.

on May 3, 2011 at 11:13 am |AveryEnjoyed this…something I’m constantly thinking about. I hadn’t heard of Marian Small so I’ll have to check her out.

Also, I wrote a similar list of “What makes for a good problem” last summer: lots of overlap.

http://mathteacherorstudent.blogspot.com/2010/05/what-makes-problem-great.html

on May 3, 2011 at 12:11 pm |John ScammellAvery, I saw yours last summer. It’s what first got me thinking about how to define a learning through problem solving process. You write it much more eloquently than I do. It’s good stuff.

on August 15, 2011 at 9:55 pm |Pool Set-up | Campbell's Corner[...] colleague, John Scammell, has identified seven steps of Learning Through Problem Solving approach. I’d like to use his framework to present how we can use this activity with [...]

on June 12, 2013 at 8:30 am |My Weekly Diigo Links (weekly)[…] Learning Through Problem Solving (LTPS) – Defined | Zero-Knowledge Proofs […]

on June 20, 2013 at 2:00 pm |dadf@hotmail.comWhere can I find elementary school lessons online that involve teaching “THROUGH” problem solving?

on June 25, 2013 at 8:19 pm |John ScammellI’ve asked around. Nobody seems to have any. I’m working on one right now that will be up soon that would work. The “A Billion Nickels” one on this blog would also work. If I find anything else, I’ll post it.

on June 26, 2013 at 10:17 am |Ticket Roll Elementary Style | Zero-Knowledge Proofs[…] get asked frequently if anyone is compiling 3-Act Math stories in the style of Dan Meyer or learning through problem solving activities specifically for elementary school. I’m not aware of anyone cataloguing them at the […]