It's taken me a while, but I think that I finally understand one of my issues with math problem-solving. I really didn't understand what "problem-solving" meant anymore. When I think about math problems, I think about the ones that I grew up with: There are 10 candies. You give five candies to your friend. How many candies are left? These are the math problems with just one solution. They're the ones that don't require a lot of thinking or a big explanation. They may help students apply some of the skills taught in class, but they are definitely not higher level thinking math problems.
As I read more and discuss more about math, my understanding of problem-solving has changed. Now I also see how some math exploration can also be problem-solving. On Thursday, I was introducing my Grade 1's and my Grade 2's to measurement. We started with non-standard measurement, and I was focusing on length. After we worked together to define the terms "non-standard" and "length," I had the students work in small groups to measure different objects are the classroom. I had seven different non-standard units that the students could use for measuring the length of various objects (from playing cards to toy bears). The non-standard units varied in size. Before the students started to measure the different objects, they predicted if they would require more "smaller non-standard units" or more "bigger non-standard units" to measure the same objects. Then they went off into groups, and I got my camera ready to take photographs (seen in the Animoto slideshow below).
I saw students helping each other. I saw students solving problems. I saw them counting, estimating, and making predictions too. Then when the measurement activity was over, we met back at the carpet to discuss the results. Students shared what they found out. When they found out that two students were the same "length," they even figured out how to compare the heights of the two students to see if this was true. They reflected on their own results. They also looked at our chart of results, and they started to make comments on the size of the non-standard units. They realized which units were larger ones and which ones were smaller ones just by the results, and they shared their thinking with the rest of the class too. This "math exploration" was "problem-solving" as well. It just took me until now to realize this.
What are some problem-solving activities that you do in your classroom? How has your definition of problem-solving changed over time? I would love to hear your thoughts too!