Reminiscing my elementary days, I don't recall doing much problem solving during mathematics lessons. It was mainly teacher-directed activities. My math teacher would normally provide the solutions as well as the answers to the problems encountered. To a very large extent, I suspect that is the reason why I can't seem to retain many of the mathematical concepts I have learned.
In the three ways that problem solving might be incorporated into mathematics instruction, teaching through problem solving literally means that students learn math through real contexts, situations, problems, and models. Personally I vouch for the importance of integrating the real environment for teaching through problem solving. It was a first-hand experience for me as my group members and I walked right into Plaza Singapura (a shopping center). We took a walk around the shops and explored many possibilities for implementing a math activity with young children.
Finally, we went into Daiso Singapore, where all the items were sold at $2 each. The shop had a wide variety of items such as gardening equipment, to food and drink items originating from Japan. We felt that it would be a very enriching experience for K1 or K2 students to plan and discuss constructing a present for their parents by purchasing materials from Daiso to make them. The plan is to give the students a meaningful reason to make real purchases from a real context by collaborating, discussing, and planning. They would also have the opportunity to count the money and plan what to spend on.
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