Structured Problem Solving

This week in class we discussed structured problem solving in math. We used the example of the growing dots problem. While completing this problem, we were told we must visualize what is happen and draw a diagram. This forced us to solve the problem in a structured way with visuals. Without these instructions many of us may have completed the problem mathematically instead of solving is using diagrams. However even though we were told to use visualizes and diagrams there were still several different approaches to the solution. Two of which can be seen in figures 1 and 2. One is the approach I took of a growing squares and since a square has 4 corners it grows by four dots every minute. The second approach was one that viewed the four corners as orbital’s that grew out by one dot each minute. Both of these approaches come to the same solution but they way the visually problem solved to reach the solution was different. As I’ve said in previous blogs, I think it is very important for teachers to realize that students can approach the same problem in many different ways, and in face teachers should encourage this creativity, as this is what leads to higher order thinking.

figure 1

figure 2

            During this class we also had Diana’s presentation on grade 10 applied math. For her activity we were to solve a problem that was different for each group and can be made based on students’ interests. My group completed a problem about choosing a banquet hall for the school athletic banquet. The solution we came up can be seen in figure 3. This activity is a creative way to show students real life situations when they would need to know how to use substitution or elimination. It was also good that we were not restricted to one method and we could choose if we wanted to use substitution or elimination. We chose substitution as that it was we were all most comfortable with, however we then saw how easy it would have been to use elimination with our two equations, and this may have been the method a grade 10 applied student would have chosen. This is an example of non structured problem solving, which is sometimes more beneficial than structured problem solving as it can lead to more creativity.

figure 3