EMTH 200 has been really helpful in emphasizing the importance of teaching mathematics through problem solving. It has helped to teach me that when students figure things out on their own, they are so much better at remembering and applying their learning, no matter the subject area, but especially in math.
There are many ways that a teacher can use problem solving to teach their students. They can use Guess and Check methods, in which students use critical thinking to guess the approximate values of things, check the answer, and then modify their approach if they need to. Students can Make a Model, in which they create some sort of graph, diagram, or picture to help themselves visualize the problem they are trying to solve. Students can try to identify Patterns, or they can use Elimination or a Table to reason their answer out. There are many things that students can do to find the answers to their given math problems, which is why it is such an effective tool, because students are able to use whatever method they find most comfortable to solve the mathematical problems that they face. That is why it is so amazing.
What I have learned in this class is that it is okay for students to struggle. Without struggle students are unable to take hold of learning and make it their own. Without struggle students are merely receptors of information, and not actors upon the school curriculum. It is also important for students to have the opportunity to collaborate. Humans are social creatures, and as such we are much more productive when we work together. Ideas very rarely pop out of just one mind, but instead advancement is made by building upon the work of others, and so students should have that same opportunity to collaborate with their peers to most thoroughly and completely solve the given problems. I have also learned that understanding takes time. People do not immediately understand things, and when solving problems may need to take a break and come back to the problem with a clear and refreshed mind, so again, students should have the same opportunity. The benefit of having classes everyday in school is that if a teacher has a difficult problem that students need to solve, and gives them a little bit of time each day to try to solve it, with patience and guidance students should be able to solve the problem. One final thing I think that I will take from this class is to encourage failure among my students, because failure should not mean that the students fail, instead failure should be taken as a learning opportunity. It is the trying, failing, and modifying process by which the world works, so why should it not work the same in classrooms? When students feel free to fail, they will be much more willing to try, which is exactly what teachers should want their students to do.
Problem solving is an incredible tool for teachers, and as a teacher I intend to use it.