As I mentioned in a previous blog, I never enjoyed problem solving and I was always intimidated when the problems were wrote on the board. After this course, I actually throughly enjoy problem solving now because I've learned to look at it in a new light and experience it in new ways. I see problem solving as not a separate section within a math course but as an approach in teaching mathematics all throughout the curriculum.
I also now realize that student's must learn through mathematics instead of being taught directly how to "perform" mathematics. Mathematics is not just a subject in school, it's a way of thinking and it's all around us in our everyday lives. I've learned the importance of not focusing on what answer students obtain but rather put focus on the process of obtaining that answer. I also see the importance of holding off on jumping in when students are struggling, it's okay to struggle! It's how we learn. I also see mistakes as a great value in mathematics because it provides great learning opportunities for all students as well as the teacher.
I'd like to create a math learning environment that supports risk taking and values making mistakes as a learning experience. I'd use problem solving and open ended problems throughout the curriculum and teach it in a way where students can adapt it to solving everyday problems. I'd like to create real life situations in the classroom where student's can apply their mathematical thinking instead of giving them traditional algorithms on worksheets to complete.
The classroom would be arranged in a way that supports collaboration team work, and active learning. Desks would be arranged in groups and at times would be pushed to the perimeters of the room to create space for the student's to be physically involved in problems. I'd also have manipulatives available around the classroom for student's to use whenever they need them. I'd also make sure to lay some manipulatives at student's desks while solving problems as a way to get them used to using them and to cut down on any embarrassment of using them.
I've learned a great deal in this course and I'm happy of the shift in my perspective. I feel now MUCH more confident with approaching the subject and (almost) prepared to teach it. :)
