In my classroom we create avenues for student discussion as well as problems of the week for students to explore. Students are given tools to go about solving problems and then discuss various ways they each perceive their own mathematical reasoning. Students spend time exploring given problems of the week and have to create their own understanding of how to go about solving the problem. During their exploration of problems of the week, as well as group discussions, students are constantly finding ways of applying their own problem solving strategies, reasoning, and critical thinking skills. When students are initially given problems of the week, as well as daily problems in class, they are given time to explore their initial thought process with their group, discuss various methods, and collaborate in their reasoning on how to go about approaching or solving the problem.
Throughout the class, the students develop methods of going about how to solve difficult problems. Students learn techniques of how to approach problems where they may feel they have no way of solving, and they begin to put to use the tools they have learned up to that point. These tools can be in form of formulas, equations, or any general mathematical reasoning they have developed. In the development of these tools of analyzing problems, students are also given the opportunity to apply their analytical reasoning to everyday life and media. Students are given content to explore from an unbiased background to see the purpose of certain message they are being sent. The purpose is to create a critical and analytical mind that holds truth to a higher standard. Inflated opinion has no weight when it comes to the logical reasoning needed to demonstrate truth in mathematics. Students are therefore learning ways of distinguishing between truths and falsities in media.
The media students are exposed to often can come from the wide range of technologies surrounding their lives and therefore the students must build up fluency with such technologies in an educational environment. Students can spend time
Throughout the class, students are always working independently, as well as in groups, as a way for them to become self-directed learners. We are starting a new way of going through problems in class, where we give students time to work through classwork without given any instruction. This will build up their ability to find ways of tackling a problem without instruction. After the first 5 minutes we check in with the students and answer questions, discuss some strategies and then let them continue working with the intention of reflecting at the end. The students are provided with this opportunity to work and interact with their classmates on a daily basis. The teams they work in will be changed regularly throughout the class every two weeks. In these groups students are also working through POWs (Problems of the Week).
When working with POWs the students are each given a different task to work through in which they are responsible for so students can get experience managing larger projects in groups.