PAcree

     In Van de Walle's book, Teaching Student Centered Mathematics in Grades 5-8, the author explains that teachers need to understand that effective mathematics teaching is based on the understanding of how children learn, how we as teachers promote learning, and how teachers can plan and assess student learning on a daily basis. In chapter 1, the authors discusses how people learn new things. Students give meaning to new ideas by connecting them to the things they already know. Understanding is defined as the quality and quantity of the connections of new ideas to the existing ideas. This idea provides the foundation of the book that student centered problem solving allows students to construct their own ideas and become learners that understand mathematics. Chapter 1 further explains problem solving is a vehicle to teach the math that students are required to know.

     The benefits of Problem-Based teaching are: focusing students attention on ideas and making sense of mathematics, developing students' belief in themselves as problem solvers, on-going assessment, students are having fun and thus engaged, and it requires students to communicate, reason, and justify their own ideas about mathematics.

     Chapters 2-4 discuss strategies for teaching whole number computations, fraction concepts and computations, and decimals and percents. These chapters highlight the concepts and offer strategies and activities for teaching the concepts through problem solving tasks.

   The use of a problem based approach to teaching mathematics is different from the traditional approach of the teacher showing how to do the steps to solve problems and students repeating the steps to produce an answer. I have used tasks to allow students the opportunity to "play" with a problem and come up with original ways and often multiple ways of solving it. I have found that facilitating while students work together, helps me to assess understanding of "big ideas" and to provide some redirection when misconceptions arise on a one-on-small group basis. Students are more confident and less afraid to ask questions or admit to not knowing what to do when working in a small group. The challenge of teaching using tasks is to have numerous tasks available and constantly revising plans based on the previous days work. Grading and scoring have also been a challenge. Rubrics are a good way to score understanding, however, must be made in advance and be geared toward a specific task.