Problem solving has been the focus of a substantial number of research studies over the past thirty years. It is well beyond the scope of this paper to even attempt to summarize this body of research. Those interested in significantly broader reviews of research related to problem solving should see Schoenfeld (1985), Charles & Silver (1988), and Lesh & Zawojewski (2007). This paper focuses on the most recent research related to problem solving that has a direct impact on the way mathematics is taught every day in secondary mathematics classrooms.
“We are surrounded by increasingly sophisticated visual images.” (Howells, 2003) Everywhere you look, information is being transmitted visually. Pick up a magazine, glance at a newspaper, look at a television news program or check out the news online. Chances are that visual models—charts, graphs, diagrams, and other forms of illustration—are the primary source of the information that you will understand and retain.
Essential Questions. Big Ideas. Backward Design. Transfer. Do these terms sound familiar? You might have heard teachers and other educators use them. They are key components of Understanding by Design (UbD)-a groundbreaking but also common-sense approach for designing curriculum, instruction, and assessment. At the core of the UbD framework is the goal that students achieve deep understanding of ideas-not just for “the test,” but for life.