We have known for a long time that reading is a complex problem-solving activity.
More recently, teachers have come to understand that becoming mathematically literate is also a complex problem-solving activity that increases in power and flexibility when practiced more often.
Our students live in an information and technology-based society where they need to be able to think critically about complex issues, and “analyze and think logically about new situations, devise unspecified solution procedures, and communicate their solution clearly and convincingly to others” (Baroody, 1998).
Mathematics education is important not only because of the “gatekeeping role that mathematics plays in students’ access to educational and economic opportunities,” but also because the problem-solving processes and the acquisition of problem-solving strategies equips students for life beyond school (Cobb, & Hodge, 2002).
Students will have opportunities to explain their ideas, respond to the ideas of others, and challenge their thinking.
Those students who think math is all about the “correct” answer will need support and encouragement to take risks.
The importance of problem-solving in learning mathematics comes from the belief that mathematics is primarily about reasoning, not memorization.
Problem-solving allows students to develop understanding and explain the processes used to arrive at solutions, rather than remembering and applying a set of procedures.
Rather than directing a lesson, the teacher needs to provide time for students to grapple with problems, search for strategies and solutions on their own, and learn to evaluate their own results.
Although the teacher needs to be very much present, the primary focus in the class needs to be on the students’ thinking processes.”Students need to have opportunities to work on complex tasks rather than a series of simple tasks devolved from a complex task.