What This Means for Instruction

Here are some tips to help educators who are planning instruction in problem solving:

• Provide a wide variety of problems for students to solve.
• Allow students adequate time to solve problems.
• Use questioning to focus students on the important parts of problems.
• Model and provide explicit instruction on various problem-solving strategies.
• Invite students to use varied strategies to solve problems.
• Provide problems that cross the mathematics curriculum and other content areas.
• Use picture books with young students to provide engaging contexts for problem solving.
• Use physical objects with very young children, and move towards pictures and figures with older students.
• Address problem solving regularly and with every grade level of students.
• Develop these three key aspects of students' cognitive abilities that are related to problem solution:
• strategies, or approaches that can be transferred to many different problem-solving situations. These might include Polya's four-step problem-solving scheme (understand the problem, devise or select a plan, carry out the plan, look back) and other problem-solving strategies, including those suggested below.
• metacognition, or ways of checking and correcting our own thinking.
• beliefs and attitudes, including confidence in an ability to find solutions and a willingness to continue to look for solutions (Van de Walle, 1994).
• Teach students in grades three through eight these additional problem-solving strategies (Van de Walle, 1994):
• try-and-adjust
• draw a picture, act it out, use models
• look for a pattern
• make a table or chart
• make an organized list
• work backward
• use logical reasoning
• try a simpler problem
• write an equation or open sentence