According to Paul Halmos, the heart of mathematics is problem solving. “The major part of every meaningful life is the solution of problems; a considerable part of the professional life of technicians, engineers, scientists, etc., is the solution of mathematical problems. It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.”
How can you expose your student to real world problems that will encourage him to think mathematically outside the pages of a math book? One way is to present him with a daily mental story problem. Listening to the problem and solving it mentally requires a higher level of thinking and encourages thinking in math strategies more than reading a problem or making rote calculations.
If your child needs help working the problem, use the Socratic method and ask questions such as “What are you trying to solve?” and “What do you know?” When needed, guide your child to the answer.
What makes a good story problem? Good Questions for Math Teaching tells us there are three main features of good questions.
- Your child must do more than remember a fact or reproduce a skill.
- Your child learns something.
- There may be more than one acceptable answer.
Keep these features in mind as you create or look for story problems for your child. Some resources are listed below for problem solving.
- Good Questions: Great Ways to Differentiate Mathematics Instruction by Marian Small
- Good Questions for Math Teaching, Why Ask Them and What to Ask, Grades K–6 by Peter Sullivan and Pat Lilburn
- Good Questions for Math Teaching: Why Ask Them And What to Ask, Grades 5–8 by Nancy Canavan Anderson and Lainie Schuster
- How to Solve It by George Polya