Improving Students' Problem Solving Ability
There are many ways in which teachers can help students become better problem solvers. This section will focus on general methods to encourage improvement that can be applied to process or application problems. Improving dissimilar learners’ problem-solving abilities occurs in lessons and activities that focus on the following suggestions, and proceed carefully through step- by-step instruction and feedback to and from teachers and students.
Establishing a Context for Interest: An important instructional technique is to embed problem solving in mathematics lessons by relating the problem to students’ interests. For example, the teacher could pose this problem:
A young boy, Daniel, wants to go to a theme park. He must earn his ticket, which costs $10.00. He can wash dishes and clean his room for $.50 per hour and rake leaves for $.75 per hour. How many hours should he work in each location to earn the ticket money?
In this problem, students are engaged in a situation in which they may have personal interest. They are encouraged to understand that the reason they are learning mathematics is to solve specific problems with number operations.
Teaching a Variety of Heuristics: Equally important is that specific problem-solving heuristics be taught. The teacher focuses on how to use a particular strategy, such as drawing a picture, using manipulatives, or finding patterns, by carrying them out with students during lessons. The teacher and students brainstorm and verbalize all the thinking done before, during, and after work. Class discussions include plans of what to do, when certain steps are taken, why steps are used (or not used), and how and why to proceed with each thought. Even second guessing is important to verbalize aloud because it helps students learn to think logically.
Not all students will learn to use all the strategies in an efficient manner. However, pupils must be familiar enough with the techniques to choose the strategies. To solve a question about buying gum, for example, students can draw a picture, act it out with currency, or use smaller numbers.
Grouping Similar Types of Problems That Call for Similar Strategies: This strategy helps students find patterns in solution attempts. Lessons on organizing data tables, drawing diagrams, or working backward toward solutions are helpful tools to increase familiarity with heuristics. Solution patterns can then be applied to new problems.
Working Cooperatively Toward a Solution: Group efforts can be less threatening to students than working individually (Johnson & Johnson 1980). “Problem solving ability is enhanced when students share opportunities to solve problems themselves and to see problems being solved” (Kilpatrick et al., 2001, p. 420).
Starting with Simple Problems: Solutions are more easily found and confidence is built when students experience success quickly. They are more willing to take risks after knowing they are, in fact, able to find solutions correctly.
Rewarding Students for Small Steps of Success: Frequent words of praise and positive comments on written work for step-by-step improvement are powerful instructional strategies for encouragement. Suggestions and hints are also helpful to students throughout the problem-solving process.
Compiling a Mathematics Dictionary Journal with Students: Important mathematics terms should be discussed in class. The words should be defined and further identified with drawings. For example, students record a definition for dividend and draw an arrow to the dividend in a long division problem. Geometric shapes can be drawn and their components, such as perimeter, area, edges, and vertices, can be marked and defined. These vocabulary words should include those that can confuse children. For example, volume refers mathematically to geometry and measurement but also to decibels of sound.
Providing Sufficient Time for Solving Problems: Solving a variety of fewer, quality problems rather than many similar problems allows time for:
- use of alternate strategies and processes
- detection of errors
- search for additional solutions
- everyday applications to other problems
Simplifying Numbers: An example of using smaller numbers follows:
A sporting goods store has 247 soccer balls worth $5.97 each and 375 footballs worth $2.95 each. What is the total value of soccer balls and footballs?
To complete the problem, students could substitute:
- 2 instead of 247 soccer balls
- $1.00 instead of $5.97
- 3 instead of 375 footballs
- 2 instead of $2.95
Reduce Reading Difficulties: Reduce the number of words and/or record the problem on a tape recorder in the same example:
- 247 baseballs worth $5.97
- 375 softballs worth $2.95
- Worth how much all together?
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