Role of verbalizations in mathematical problem solving by Lee Wee Hoon

While viewing the video of the primary level problem-solving lesson, I focused my attention on the students and made the following observations. The teacher had given the class a task to do in groups. She wanted them to consider the different sizes of squares in a chess board and find out the total number of squares. A group of three female students was observed working on the task. One student made the following statements:
o "find pattern lah. Like that easier."
o "see got any pattern or not"
o " try 3 first"
o "3 by 3"

Researchers have established several models of the problem solving processes which describe how problem solvers approach a problem. The most frequently used model is Polya's four-stage problem solving model (http://www.drkhamsi.com/classe/polya.html). According to his model, there are four stages in a problem solving process:
1. Understand the problem
2. Devise a plan
3. Carry out the plan
4. Looking back

The above statements made by the student show that she is making a plan to solve the problem. This corresponds to the second stage of Polya's model i.e. devising a plan. Several studies revealed that in most students' solution attempts, self-regulatory activities such as analyzing the problem, monitoring the solution process, and evaluating its outcome are absent. A typical approach used by many students is as follows: the student takes a quick look at the problem, decides the calculations to perform using the numbers given in the problem, and proceeds with the calculations without considering any alternatives even if no progress is made at all.

Through verbalizations, teachers can attempt to identify the processes students use (or do not use) when solving mathematical problems. Teachers can utilize this knowledge to help their students become better problem solvers. Therefore, I propose to do a research to investigate the following:
1. What do the verbalizations of students with different abilities reveal about their problem solving process?
2. To what extent can verbalizations be used in positively affecting students’ problem solving performance?

In this study, verbalizations refer to students' oral descriptions of their problem solving process. Three students with varying mathematical abilities (high, average and low) will be selected to take part in the study. A set of problems of varying levels of difficulty (high, moderate and low) will be given to the students. They will be asked to provide oral descriptions of their problem solving processes while solving these problems. All the students will be videotaped while solving the problems. If the student was silent for twenty seconds, he/she will be prompted “Please tell me what you are thinking.” The videotaped sessions will be categorized according to problem and student. Their verbalizations will be examined and coded according to Polya's four-stage problem solving model. Students will be asked to solve another set of problems with similar levels of difficulty quietly. Their work for both set of problems will be collected and analyzed according to student and problem. The frequency of correct and incorrect answers for all problems will also be recorded.

The findings from this research will allow teachers to have a greater understanding of students' problem solving processes based on their verbalizations. Teachers can then model the problem solving process to students so that they can be more successful in their attempts at problem solving.

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