Teachers and Students Mathematical Problem-Solving Beliefs and Skills with a Focus on PISA Problems

Problem-solving skills, as a major component of mathematics curriculum, assist students to become equipped and competent individuals for the requirements of the century. The researcher used mixed method approaches to examine the relationship among in-service high school mathematics teachers’ backgrounds, beliefs, and skills about mathematical problem solving, and to analyze students’ approaches during problem-solving, and how they describe their problem-solving beliefs and their teachers’ mathematics instruction. Seven teachers and 91 students from one private and one public high school in the New York City area participated in the study. Both groups of participants completed belief questionnaires and mathematics activities which included problems with real-life contexts. Teachers also completed a background/opinion questionnaire. This study contributes deeper comprehension of the reasons behind developing problem-solving beliefs and skills. Statistical analysis did not reveal any significant correlation between teachers’ questionnaire responses and mathematics activity scores. However, working at these particular public and private school was an indicator of teachers’ belief scores, mathematics activity scores, and preferences of instructional methods. The qualitative analysis indicated that, for in-service teachers, taking problem solving courses in graduate school, participating in problem-solving related professional development activities, and enjoying freedom in the workplace to adopt more problem-solving centered instruction affected teachers’ problem solving skills and beliefs beneficially. The qualitative analysis of mathematics activities highlighted some common misunderstandings about certain mathematical contents and common approaches among students, such as performing random calculations with no apparent strategy, using wrong formulas, substituting erroneous numbers into equations. Also, most students experienced difficulties in understanding a problem and devising a plan to solve it. Although most students did not see themselves as strong problem solvers, they tended to stick with a problem until they solved it, tried new approaches, and were comfortable with making mistakes. Students generally showed agreement levels similar to those of their teachers for statements about looking back at answers, using different representatives, and encouraging different ways to solve the same problem. Students generally received lower scores on belief questionnaires and mathematics activities than did their teachers