The mathematical problem solving of 4th- and 5th-grade students based on the beliefs and practices of their teachers
The purpose of this study was to determine the effects that beliefs and practices of teachers have on problem-solving skills of 4th - and 5th -grade students in the five areas of algebra, chance and data, measurement, number, and space. The literature review showed how teacher beliefs, teacher practices, and a consonance between the beliefs and practices of teachers all play an important part in the reform of mathematics education. Teacher attitudes and beliefs are the key components in changing the ways of teaching mathematics in schools. The National Council of Teachers of Mathematics (NCTM) in The Curriculum and Evaluation Standards advocated the constructivist approach enabling students through mathematical tasks and activities to construct their own knowledge enthusiastically through investigation and discourse. Teachers (n = 123) were surveyed using the Mathematics Beliefs Scale to determine those with high constructivist beliefs. Teachers (n = 6) were observed using the Problem-Solving Observation List to determine high (n = 4) and low (n = 2) constructivist practices. Students ( n = 76) in these classrooms were administered the Collis-Romberg Problem-Solving Profiles to measure their problem-solving skills on five different subtests (algebra, chance, measurement, number, and space). This study showed that when teachers (n = 3) had high constructivist beliefs their students scored higher in problem solving. When teachers (n = 4) had high constructivist practices their students scored higher on two of the five subtests and the total test. When there was a consonance between high constructivist beliefs and high constructivist practices there was a significant difference in performance. The students ( n = 35) whose teachers had consonance in their constructivist beliefs and constructivist practices scored higher (mean difference = 4.0) in the area of problem solving from either the students (n = 14) in classrooms where there was a dissonance in their teachers' beliefs and practices or students (n = 27) whose teachers had low constructivist beliefs and low constructivist practices (mean difference = 1.4).