Students’ Motivation in the Mathematics Classroom. Revealing Causes and Consequences

Students’ affective domain has been popular in the mathematics education community in an ongoing attempt to understand students’ learning behavior. Specifically, enhancing students’ motivation in the mathematics classroom is an important issue for teachers and researchers, due to its relation to students’ behavior and achievement. This paper utilized achievement goal theory—an important theoretical prospect on students’ motivation in school settings—to investigate the existence of a model presenting the relation between motivation and other affective constructs and students’ performance in mathematics. In this regard, two types of tests were administered to 321 sixth grade students measuring their motivation and other affective constructs and their performance in mathematics. Using structural equation modeling, we examined the associations among the affective constructs, motivation, and the extent to which these constructs influence students’ performance and interest in mathematics. The data revealed that students’ performance and their interest in mathematics were influenced by fear of failure, self-efficacy beliefs, and achievement goals. We discuss these findings in terms of teaching implications in the mathematics classroom.     

Using diagrams as tools for the solution of non-routine mathematical problems

The Mathematics education community has long recognized the importance of diagrams in the solution of mathematical problems. Particularly, it is stated that diagrams facilitate the solution of mathematical problems because they represent problems’ structure and information (Novick & Hurley, 2001; Diezmann, 2005). Novick and Hurley were the first to introduce three well-defined types of diagrams, that is, network, hierarchy, and matrix, which represent different problematic situations. In the present study, we investigated the effects of these types of diagrams in non-routine mathematical problem solving by contrasting students’ abilities to solve problems with and without the presence of diagrams. Structural equation modeling affirmed the existence of two first-order factors indicating the differential effects of the problems’ representation, i.e., text with diagrams and without diagrams, and a second-order factor representing general non-routine problem solving ability in mathematics. Implicative analysis showed the influence of the presence of diagrams in the problems’ hierarchical ordering. Furthermore, results provided support for other studies (e.g. Diezman & English, 2001) which documented some students’ difficulties to use diagrams efficiently for the solution of problems. We discuss the findings and provide suggestions for the efficient use of diagrams in the problem solving situation.     

Students’ Motivation in the Mathematics Classroom. Revealing Causes and Consequences

Students’ affective domain has been popular in the mathematics education community in an ongoing attempt to understand students’ learning behavior. Specifically, enhancing students’ motivation in the mathematics classroom is an important issue for teachers and researchers, due to its relation to students’ behavior and achievement. This paper utilized achievement goal theory—an important theoretical prospect on students’ motivation in school settings—to investigate the existence of a model presenting the relation between motivation and other affective constructs and students’ performance in mathematics. In this regard, two types of tests were administered to 321 sixth grade students measuring their motivation and other affective constructs and their performance in mathematics. Using structural equation modeling, we examined the associations among the affective constructs, motivation, and the extent to which these constructs influence students’ performance and interest in mathematics. The data revealed that students’ performance and their interest in mathematics were influenced by fear of failure, self-efficacy beliefs, and achievement goals. We discuss these findings in terms of teaching implications in the mathematics classroom.

     

Levels of students’ “conception” of fractions

In this paper, we examine sixth grade students’ degree of conceptualization of fractions. A specially developed test aimed to measure students’ understanding of fractions along the three stages proposed by Sfard (1991) was administered to 321 sixth grade students. The Rasch model was applied to specify the reliability of the test across the sample and cluster analysis to locate groups by facility level. The analysis revealed six such levels. The characteristics of each level were specified according to Sfard’s framework and the results of the fraction test. Based on our findings, we draw implications for the learning and teaching of fractions and provide suggestions for future research.