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In a previous article of the same journal, we have discussed the interrelations of students' beliefs and self-efficacy beliefs for the use of representations and their respective cognitive performance on the learning of fraction addition. In the present paper, we confirm a similar structure of cognitive and affective factors on using representations for the concept of decimals and mainly we discuss the various interrelations among those factors. Data were collected from 1701 students in Grades 5-8 (11-14-years-old). Results revealed that multiple-representation flexibility, ability on solving problems with various modes of representation, beliefs about the use of representations and self-efficacy beliefs about using them constructed an integrated model with strong interrelations that has differences and similarities with the respective model concerning the concept of fractions. (Contains 3 tables and 2 figures.)

The dynamic model of educational effectiveness defines school level factors associated with student outcomes. Emphasis is given to the two main aspects of policy, evaluation, and improvement in schools which affect quality of teaching and learning at both the level of teachers and students: a) teaching and b) school learning environment. Five measurement dimensions are used to define each factor: frequency, stage, focus, quality and differentiation. This paper reports the results of a longitudinal study testing the validity of the dynamic model at the school level. The multidimensional approach to measure the school level factors was supported and most of the factors and their dimensions were found to be associated with student achievement in different learning outcomes. Implications for the development of the dynamic model and for educational practice are drawn. (Contains 5 tables and 3 figures.)

Drawing on data from the Republic of Cyprus, this paper uncovers elementary teachers' epistemological beliefs about mathematics. Twenty-two experienced teachers were invited to individual semi-structured interviews. Thematic data-driven analyses identified three themes and eight sub-themes, which I discuss, taking their socio-cultural context into consideration. This study suggests that applying predetermined frameworks directly taken from the literature when examining teachers’ epistemological beliefs in mathematics can be problematic, as they might hinder other culturally specific beliefs from emerging. In closing, this paper presents some implications for the results on teacher education and professional development, as well as ideas for future research. [ABSTRACT FROM AUTHOR]

In this paper, we report on a comparison of the treatment of addition and subtraction of fractions in primary mathematics textbooks used in Cyprus, Ireland, and Taiwan. To this end, we use a framework specifically developed to investigate the learning opportunities afforded by the textbooks, particularly with respect to the presentation of the content and the textbook expectations as manifested in the associated tasks. We found several similarities and differences among the textbooks regarding the topics included and their sequencing, the constructs of fractions, the worked examples, the cognitive demands of the tasks, and the types of responses required of students. The findings emphasized the need to examine textbooks in order to understand differences in instruction and achievement across countries. Indeed, we postulate that within a given country there may exist a recognizable “textbook signature.” We also draw on the results and the challenges inherent in our analysis to provide suggestions and directions for future textbook analysis studies. [ABSTRACT FROM AUTHOR]