Scholars and teacher educators alike agree that teachers' beliefs and attitudes toward mathematics are key informants of teachers' instructional approaches. Therefore, it has become clear that, in addition to enriching preservice teachers' (PSTs) knowledge, teacher education programs should also create opportunities for prospective teachers to develop productive beliefs and attitudes toward teaching and learning mathematics. This study explored the effectiveness of a mathematics preparatory program based on the history of mathematics that aimed at enhancing PSTs' epistemological and efficacy beliefs and their attitudes toward mathematics. Using data from a questionnaire administered four times, the study traced the development of 94 PSTs' beliefs and attitudes over a period of 2 years. The analysis of these data showed changes in certain dimensions of the PSTs' beliefs and attitudes; however, other dimensions were found to change in the opposite direction to that expected. Differences were also found in the development of the PSTs' beliefs and attitudes according to their mathematical background. The data yielded from semi-structured follow-up interviews conducted with a convenience sample of PSTs largely corroborated the quantitative data and helped explain some of these changes. We discuss the effectiveness of the program considered herein and draw implications for the design of teacher education programs grounded in the history of mathematics.

The present study explores pupils' constructed definitions of the concept of function in relation to their abilities in dealing with tasks of functions involving different forms of representations and problem solving tasks. A major concern is also to examine the interrelations between these three ways of thinking about or dealing with the concept of function. The sample of the study consisted of secondary school pupils in Cyprus. A test was developed which involved seven items: one item requested pupils to provide a definition of what function is and the other six items were developed in order to investigate pupils' ability to transfer information from one representation to another and to solve problems on function. Findings revealed pupils' difficulties in giving a proper definition for the concept of function and resolving problems on functions involving conversions between diverse modes of representation. Several inconsistencies among pupils' constructed definitions, their competence to use different representations of functions and their problem solving ability, were also uncovered, indicating lack of flexibility between different ways of approaching functions.

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Many studies investigated the use of collaboration at conventional teaching environment in different educational levels. The present study examines students’ behavior during a collaborative assignment in an online learning environment in higher education. Data were collected by graduate students who were attending a course at a distance learning master degree program in Special Education. The developed group dynamics and students’ beliefs about their role during the activity were “revealed” by their reactions to the discussion forum, their private e-mails to the instructor, their activity at the platform and their contribution on the assignment, for which the wiki tool was used. Results indicated that although students were at the same time in-service or pre-service teachers at primary and secondary education and they were expected to implement group work at their teaching, they had low self-efficacy beliefs in using it as students in online learning environment. Their major difficulties were related with their fear about possible negative consequences concerning their marks due to other members’ behavior and the lack of experiences. Suggestions on how the group work and the collaborative assignment can be integrated more effectively in an online learning environment in higher education courses are discussed

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