Does Training in Alternative Assessment Matter? The Case of Prospective and Practicing Mathematics Teachers’ Attitudes Toward Alternative Assessment and Their Beliefs About the Nature of Mathematics

This study explored the training of prospective and practicing mathematics teachers in alternative assessment and its impact on their attitudes toward alternative assessment methods and their beliefs about the nature of mathematics. Data were collected from 51 prospective teachers and 50 practicing teachers who took a course on alternative assessment in mathematics. Findings indicated a significant change in the correlation between the positivist and constructivist dimensions of their beliefs about the nature of mathematics following the course. No significant differences were found between the prospective and practicing teachers’ beliefs either before or after the course nor in their attitudes toward alternative assessment after the course. Before the course, however, the two groups differed significantly in their attitudes toward alternative assessment. Findings also revealed significant changes in attitudes toward alternative assessment and beliefs about the nature of mathematics following participation in the course. These changes in attitudes and beliefs were accompanied by a shift in the nature of the assessment tasks written by the participants. Participants who demonstrated more positive attitudes and constructivist beliefs tended to write more conceptual problems and less procedural exercises. Implications for mathematics teacher training and professional development in alternative assessment are discussed.     

Modelling in Primary School: Constructing Conceptual Models and Making Sense of Fractions

This article describes sixth-grade students’ engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students were also able to generalize the fraction model and transfer it to a new situation. Analysis of the students’ work demonstrates that they made use of four fraction constructs—part-whole, operator, quotients, and ratio. The activities also revealed difficulties in the students’ knowledge of fractions, some of which were overcome in the process of organizing and mathematizing the problem.