No abstract

No abstract

Learner affect and beliefs about mathematics are complex and multifaceted aspects of mathematical learning. Traditional teaching and learning approaches in mathematics education often result in problematic beliefs about mathematics. Since beliefs influence what learners learn and how they deal with learning mathematics, it is essential that the roles of beliefs and affect in mathematics classrooms are carefully examined. In solving modelling problems, learners and teachers take on new roles in the classroom: learners are placed in an active, self-directing situation in which they solve real-world problems. When learners engage in modelling tasks, they display and integrate cognitive, meta-cognitive and affective competencies. A modelling approach therefore allows one to detect learner beliefs in an authentic learning environment. Will this environment lead to students having more positive and productive dispositions towards mathematics? This article presents partial results of a study documenting the development of modelling competencies in learners working in groups over a period of 12 weeks. Through a design research approach, 12 learners working in groups solved three modelling problems, and transcriptions of learner interactions, questionnaires and informal interviews revealed that learner beliefs improved over this short period when exposed to modelling tasks. The results are encouraging, and may provide mathematics education with an avenue to develop more positive learner beliefs in mathematics.

This article sets out a professional development programme for primary school mathematics teachers. Clark and Hollingsworth’s model of teacher change provided the theoretical framework necessary to understand teacher change. A design study allowed for increased programme flexibility and participator involvement. Five volunteer primary school teachers teaching at South African state schools were involved in the programme for a period of one year and their pedagogy, use of mathematical content and context developed during the programme. Twenty lessons were observed over the year-long period. An observation rubric that specifically focused on mathematical pedagogy, use of context and mathematical content scale guided the researcher to gauge global changing teacher practices. Teacher growth was evident through their professional experimentation and changes in their personal domain. The design features emanating from the study are that teachers be given opportunities to experience reform tasks (e.g. model-eliciting tasks) in the role of learners themselves and teachers should be encouraged to use contextual problems to initiate concept development. More mathematical detail in lesson planning is also necessary. Furthermore, teachers need appropriately designed resource materials to teach in new ways. It is recommended that professional development includes teachers engaging collaboratively in solving rich tasks. This study adds to the growing body of knowledge regarding teacher development programmes that focus on how teachers change their own classroom practices.

No abstract