Browsing by Author "Biccard, Piera"

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    Development of affective modelling competencies in primary school learners
    (AOSIS Publishing, 2011) Biccard, Piera; Wessels, Dirk
    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.
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    The didactisation practices in primary school mathematics teachers through modelling
    (Stellenbosch : Stellenbosch University, 2013-12) Biccard, Piera; Wessels, D. C. J.; Stellenbosch University. Faculty of Education. Dept. of Curriculum Studies.
    ENGLISH ABSTRACT: Mathematics teacher development is a source of national and international concern. This study describes how primary school mathematics teachers develop didactisation practices. In considering how teachers could develop, so that student learning is optimised; the concepts of didactisation and the mathematical work of teaching were sourced from existing literature. The concept didactisation is explored and defined; and is incorporated with the concept of mathematical work of teaching. Nine practices were made explicit through this incorporation: active students, differentiation, mathematisation, vertically aligned lessons, access, probe, connect and assess student thinking, and teacher reflection. These nine practices become the framework for the professional development program and the data generation structure. Five primary school teachers were involved in a professional development program that used model-eliciting activities (MEAs) as a point of departure. A modelling perspective to teacher learning was chosen for the professional development program. The methodology followed the principles of design research and from this, a three phase teaching experiment was designed and implemented. The teachers and researcher met for development sessions and teachers were observed in practice at intervals throughout the program. Their developing didactisation practices were documented through a qualitative analysis of the data. It was established that teachers’ didactisation practices did develop during the nine-month program. Furthermore it was found that didactisation practices developed at different rates and consequently, a hierarchy of didactisation practice development is presented. The impact of the program was also gauged through teachers’ changing resources, goals and orientations. These three aspects also evolved over time. The program proposed in this study may be a suitable model to develop in-service and pre-service mathematics teachers. The study contributes to understanding teacher action in a classroom and how teachers can change their own thinking and practice.
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    An investigation into the development of mathematical modelling competencies of grade 7 learners.
    (Stellenbosch : University of Stellenbosch, 2010-12) Biccard, Piera; Wessels, D. C. J.; University of Stellenbosch. Faculty of Education. Department of Curriculum Studies.
    ENGLISH ABSTRACT: Mathematical modelling is becoming a popular teaching and learning approach in mathematics education. There is however a need within the modelling domain to identify exactly what modelling competencies are and how these competencies develop. This study examines how mathematical modelling competencies develop in Grade 7 students working in groups. Modelling is placed in the field of mathematics teaching and learning as a significant means of learning mathematics. Modelling competencies are identified and characterised from existing literature and explored through empirical generation and collection of data. The study is qualitative in nature and uses a mixed approach of design research and some aspects of grounded theory. Students’ progress through a modelling program is documented while the modelling competencies of students stereotyped as weak and strong are also investigated. The findings firmly support earlier research that competencies do develop in students who are exposed to modelling. A comprehensive picture of the modelling situation is presented since this study merges competencies from other studies into a detailed analysis of the modelling situation - it presents an authentic modelling situation of students working in groups and furthers the discussion on modelling competencies. The analysis of the data suggests that the development of modelling competencies is complex and interrelated but that competencies do develop progressively in groups involved in modelling tasks. Recommendations for additional studies include studies of a longer duration and a full investigation into the link between modelling and language ability.
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    Student mathematical activity as a springboard to developing teacher didactisation practices
    (AOSIS Publishing, 2015-12-07) Biccard, Piera; Wessels, Dirk
    This article is part of a larger study on teacher development. The main study investigated teacher development within primary school Mathematics teachers’ classrooms to determine if teaching practices could be enhanced through a didactisation-based programme. It sought to develop teachers within their own environments and classrooms. Design research (both designing the conditions for change and studying the results of those conditions) enabled the researchers to design a programme that was congruent with teachers’ own needs and experiences. The programme ran for a period of a year with regular contact between the teachers and the researcher conducting the programme (the first author). The programme set out nine didactisation practices: active students, differentiation, mathematisation, vertically aligned lessons, accessing student thinking and ideas, probing student thinking and ideas, connecting student ideas, assessing students and reflecting on practice. One practice, student activity, is the focus of this article. It was found that by initiating discussion and cognitive conflict in teachers by using modelling problems, and further allowing teachers to observe pupils working in groups with modelling problems, teachers were starting to incorporate the didactisation practices within their own classrooms. This article documents specifically the fundamental role of student mathematical activity and the importance of improving student mathematical experiences, both for teacher development and for student mathematical learning. The study may be valuable in structuring and planning further effective teacher development programmes.