2 research outputs found
Pre-Service Mathematics Teachers’ Understanding of Quadrilaterals and the Internal Relationships between Quadrilaterals: The Case of Parallelograms
This study attempts to reveal pre-service teachers’ conceptions, definitions, and understanding of quadrilaterals and their internal relationships in terms of personal and formal figural concepts via case of the parallelograms. To collect data, an open-ended question was addressed to 27 pre-service mathematics teachers, and clinical interviews were conducted with them. The factors influential on pre-service teachers’ definitions of parallelograms and conceptions regarding internal relationships between quadrilaterals were analyzed. The strongest result involved definitions based on prototype figures and partially seeing internal relationships between quadrilaterals via these definitions. As a different result from what is reported in the literature, it was found that the fact that rectangle remains as a special case of parallelogram in pre-service teachers’ figural concepts leads them not to adopt the hierarchical relationship. The findings suggested that learners were likely to recognize quadrilaterals by a special case of them and prototypical figures, even though they knew the formal definition in general. This led learners to have difficulty in understanding the inclusion relations of quadrilaterals
Transitions Toward Digital Resources: Change, Invariance, and Orchestration
This chapter reports on the work of Working Group 4 and focuses on the
integration of digital resources into mathematics teaching and learning
practices. There are five central sections, focusing on, instrumental
genesis, instrumental orchestration, the documentational approach to
didactics, digital resources and teacher education, and the design of
learning environments with the use of digital resources. A range of
constructs and theoretical approaches are covered in these five
sections, and the opening section comments on construct validity and
issues in “networking” theoretical frameworks. The chapter can be
viewed as a literature review which surveys past and present (at the
time of writing) scholarship with an eye to possible future research.
The chapter is extensive in several dimensions: a large range of digital
resources and applications are considered; the subjects using digital
resources are not just teachers but also students, student teachers and
student teacher educators. Issues raised in the sections include
individual and collective use of resources, the adaptation of these
resources for specific learning goals and to prepare (pre- and
in-service) teachers for the use of digital resources