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Concerns about teachers’ mathematical knowledge for teaching suggest the need for ongoing studies to consider innovative professional-learning approaches to help them to enhance this knowledge. This paper reports on a project that investigates such an approach involving self-based collaborative concept exploration (SCCE). It presents the theoretical framework of the SCCE. It focuses on the project’s initial stage that explored whether the knowledge a group of ten experienced teachers of different grades shared about a mathematics concept would support the SCCE and lead to enhanced mathematical knowledge for them. Findings suggested that teachers could share the type of practice-based mathematical knowledge needed to support the SCCE and form a basis to further explore the concept to enhance their horizon content knowledge.