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Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

Abstract

"This paper describes the diversity of ideas middle school mathematics teachers have regarding 1) what constitutes a mathematical model of a real-world phenomenon, and 2) the relationships between models and empirical data. Moreover, the paper explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers (grades 5-9). We analyzed teachers' written responses to three open-ended questions through content analysis. A varied landscape of ideas was identified. Teachers referred to different entities as constituting models, expressed different ideas about whether data points can be part of models and whether models convey more information than data. Interesting patterns depending on teachers educational background were identified, especially between teachers with and without a mathematics background. We discuss our findings and suggest implications for teacher professional development."

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