Abstract
This study examined prospective teachers’ (PSTs) ability to recognize evidence of children’s conceptual understanding of mathematics in three content areas before and after an instructional intervention designed to support this ability. It also investigates the role PSTs’ content knowledge plays in their ability to recognize children’s mathematical understanding. Results of content knowledge assessments administered at the beginning of the study revealed that content knowledge did seem to support PSTs’ analyses of children’s understanding when the child’s response demonstrated understanding or demonstrated a misconception. Content knowledge did not seem to support PSTs’ analyses of children’s procedural responses, as many PSTs with good content knowledge initially characterized procedural solutions as evidence of conceptual understanding. Similarly, content knowledge did not seem to support PSTs’ analyses of children’s responses with features commonly associated with understanding but not evidence of understanding. After the instructional intervention consisting of three multifaceted lessons in which PSTs examined many examples of student thinking, they showed improved ability to analyze responses with conceptual features and no evidence of conceptual understanding and responses demonstrating procedural knowledge. Results suggest that content knowledge is not sufficient for supporting PSTs’ analysis of children’s thinking, and that building activities such as the intervention into content courses may help develop this ability. Implications for teacher education programs and future research are considered.
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Notes
We use “content knowledge” to refer to PSTs’ conceptual understanding of mathematics so as to be clear when we are talking about PSTs’ conceptual understanding versus the conceptual understanding of children.
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Acknowledgments
This research was supported by a grant from the National Science Foundation (Grant 0083429 to the Mid-Atlantic Center for Teaching and Learning Mathematics). The views expressed are those of the authors and not necessarily those of the Foundation. We would like to thank Sandy Spitzer and Christine Phelps for their comments regarding early ideas for the design of this study.
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Bartell, T.G., Webel, C., Bowen, B. et al. Prospective teacher learning: recognizing evidence of conceptual understanding. J Math Teacher Educ 16, 57–79 (2013). https://doi.org/10.1007/s10857-012-9205-4
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DOI: https://doi.org/10.1007/s10857-012-9205-4