Abstract
This chapter presents examples from classrooms to illustrate how work within two branches of early algebra—functions and generalized arithmetic—can provide a context for highlighting the operations as distinct objects. The examples emphasize two major themes: the role of representations in the study of structures associated with the operations and teachers’ actions that draw students’ attention to those structures.
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Notes
- 1.
The work presented in this chapter was supported by the National Science Foundation under Grant Nos. ESI-0242609 (awarded to EDC), ESI-0550176 (awarded to TERC), and ESI-1019482 (awarded to TERC). Any opinions, findings, conclusions, or recommendations expressed in this work are those of the author and do not necessarily reflect the views of the National Science Foundation.
- 2.
Ms. Bergeron is a composite of teachers whose lessons were video recorded. Students’ names are pseudonyms.
- 3.
Ms. Bergeron was among 40 teachers who field tested the second edition of the curriculum Investigations in Number, Data, and Space (Russell et al. 2008) and provided cases for the professional development curriculum module, Patterns, Functions, and Change (Schifter et al. 2017). Field-test teachers met with curriculum writers for professional development for one week during the summer prior to field testing, two full days during the school year, and three-hour monthly after-school meetings. Many of the teachers had worked with the curriculum writers in previous projects that focused on deepening teachers’ understanding of mathematics content and attending to student thinking.
- 4.
- 5.
The classroom interactions described here were taken from video recordings and teachers’ written narratives based on audio recordings. Ms. Fried is a composite character composed of several teachers who taught the same lesson sequence, which appears in Russell et al. (2017, pp. 88–111). The same resource also includes video and more detailed textual descriptions of the classroom lessons (pp. 45–75).
- 6.
The teachers who comprise Ms. Fried are among 21 teachers who participated in a professional development project. In monthly after-school sessions and three full-day meetings each year, participants investigated mathematics, shared written narratives of their classrooms, and discussed video of their lessons. Nine teachers participated for four years; 12 teachers for two. Some teachers had participated in professional development with the researchers prior to this project.
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Schifter, D. (2018). Early Algebra as Analysis of Structure: A Focus on Operations. In: Kieran, C. (eds) Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-68351-5_13
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