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Teacher Development Structured Around Reasoning About Functions

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Abstract

We report on a teacher development program aimed at improving mathematics teaching and learning from grades 5–9. The 18-month largely online program arose from a partnership of mathematics education researchers, mathematicians, physicists, and nine school districts. The program employed functions as a lens to reinterpret and interconnect content topics in the mathematics curriculum. It was designed to promote a deep understanding of mathematics while drawing upon students’ spontaneous reasoning, generalizations, representations, and discussions about relations between physical quantities and numbers. We describe the program’s foundations and activities and analyze changes in teaching and in student learning during 3 years of implementation. Results suggest that the teacher development program contributed to improved teaching in the target districts and to positive changes in the performance of target district students on state-mandated tests.

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Notes

  1. The expression “algebraic thinking” conveys the idea that one can express relations among variables without necessarily utilizing letter symbolic notation. A simple statement such as “any number times one equals the number itself,” for example, suggests that the speaker is referring to an arbitrary member of a set of possible values, a variable.

  2. Data from participating districts in the other two states are not included due to the adoption of different assessment systems in these states. Data for the third cohort are not included because part of the districts had adopted different state assessments from year 2015.

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Acknowledgments

We thank Alfredo Bautista, Bárbara Brizuela, Mary Caddle, Corinne Glennie, Caroline Hagen, Chunhua Liu, Ken Wright, and John Zuman for their contributions to data collection and analyses.

Funding

This study is part of a Math Science Partnership awarded by the National Science Foundation (NSF), grant #0962863, to Tufts University, TERC, and nine school districts (https://sites.tufts.edu/poincare/).

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Authors and Affiliations

  1. Department of Education, Tufts University Professor Emerita, MA, 02155, Medford, USA

    Analúcia D. Schliemann

  2. TERC Retired Senior Scientist, Cambridge, USA

    David W. Carraher

  3. Department of Mathematics, Tufts University, Medford, USA

    Montserrat Teixidor-i-Bigas

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  1. Analúcia D. Schliemann
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  2. David W. Carraher
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  3. Montserrat Teixidor-i-Bigas
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Correspondence to Analúcia D. Schliemann.

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Schliemann, A.D., Carraher, D.W. & Teixidor-i-Bigas, M. Teacher Development Structured Around Reasoning About Functions. Int J of Sci and Math Educ 20, 793–816 (2022). https://doi.org/10.1007/s10763-021-10169-y

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