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Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds pp 107–138Cite as

Cultivating Early Algebraic Thinking

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Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

This chapter describes a functions approach to early algebraic thinking developed in the context of classroom research with young students. We outline our approach, examine examples of students’ reasoning in the classroom, and present interview and written assessment evidence of student learning. We also describe and evaluate a related program aimed at preparing teachers to promote algebraic thinking across the curriculum. Throughout, we attempt to identify conditions favorable to the cultivation of algebraic thinking in mathematics education.

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Notes

  1. 1.

    As others have noted (Moss and Beatty 2006), if one intends to eventually arrive at a closed form expression of the function, as opposed to a sequential listing, it is important to systematically keep track of the step number as well as the corresponding value of the function; this is easily achieved by using a table with a column for step numbers and another for the corresponding values of the function.

  2. 2.

    Such remarks reflect a student’s proclivity to frame the co-variation among the variables in terms of a story unfolding over time.

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Acknowledgements

The studies described in this chapter were sponsored by the National Science Foundation (NSF), grants 9772732, 9909591, 0310171, 0633915, and #0962863. Opinions, conclusions, and recommendations are those of the authors and do not necessarily reflect NSF’s views. Special thanks to Bárbara Brizuela for her many contributions to the studies on algebra in the early grades and to Montserrat Teixidor-i-Bigas for her central role in the Poincaré Institute for Mathematics Education.

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  1. TERC, 2067 Massachusetts Ave., Cambridge, MA, 02140, USA

    David W. Carraher

  2. Department of Education, Tufts University, Medford, MA, 02155, USA

    Analúcia D. Schliemann

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  1. David W. Carraher
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Correspondence to David W. Carraher .

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  1. Département de Mathématiques, Université du Québec à Montréal, Montréal, Québec, Canada

    Carolyn Kieran

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Carraher, D.W., Schliemann, A.D. (2018). Cultivating Early Algebraic Thinking. 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_5

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