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From math drawings to algorithms: emergence of whole number operations in children

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An Erratum to this article was published on 10 December 2013

Abstract

This paper provides a longitudinal account of the emergence of whole number operations in second- and third-grade students (ages 7–8 years) from the initial visual processing phase to the converted final phase in numeric form. Results of a notational documentation and analysis drawn from a series of classroom teaching experiments implemented over the course of two consecutive school years indicate successful conceptual progressions in participants’ epistemological and synoptical use of visual representations. Further, their developing symbolic competence in whole number operations underwent several phases from initially linking notations with their respective signifieds to developing, elaborating, and routinizing symbol manipulation rules. Progressive emergence in both use and competence operated within interacting cycles of abduction, induction, and deduction.

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Acknowledgments

This research has been supported by a grant from the National Science Foundation (DRL 0448649). The opinions and views expressed are solely the author’s responsibility and do not represent the views of the foundation. The author expresses his sincere thanks to the reviewers who provided very insightful and helpful remarks.

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  1. Department of Mathematics and Statistics, San Jose State University, 1 Washington Square, San Jose, CA, 95129, USA

    F. D. Rivera

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  1. F. D. Rivera
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Correspondence to F. D. Rivera.

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Rivera, F.D. From math drawings to algorithms: emergence of whole number operations in children. ZDM Mathematics Education 46, 59–77 (2014). https://doi.org/10.1007/s11858-013-0543-1

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