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Making Associativity Operational

Asghari, AH and Khosroshahi, LG (2016) Making Associativity Operational. International Journal of Science and Mathematics Education, 15 (8). pp. 1559-1577. ISSN 1571-0068

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Abstract

The purpose of this paper is to propose an operational idea for developing algebraic thinking in the absence of alphanumeric symbols. The paper reports on a design experiment encouraging preschool children to use the associative property algebraically. We describe the theoretical basis of the design, the tasks used, and examples of algebraic thinking in 5–6-year-old children. Theoretically, the paper makes a critical distinction between operational and structural meanings of the notion of equality. We argue that mathematical thinking involving equality among young learners can comprise both an operational and a structural conception and that the operational conception has a side that is productively linked to the structural conception. Using carefully designed hands-on tasks, the crux of the paper is the realization of algebraic thinking (in verbal mathematics) as operationally experienced in the ability to transform one number structure, with a quantity that is subject to change, into another through equality-preserving transformations.

Item Type: Article
Uncontrolled Keywords: 1302 Curriculum And Pedagogy
Subjects: L Education > L Education (General)
L Education > LB Theory and practice of education > LB1139.2 Early childhood education
Divisions: School of Education
Publisher: Springer
Related URLs:
Date Deposited: 25 Sep 2018 08:52
Last Modified: 25 Sep 2018 10:35
DOI or Identification number: 10.1007/s10763-016-9759-1
URI: http://researchonline.ljmu.ac.uk/id/eprint/9315

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