Developing Number Sense: An Approach to Initiate Algebraic Thinking in Primary Education

Natividad Adamuz-Povedano, Elvira Fernández-Ahumada, M. Teresa García-Pérez and Jesús Montejo-Gámez
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Natividad Adamuz-Povedano: Department of Mathematics, University of Córdoba, 14071 Córdoba, Spain
Elvira Fernández-Ahumada: Department of Mathematics, University of Córdoba, 14071 Córdoba, Spain
M. Teresa García-Pérez: CEIP Al Andalus, 14004 Córdoba, Spain
Jesús Montejo-Gámez: Department of Didactics of Mathematics, University of Granada, 18011 Granada, Spain

Mathematics, 2021, vol. 9, issue 5, 1-25

Abstract: Traditionally, the teaching and learning of algebra has been addressed at the beginning of secondary education with a methodological approach that broke traumatically into a mathematical universe until now represented by numbers, with bad consequences. It is important, then, to find methodological alternatives that allow the parallel development of arithmetical and algebraic thinking from the first years of learning. This article begins with a review of a series of theoretical foundations that support a methodological proposal based on the use of specific manipulative materials that foster a deep knowledge of the decimal number system, while verbalizing and representing quantitative situations that underline numerical relationships and properties and patterns of numbers. Developing and illustrating this approach is the main purpose of this paper. The proposal has been implemented in a group of 25 pupils in the first year of primary school. Some observed milestones are presented and analyzed. In the light of the results, this well-planned early intervention contains key elements to initiate algebraic thinking through the development of number sense, naturally enhancing the translation of purely arithmetical situations into the symbolic language characteristic of algebraic thinking.

Keywords: number sense; algebra thinking; relational thinking; generalized arithmetic; tactical calculation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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