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.
Highlights
Universal references to mathematics education as current policy frameworks of developed countries argue the importance of promoting experiences to develop the so-called number sense in early school activities [1]
One of the main objectives of mathematics at the beginning of secondary education focuses on becoming familiar with algebraic language and with the use of algebraic expressions to describe numerical relationships, which often present difficulties and even frustration for both students and teachers [3]
1960s it was already well-known that divergences between arithmetic and algebra can cause great difficulties in early algebra learning. [5] and [6] stand out for the lack of understanding of arithmetic relationships. [7] indicates that there is a significant body of research that argues that children’s misconceptions in algebra are due to a short-sighted approach to learning arithmetic in the early years
Summary
Universal references to mathematics education as current policy frameworks of developed countries argue the importance of promoting experiences to develop the so-called number sense in early school activities [1]. One of the main objectives of mathematics at the beginning of secondary education focuses on becoming familiar with algebraic language and with the use of algebraic expressions to describe numerical relationships, which often present difficulties and even frustration for both students and teachers [3]. These difficulties are manifested in secondary education, their origin is long before, at the early levels of primary education, and due to various causes. According to [8], there is a lack of work with properties of operations, regularities and patterns in elementary school
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