Structures
The notion of structure is present in most conceptions or approaches recognized in school algebra (Molina and Cañadas, 2018). Within the framework of generalized arithmetic, the term structure refers to a system comprised of a set of mathematical objects, one or more operations, as well as certain properties and relations of and between said objects and operations (Castro, Rico and Romero, 1997).
In the functional conception of algebra, the term structure is equal to regularity or pattern of the values of the two related variables (Torres, Cañadas, Moreno & Gómez, under review). In the study of patterns, this term is used less precisely which makes it difficult at times to distinguish between the notion of pattern and the notion of structure. We consider the former one as broader and containing the latter. It is our understanding that the notion of structure refers to identifying the pattern through particular cases, and the expression or application of the same for general cases.
Based on the conception of algebra as a tool to express general methods that solve classes of problems, the term structure is used to refer to the semantic structure of the problem, which allows distinguishing meanings assigned to the operations in the verbal problems (Molina and Cañadas, 2018).
Castro E., Rico, L. y Romero, I. (1997). Sistemas de representación y aprendizaje de estructuras numéricas. Enseñanza de las Ciencias, 15(3), 361-371.
Molina, M., & Cañadas, M. C. (2018). La noción de estructura en el Early algebra [The notion of structure in Early algebra]. In P. Flores, J. L. Lupiañez, & I. Segovia (Eds.), Enseñar matemáticas. Homenaje a los profesores Francisco Fernández y Francisco Ruiz (pp. 129-141). Granada, Spain: Atrio.
Torres, M. D., Cañadas, M. C., Moreno, A, & Gómez, P. (2021). Structures in the direct and inverse forms of a function by 7-8 years old students.
