Abstract:

Early algebra, as a curriculum proposal grounded in research in mathematics education, aims to facilitate the transition from arithmetic to algebra by fostering reasoning flexibility, the ability to generalize, justify, and reason with generalities that often arise from work with numbers. Research addressing the development of algebra in primary education focuses on understanding equivalence, generalization, and functional relationships. However, few studies have investigated real-world problem solving modeled through equations and systems, or the role of proportional reasoning as a pathway for developing algebraic thinking.

This study analyzes the ability of a group of 72 students in their final year of primary education (ages 11–12), who have no formal instruction in early algebra, to solve three problems that specifically involve essential aspects of early algebra: proportional reasoning, equations, and functional thinking. The results show that students were more successful (more than 46% correct responses) when solving the problem involving proportional reasoning (a part–part–whole sharing situation). Although multiplicative strategies predominated, they were not always correct; in fact, some correct responses employed additive-type strategies. About 55% of the students incorrectly solved the problem modeled through equations. When they answered correctly, they used multiplicative relationships between the known values of the quantities involved to determine the unknowns.

The problem designed to assess students’ functional thinking proved to be the most complex (less than 10% correct responses). However, many of the incorrect answers displayed signs of emerging functional thinking, showing recognition of functional dependence and of the variable as a changing unknown quantity.

The study concludes that the nature of the task influences both the degree of success and the algebraic character of the mathematical practices developed by primary school students. It also highlights the importance of working with different approaches to early algebra in order to develop students’ algebraic reasoning.

Keywords:

Early algebra, primary education, proportional reasoning, equations, functional thinking.