Demetriou’s tests and levels of algebraic abilities and proportional reasoning in seventh, eighth, and ninth grades

Abstract

Developing algebraic thinking is a key factor in learning mathematics. Despite its importance, many students still struggle with algebraic concepts. This research investigates students’ achievements in algebraic thinking using Demetriou’s test across 7<sup>th</sup> (approximately 12-13 years old), 8<sup>th</sup> (approximately 13-14 years old), and 9<sup>th</sup> (approximately 14-15 years old) grades. The study analyzes performance in different levels of algebraic tasks (i.e., [1] extrapolation of relationships, [2] coordinating simple structures, [3] operating with undefined symbolic structures, and [4] coordination with undefined structures), revealing a significant developmental leap in algebraic abilities during the 9<sup>th</sup> grade. While no statistically significant differences were found in the first level, 9<sup>th</sup> grade students demonstrated superior performance in levels 2, 3, and 4, suggesting cognitive readiness for abstract algebraic concepts around the age of 14. The research unveils a disjointed development in algebraic abilities, indicating a progression from basic arithmetic operations to proportional reasoning before the full integration of algebraic thinking. Notably, tasks involving variables in the third level pose persistent challenges for students. The findings contribute to understanding the optimal age for introducing algebraic concepts and underscore the importance of considering cognitive development in mathematics education. The study proposes implications for educators, such as emphasizing proportional reasoning in earlier grades and employing differentiated instruction based on individual students’ abilities.