Enhancing functional thinking in grade 5–6 students through a dynamic mathematics intervention program

Abstract

AbstractThe aim of this study was to develop, implement, and evaluate an intervention program focusing on developing Grade 5 and 6 students’ functional thinking. The innovative aspect lies in addressing simultaneously various aspects of function—input–output, covariation, correspondence, and object— in terms of manipulating tasks that involve functional relationships. The program adopts promising design principles, including an inquiry-based approach, engaging students in embodied dynamic mathematics learning environments, and making connections to real-world situations. A sample of 104 students took part in the program. The results showed a significant improvement in students’ performance related to functional thinking between the pre- and post-tests. Grade 5 students’ mean value improved from 0.29 to 0.58 and Grade 6 students from 0.37 to 0.60, respectively. Analysis indicated that students with varying performance potential in developing functional thinking are likely to be significantly affected by the program. Regression analysis showed that students’ gender as well as mathematics- and functions-related self-concept and interest did not serve as predictive factors of students’ gain score magnitude. Students' progression goes along with a significant shift in strategies used. While the dominant strategies in the pre-test relied on recursive and single variation, in the post-test, students moved to covariational and correspondence approaches. The findings indicate that upper primary school students are capable of grappling abstract facets of functions. This underscores the potential effectiveness of targeted interventions that adopt innovative design principles, particularly in light of the limitations of conventional curricula in adequately preparing students to explore functional relationships across diverse contexts.