A learning trajectory in Kindergarten and first grade students’ thinking of variable and use of variable notation to represent indeterminate quantities

VENTURA, ANA CLARA; BRIZUELA, BÁRBARA M.; BLANTON, MARIA; SAWREY, KATHARINE; GARDINER, ANGELA MURPHY; NEWMAN-OWENS, ASHLEY

THE JOURNAL OF MATHEMATICAL BEHAVIOR

JAI

Año: 2021 vol. 62

0732-3123

Given the importance of understanding and using indeterminate quantities in algebraic thinking, the development of learning trajectories about how Kindergarten and first grade students understand variable and use variable notation in the context of algebraic expressions is critical. Based on an empirically developed learning trajectory, we analyzed children´s responses at three different points in a classroom teaching experiment. Our purpose was to describe levels of thinking among 16 students (eight in Kindergarten and eight in first grade). Our results revealed qualitative changes in the thinking about indeterminate quantities of most student participants. As students progressed through the experiment, we found that they advanced from what we characterized as a Pre-variable Level to a Letters as representing indeterminate quantities as varying unknowns; explicit operations on indeterminate quantities Level. Learning trajectories such as that developed here hold promise for informing the design of interventions that support young childrens early algebraic thinking. PUBLICACIÓN INDEXADA EN: Scopus, PsycINFO, Contents Pages in Education, ERA (Educational Research Abstracts Online), Education Technology Abstracts, Research into Higher Education Abstracts, Technical Education & Training Abstracts, MathEduc.