IPEHCS   26259
INSTITUTO PATAGONICO DE ESTUDIOS DE HUMANIDADES Y CIENCIAS SOCIALES
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
A Learning Trajectory in Kindergarten and First-Grade Students' thinking about variable with indeterminate quantities.
Autor/es:
BRIZUELA, BÁRBARA; GARDINER, ANGELA; VENTURA, ANA CLARA; SAWREY, KATHARINE ; BLANTON, MARÍA; NEWMAN-OWENS, AHSLEY
Lugar:
Toronto
Reunión:
Congreso; American Educational Research Association Annual Meeting.; 2019
Institución organizadora:
American Educational Research Association (AERA)
Resumen:
Objectives: In our presentation we will share results from a study in which we expanded on an existing trajectory in first grade students? thinking about variable and variable notation in functional relationships (Authors, 2017). We revised the prior trajectory to include Kindergarten students and generalized arithmetic. Perspective: In our current study, we used learning trajectories (Clements & Sarama, 2004, 2009; Confrey, Maloney, & Nguyen, 2011; Simon, 1995) as the theoretical framework to identify a progression in Kindergarten and first grade students? understanding of variable notation focused on indeterminate quantities and their relationships within generalized arithmetic. Learning trajectories rely on empirical findings to construct content-specific learning goals and instructional sequences to hypothesize increasingly sophisticated ways of thinking (Baroody et al., 2004; Sarama & Clements, 2014). With this framework in mind, we consider the following question: In what ways do Kindergarten and first grade students understand variable notation as a way to represent both indeterminate quantities and their relationships in problems of generalized arithmetic? Specifically, we consider what levels of understanding students exhibited at different moments (beginning vs. middle vs. ending) of 7-week classroom teaching experiments (CTEs) and at different grade levels (Kindergarten vs. first grade). We employed design research (Cobb, et al., 2003) to develop our learning trajectory. Data Sources: We draw on data from CTEs conducted in four classrooms?two at each of grades Kindergarten and first grade?from two demographically diverse elementary schools in the Northeast. The CTE consisted of two 30-minute lessons per week (14 lessons total). The data used to expand Author?s (2017) learning trajectory are interviews held at three points during the CTE (beginning, middle, and end) with eight Kindergarten and eight first-grade students of varying mathematical proficiency. For comparison purposes, the interview data focused on tasks that can be represented with the expression y = x + b. Results: The results of our study confirm the general trajectory laid out by Authors (2017), expanding it in important ways. Specifically, the expanded and revised trajectory considers the importance of indeterminate quantities as a basis for students? understandings of variable notation. Our data confirmed three levels in the trajectory: Pre-variable/Pre-symbolic; Letters as representing variables as arbitrarily chosen values; Letters as representing variables that are varying unknowns. The data from this study did not confirm the levels Pre-variable/letters as labels or as representing objects; Letters as representing variables with fixed, deterministic values; or Letters representing variables as mathematical objects. Moreover, the data from this study provided more nuance to the first (Pre-variable/Pre-symbolic) and last levels (Letters as representing variables that are varying unknowns). Significance: It is significant that even Kindergarten students, after 7 hours of instruction in a CTE (14 lessons of 30-minutes each) were able to use variable notation to represent variable quantities. The significance of our study lies at least in part in the stark contrast it provides with research that has shown that adolescents struggle with the concept of variable and the use of variable notation (e.g., Knuth et al., 2011; Küchemann, 1981).