Fluency, Accuracy, and Gender Predict Developmental Trajectories of Arithmetic Strategies

The purpose of this study was to determine whether there are different growth trajectories of arithmetic strategies and whether these trajectories result in different achievement outcomes. Longitudinal data were collected on 240 students who began the study as 2nd graders. In the 1st year of the study, the 2nd-grade students were assessed on fluency and accuracy on simple arithmetic problems. During the fall of the 2nd, 3rd, and 4th grades, they were assessed on strategies for complex (multiple-digit) arithmetic. They were assessed on mathematics competency at the end of 4th grade. Growth mixture modeling was used to assess developmental trajectories in arithmetic strategies; the roles of fluency, accuracy, and gender in the development of latent class; and the impact of latent class on 4th-grade mathematics competency. The data indicated 2 latent classes of growth trajectories for correct cognitive strategy use and for attempted manipulative strategy use. Three latent classes were needed to explain the development of attempted cognitive strategy use. Fluency appeared to have the most significant impact on the growth rate, whereas accuracy and gender tended to influence the initial level of performance. Not all children transitioned away from manipulatives easily. A small latent class of children slightly increased their use of manipulatives over the course of the study, with the girls in this group being less likely than boys to abandon manipulatives. Finally, what appears to be the normal developmental trajectory for strategies was not found to serve many children well in regard to later mathematics achievement.