Evaluating the Efficacy of Learning Trajectories in Early Mathematics
Co-Principal Investigators: Julie Sarama (University of Denver), Arthur Baroody (University of Denver), and David Purpura (Purdue University)
Purpose: The purpose of this study is to evaluate the efficacy of using a learning trajectories approach to mathematics instruction to foster the development of early mathematics skills which are predictive of later school achievement. A learning trajectories approach includes a goal for teaching a mathematics concept, a developmental progression of levels of thinking about the concept, and instructional activities and content for each developmental level. Although research has shown that educational programs based on learning trajectories are effective at promoting academic achievement, no studies have evaluated the degree to which a learning trajectories approach to mathematics instruction improves learning and instruction. The researchers will evaluate whether instruction based on learning trajectories for early mathematics is more efficacious than other instructional approaches for promoting young children's knowledge and understanding of mathematics concepts. The results of this study will provide information about the use of a learning trajectories approach in preschool and kindergarten classrooms.
Project Activities: Over a four year period, the researchers will implement eight experiments and evaluate the impact of the learning trajectories instructional approach on children's early mathematics knowledge and skills. The research team will conduct two experiments each year. The researchers will compare the learning trajectories approach to three alternative approaches to math instruction. The team will implement the different instructional approaches, collect data, and conduct analyses to examine the impact of each approach on child outcomes. Researchers will also collect data to conduct a cost analysis to determine the cost of implementing the learning trajectories instructional approach in preschool and kindergarten classrooms.
Products: Researchers will produce evidence of the efficacy of the learning trajectories approach to early mathematics instruction for a diverse group of children in prekindergarten and kindergarten classrooms. The research team will also produce peer-reviewed publications.
Setting: This study will take place in prekindergarten and kindergarten classrooms in two large school districts in Colorado.
Sample: Study participants will include more than 2,064 4- and 5-year old year old children from different racial/ethnic groups.
Intervention: A learning trajectories approach to early mathematics instruction includes the goal for teaching a mathematics concept, a developmental progression of levels of thinking about the concept, and specific instructional tasks and teaching strategies based on the processes that will support learning at each developmental level. In this study a learning trajectories approach will be used to teach children about several early math concepts, including the foundations of number (counting, subitizing, comparing numbers); early arithmetic (number successor principle, addition/subtraction word problems), measurement, number line, and spatial structuring; and the beginnings of algebraic thinking (patterning and mathematical reasoning). Members of the research team will serve as instructors and work with small groups of children in prekindergarten and kindergarten classrooms.
Research Design and Methods: The researchers will conduct eight experiments over a four year period to address two primary research questions: (1) does instruction aligned with a learning trajectories sequence result in greater learning than instruction using a traditional or theme-based approach? and (2) does instruction in which learning trajectory levels are taught consecutively result in greater learning than instruction that immediately and solely targets a particular level of knowledge or understanding (the skip level approach)? Four experiments will be conducted to address the first research question and four experiments will address the second research question. Two experiments will be conducted each year. For research question one, the researchers will randomly assign children to small groups then assign the small groups to one of the three experimental conditions: (1) a learning trajectories approach; (2) a traditional/conventional approach; or (3) a theme-based approach to early math instruction. For research question two, the researchers will randomly assign children to small groups then assign the small groups to one of the two experimental conditions, a learning trajectories approach or a skip levels approach. For each research question, two of the four experiments will focus on four year olds; the other two on five year olds. The researchers will collect pre- and post-test data to evaluate the impact of the intervention on child outcomes. They will also conduct a cost analysis and disseminate the study findings.
Control Condition: The research team will implement and compare three alternative instructional approaches to the learning trajectories approach. In the traditional/conventional approach, early math instruction is presented in a sequence of mathematical concepts that children should learn and know, but there is no focus on children's developmental levels and tailoring instruction to support learning at each level and progression to the next level. In the theme-based approach, instruction is based on the day's theme in the classroom. Math instructional activities are embedded in thematically-based projects. In the theme-based approach, activities are the same as in the learning trajectories approach but are not pre-ordered; instead, they are selected so that they connect to the day's theme, such as playing a "pizza game." In the "skip-level" approach, instructors might skip one or more levels of a learning trajectories developmental sequence and teach a target concept before children understanding less advanced content.
Key Measures: Primary measures include direct assessments of children's knowledge and understanding of key math concepts, including the Tools for Early Assessment of Mathematics (TEAM) and the Test of Early Mathematics Ability (TEMA-3). Observational data will be collected and coded to measure fidelity of implementation.
Data Analytic Strategy: The research team will use multilevel models to account for the nesting of children in small groups in classrooms. The research team will conduct analyses to examine the impact of the learning trajectories approach on child outcomes. Researchers will include child demographic and socio-economic characteristics and classroom-level variables in their analyses to control for other factors that may explain variability in child outcomes.
Journal article, monograph, or newsletterBaroody, A.J. (2017). The Use of Concrete Experience in Early Childhood Mathematics Instruction. Advances in Child Development and Behavior, 53: 43–94.