Christopher B. Wolfe

Longitudinal Evaluation of a Scale-Up Model for Teaching Mathematics With Trajectories and Technologies: Persistence of Effects in the Third Year

Using a cluster randomized trial design, we evaluated the persistence of effects of a research-based model for scaling up educational interventions. The model was implemented in 42 schools in two city districts serving low-resource communities, randomly assigned to three conditions. In pre-kindergarten, the two experimental interventions were identical, but one included follow-through in the kindergarten and first-grade years, including knowledge of the pre-K intervention and ways to build upon that knowledge using learning trajectories. Students in the experimental group scored significantly higher than control students (g = .51 for those who received follow-through intervention in kindergarten and first grade; g = .28 for non–follow-through), and follow-through students scored significantly higher than non–follow-through students (g = .24).

Early mathematics assessment: validation of the short form of a prekindergarten and kindergarten mathematics measure

In recent years, there has been increased interest in improving early mathematics curricula and instruction. Subsequently, there has also been a rise in demand for better early mathematics assessments, as most current measures are limited in their content and/or their sensitivity to detect differences in early mathematics development among young children. In this article, using data from two large samples of diverse populations of prekindergarten and kindergarten children, we provide evidence regarding the psychometric validity of a new theory-based early mathematics assessment. The new measure is the short form of a longer, validated measure. Our results suggest the short form assessment is valid for assessing prekindergarten and kindergarten children’s numeracy and geometry skills and is sensitive to differences in early mathematics development among young children.

Longitudinal Evaluation of a Scale-Up Model for Teaching Mathematics With Trajectories and Technologies

Abstract We used a cluster randomized trial to evaluate the effectiveness of a research-based model for scaling up educational interventions, focusing on the persistence of effects with and without a follow-through intervention. The instantiation of the Technology-enhanced, Research-based, Instruction, Assessment, and professional Development (TRIAD) model emphasized teaching early mathematics for understanding via learning trajectories and technology. The TRIAD implementation began in 42 schools in two city districts serving low-resource communities, randomly assigned to three conditions. In pre-kindergarten, the 2 experimental interventions were identical, but 1 included follow-through in the kindergarten year, including knowledge of the pre-K intervention and ways to build upon that knowledge using learning trajectories. Intent-to-treat analyses showed that students in both the follow-through condition (g = .33) and non-follow-through condition (g = .22) scored statistically significantly higher than children in the control condition. Both groups outperformed the control condition in treatment-on-the-treated analyses (g = .38, follow-through; g = .30 non-follow-through). Moderators and mediators were also analyzed. We conclude that the instantiation of the TRIAD model was successful and that follow through may contribute to the persistence of the effects of preschool interventions.

Sustainability of a Scale-Up Intervention in Early Mathematics: A Longitudinal Evaluation of Implementation Fidelity.

Research Findings: We evaluated the fidelity of implementation and the sustainability of effects of a research-based model for scaling up educational interventions. The model was implemented by 64 teachers in 26 schools in 2 distal city districts serving low-resource communities, with schools randomly assigned to condition. Practice or Policy: Although a logical expectation would be that, after the cessation of external support and professional development provided by the intervention, teachers would show a pattern of decreasing levels of fidelity, these teachers actually demonstrated increasing levels of fidelity, continuing to demonstrate high levels of sustained fidelity in their implementation of the underlying curriculum 2 years past exposure. Different profiles of variables predicted separate aspects of sustainability.

Does Early Mathematics Intervention Change the Processes Underlying Children's Learning?

ABSTRACT Early educational intervention effects typically fade in the years following treatment, and few studies have investigated why achievement impacts diminish over time. The current study tested the effects of a preschool mathematics intervention on two aspects of childrens mathematical development. We tested for separate effects of the intervention on “state” (occasion-specific) and “trait” (relatively stable) variability in mathematics achievement. Results indicated that, although the treatment had a large impact on state mathematics, the treatment had no effect on trait mathematics, or the aspect of mathematics achievement that influences stable individual differences in mathematics achievement over time. Results did suggest, however, that the intervention could affect the underlying processes in childrens mathematical development by inducing more transfer of knowledge immediately following the intervention for students in the treated group.