Numbers and variables often follow the same principles of arithmetic operations, yet numbers can be computed to a value whereas variables cannot. We examined the effect of symbols--numbers versus variables--on middle school students' problem-solving behaviors in a dynamic algebra notation system by presenting problems in numbers (e.g., 3+5-3) or…

A socioeconomic status- (SES-) related achievement gap in mathematics emerges prior to school entry, and increases as children move through elementary school. This gap makes implementation of demanding mathematics standards (e.g., the Common Core State Standards) an ongoing challenge. Early educational intervention is a strategy for addressing…

California State University, San Bernardino (CSUSB) and the Riverside County Office of Education (RCOE) were awarded an Investing in Innovation (i3) Development grant in 2015 to investigate the impact of an early education mathematics program on English Learner students at two rural school districts in Riverside, CA. Teaching English Learners…

Preschoolers' repeating patterning knowledge is predictive of their concurrent and later math and numeracy knowledge, but strong experimental evidence is needed to determine if these relations are causal. The purpose of the current Study was to examine the causal effects of repeating patterning and numeracy tutoring on repeating patterning,…

This project tested the effects of adding instruction of trios of children in patterning, mathematics, early literacy, or social studies to ongoing instruction in kindergartens. Children were randomly assigned to trios which were randomly assigned to one of four kinds of instruction. A quarter of the trios received patterning instruction with a…

Introduction: Participants' perspectives are valuable in evaluating the effectiveness of an intervention. Methods: Interviews were conducted with teachers of students with visual impairments and students who completed an intervention designed to build graphics literacy skills. Results: Six themes were identified with corresponding subthemes. The…

A concerning number of students enter kindergarten facing an intractable variation of mathematics difficulties (MD). This study investigated the impact of an explicit, core kindergarten mathematics program on the mathematical outcomes of kindergartners who demonstrated severe MD at kindergarten entry and examined whether these students improved…

This research shares progressions in thinking about equations and the equal sign observed in ten students who took part in an early algebra classroom intervention across Kindergarten and first grade. We report on data from task-based interviews conducted prior to the intervention and at the conclusion of each school year that elicited students'…

This research focuses on the retention of students' algebraic understandings 1 year following a 3-year early algebra intervention. Participants included 1,455 Grade 6 students who had taken part in a cluster randomized trial in Grades 3-5. The results show that, as was the case at the end of Grades 3, 4, and 5, treatment students significantly…

This paper describes "the development and technical adequacy of the Classroom Observations of Student Teacher Interactions (COSTI) instrument," a tool for measuring the frequency and rate of explicit instructional interactions, such as those used in Direct Instruction curricula, for teaching children basic reading and math skills.…

Many studies conducted in the last decades report that very few elementary-grades students understand the meaning of = in mathematics, and that upper-elementary students do not understand it any better than the lower-elementary students do. Using data from thousands of Florida elementary students, we show that students in Florida perform ten to…

Existing literature on the impact of Common Core State Standards in Math has shown little benefit, but has not examined variation in outcomes based on implementation strategies, student subgroups, or outcomes other than test scores. We use a difference-in-differences approach with school fixed effects to compare outcomes in pre- and post-standards…

Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…

Determining the effectiveness of core mathematics curricula is foundational to evidence-based practice. Examining effectiveness heterogeneity is also crucial to better understanding mathematics achievement among English language learners (ELLs). In this study, we used a quasi-experimental design (difference-in-differences) to examine the impact of…

There has been a long-standing issue of sparse discussion forums participation in online learning, which can impede students' help seeking practices. Researchers have examined AI techniques such as link prediction with network analysis to connect help seekers with help providers. However, little is known whether these AI systems will treat…