Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

Using data from the Early Childhood Longitudinal Study Kindergarten Cohort of 1998 (n = 15,070), this study used propensity scores to examine the short- and long-term academic and psychosocial benefits of preschool education for a diverse sample of middle-class children. Compared with children who attended informal care at age 4, preschool…

This guide was created as a resource to help families better understand "Measures of Academic Progress"® (MAP®), and their child's results. The guide provides answers to a variety of questions such as: "What is MAP?"; "What does MAP measure?"; "How do schools and teachers use MAP scores?"; "Can MAP tell…

This Framework builds upon the foundation of the 2010 Massachusetts Curriculum Framework for Mathematics as well as versions of the Massachusetts Mathematics Framework published since 1995. The current Framework incorporates improvements suggested by Massachusetts educators after six years of experience in implementing the 2010 standards in their…

Understanding what children know is paramount to planning effective science instruction; however, in any classroom, the students hold a variety of ideas. Representing these differences in ways that also acknowledge the common trends among students might facilitate the process of differentiation. To exemplify one such possible process of…

This article reports the findings from a comparative analysis that examined several mathematical content strands, reasoning processes, and emphasis on technology in prior K-8 state mathematics standards and the Common Core State Standards for Mathematics (CCSSM). Various methodological tools were utilized to compare and contrast CCSSM with prior…

Using sequences of coin flips as a model of serial independent events, we asked schoolchildren in grades 1 through 5 to estimate the likelihood of the next flip. Most children in each grade expected short patterns to continue.

Because random assignment is not possible in observational studies, estimates of treatment effects might be biased due to selection on observable and unobservable variables. To strengthen causal inference in longitudinal observational studies of multiple treatments, we present 4 latent growth models for propensity score matched groups, and…

It is important to use rich problem-solving tasks to develop students' understanding of important mathematical ideas (NCTM 2000). Rich tasks are complex, nonalgorithmic, and nonroutine, requiring reasoning, problem solving, and communication of thinking. Evidence has shown that using rich tasks in student-centered classrooms is especially…

The No Child Left Behind Act requires schools to begin testing new English Learners (EL) in English language arts within three years after they enter school and holds schools accountable for their performance on these exams. Yet very little empirical work has examined exactly how long it takes EL students to become proficient in English and how…