Curricular analysis indicates that the U.S. students are introduced to multiplication in additive terms (as the replication of equal groups and repeated addition). But the virtue of this introduction for supporting students' understanding of the full range of multiplicative relationships is unclear. This paper reports an analysis of all grade 4…

Students' explanations of their mathematical thinking and conclusions have become a greater part of the assessment landscape in recent years. With a sample of 71 fourth-grade students at risk for mathematics learning disabilities, we investigated the relation between student accuracy in comparing the magnitude of fractions and the quality of…

Using restricted-use data from the 2011 National Assessment of Educational Progress mathematics assessment, the current study examined the relationship between the presence of elementary mathematics coaches and specialists (MCSs) and the mathematics achievement of more than 190,000 fourth-grade students in more than 7,400 schools nationwide. In…

"Mathematical Thinking: From Assessment Items to Challenging Tasks" is a compilation of 36 problem-based lessons that encourage students to engage in productive struggle and deep thinking. Its 36 full-length lessons for grades 2-8 are each inspired by an actual test item from the National Assessment of Educational Progress (NAEP).…

Comparability studies between CBT and PPT studied if there were score differences between these two versions. However, there were no consistent results across studies and time. The purpose of this study is to summarize the testing mode effects for K-12 mathematics tests by conducting a meta-analysis. 103 effect sizes of 32 studies were collected…

Student explanations of their mathematical thinking and conclusions have become a greater part of the assessment landscape in recent years. With a sample of 71 4th-grade students at-risk for mathematics learning disabilities, we investigated the relation between student accuracy in comparing the magnitude of fractions and the quality of students'…

The three purposes of this study were to (a) describe fraction ordering errors among at-risk fourth grade students, (b) assess the effect of part-whole understanding and accuracy of fraction magnitude estimation on the probability of committing errors, and (c) examine the effect of students' ability to explain comparing problems on the probability…

It has long been argued that U.S. states' differential performance on nationwide assessments may reflect differences in students' opportunity to learn the tested content that is primarily due to variation in curricular content standards, rather than in instructional quality or educational investment. To quantify the effect of differences in…

The National Council of Teachers of Mathematics (NCTM) continues to emphasize the importance of early statistical learning; data analysis and probability was the Council's professional development "Focus of the Year" for 2007-2008. Such a focus is needed, especially given the results of the statistics items from the 2003 NAEP. As…

This study investigated whether individual differences in working memory (WM) moderate effects of 2 variations of intervention designed to improve at-risk 4th graders' fraction knowledge. We also examined the effects of each intervention condition against a business-as-usual control group and assessed whether children's measurement interpretation…

This study investigated whether individual differences in working memory (WM) moderate effects of 2 variations of intervention designed to improve at-risk 4th graders' fraction knowledge. We also examined the effects of each intervention condition against a business-as-usual control group and assessed whether children's measurement interpretation…

The 2013 study, "Does Working Memory Moderate the Effects of Fraction Intervention? An Aptitude-Treatment Interaction," examined the impacts of the fluency and conceptual versions of "Fraction Face-Off!," a math instruction program designed to improve knowledge of fractions and decimals in fourth-graders at risk for low…

Research and history has demonstrated the overwhelming disparity and gap of mathematical achievement between African Americans and their White counterparts. According to the National Assessment of Educational Progress (NAEP), the achievement gap on a national level is prevalent. The USA jurisdiction has Black 8th grade math students results at 12%…

This study investigated longitudinal pathways leading from early spatial skills in first-grade girls to their fifth-grade analytical math reasoning abilities (N = 138). First-grade assessments included spatial skills, verbal skills, addition/subtraction skills, and frequency of choice of a decomposition or retrieval strategy on the…

This document represents one of three appendices associated with "The Nation's Report Card: A First Look--2013 Mathematics and Reading. National Assessment of Educational Progress at Grade 4 and 8. NCES 2014-451." It includes tabular data relating to the mathematics portion of the Tables of Education Progress at Grade 4 and 8. [For the…