These are the appendixes for the report, "What Grade 7 Foundational Knowledge and Skills Are Associated with Missouri Students' Algebra I Achievement in Grade 8?" To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for…

This paper illustrates a biological application of the concepts of relative change and area under a curve, from mathematics. We study two biological measures "relative change in cardiac output" and "cardiac output", which are predictors of heart blockages and other related ailments. Cardiac output refers to the quantity of…

Contemporary state math standards emphasize that students must demonstrate an understanding of the mathematical ideas underlying the computations that have typically been the core of the elementary school math curriculum. The standards have put an increased emphasis on the study of fractions in upper elementary grades, which are the years during…

The purpose of this study was to examine the cognitive predictors of calculations and number line estimation with whole numbers and fractions. At-risk 4th-grade students (N = 139) were assessed on 6 domain-general abilities (i.e., working memory, processing speed, concept formation, language, attentive behavior, and nonverbal reasoning) and…

The purpose of this report is to describe the technical qualities of the 2018-2019 operational administration of the English language arts/literacy (ELA/L) and mathematics summative assessments in grades 3 through 8 and high school. The ELA/L assessments focus on reading and comprehending a range of sufficiently complex texts independently and…

The purpose of this report is to describe the technical qualities of the 2018-2019 operational administration of the English language arts/literacy (ELA/L) and mathematics assessments in grades 3 through 8 and high school. New Meridian, in coordination with multiple states and vendors, developed an alternate form of the summative assessment to…

More than ever, students need to engage with mathematics concepts, think quantitatively and analytically, and communicate using mathematics. All these skills are central to a young person's preparedness to tackle problems that arise at work and in life beyond the classroom. But the reality is that many students are not familiar with basic…

Making the transition from arithmetic to mathematics, especially algebra, is critical to future academic and economic success, yet many students find this transition difficult and success in algebra elusive. This paper reports on the outcomes achieved from a three year course of professional development, POWERSOURCE[c], that helped teachers apply…

Understanding the meaning of rational numbers and how to perform mathematical operations with those numbers seems to be a perennial problem in the United States for both adults and children. Based on previous work, we hypothesized that giving students more time to practice using rational numbers in an environment that enticed them to apply their…

In 2006-07, seven Wake County Public School System (WCPSS) middle schools piloted Algebraic Thinking as an alternate approach to teaching middle school mathematics. Algebraic Thinking was developed to help students in grade 6 reach higher mathematics courses by combining the regular and advanced middle school mathematics courses into one…

The report shares what everyone has learned from the 2010-2011 Maryland Model for School Readiness (MMSR) data about the school readiness of Maryland's children: statewide, by subgroups, and for each of Maryland's 24 local jurisdictions. Some of the highlights are: (1) The percentage of Maryland kindergarteners fully ready to start school…

This report presents results of the 2009 National Assessment of Educational Progress (NAEP) in mathematics at grades 4 and 8. The results from the 2009 assessment presented in this report are compared to those from previous years, showing how students' performance in mathematics has progressed over time. Results for students in the nation, the 50…

The standard reverse-order law for the Moore-Penrose inverse of a matrix product is (AB)[dagger] = B[dagger]A[dagger]. The purpose of this article is to give a set of equivalences of this reverse-order law and other mixed-type reverse-order laws for the Moore-Penrose inverse of matrix products.

This classroom note presents a final solution for the functional equation: f(xy)=xf(y) + yf(x). The functional equation if formally similar to the familiar product rule of elementary calculus and this similarity prompted its study by Ren et al., who derived some results concerning it. The purpose of this present note is to extend these results and…

This report describes results from field-testing of POWERSOURCE[C] formative assessment alongside professional development and instructional resources. The researchers at the National Center for Research, on Evaluation, Standards, & Student Testing (CRESST) employed a randomized, controlled design to address the following question: Does the…