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…

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…

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…

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…

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…

Compares the mathematical understandings of 1983-85 elementary teachers with similar teachers of two earlier testing periods. Discusses the change in the measured mathematical competency levels of preservice and inservice elementary teachers with graphs and data tables. (YP)

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…

The Provincial Assessment of Mathematics was conducted at grades 3, 6, 9 and 12. There are three major components to the assessment: (1) a written test of the curriculum objectives carried out in May, 1987 for grades 3, 6, and 9, and in June, 1987 for grade 12 (Mathematics 300 and Mathematics 301); (2) a survey of teachers at these grade levels;…

The purpose of this study was to describe elementary preservice teachers' difficulties with understanding algebraic generalizations that were set in an authentic context. Fifty-eight preservice teachers enrolled in an elementary mathematics methods course participated in the study. These students explored and practiced with authentic, hands-on…

This report contains a brief description of the study in the province of Manitoba, Canada along with recommendations based upon the judgements of the Technical Advisory Committee. Grade levels 3, 6, 9, and 12 were administered the test. The purposes of the test were to: (1) provide benchmark indicators relative to the level of mathematics…