The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…

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…

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 Educational Policy Improvement Center (EPIC) conducted an investigation of the Intersegmental Committee for the Academic Senates (ICAS) Statements of Competencies for Mathematics and Academic Literacy. The purpose of this work is to understand how the ICAS competencies relate to college and career readiness, as represented by the augmented…

Due to their motivational nature, there has been growing interest in the potential of games to help teach academic content and skills. This report examines how different levels of detail about a game's scoring rules affect math learning and performance. Data were collected from 164 students in the fourth to sixth grades at five after-school…

This is the second and final report of the Middle School Mathematics Professional Development Impact Study, which examines the impact of providing a professional development (PD) program in rational number topics to seventh-grade mathematics teachers. An interim report (Garet et al. 2010) described the findings after one year of PD. The current…

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…

Student achievement in mathematics has been a focal concern in the United States for many years. The National Research Council's 2001 report and the recent report of the National Mathematics Advisory Panel (2008) both called attention to student achievement in mathematics, and both called for all students to learn algebra by the end of eighth…

This document shows a different way of adding lists of numbers to find a way of getting general formulae for figurate numbers and use Gauss?s method to check it.

In this note we give closed forms for a class of logarithmic integrals in terms of Bernoulli polynomials. This provides a method for unifying a large class of definite integrals.

The booklet presents a report on the operation and use of person numbering (PN) systems for vital and health statistics in Israel and Scandinavia. A PN system involves assigning a different number to each individual within a given society and using that number for commercial, governmental, and military identification. The purpose of the report is…

In this paper, using the Lambert series and other known results, the authors consider the computation of a class of series involving the powers of generalized Fibonacci and Lucas numbers, and obtain their approximate values.

Twenty classes in ten schools with 627 sixth-grade students in five cities in Taiwan participated in this study. The research provides information on the performance differences among written computation, pictorial representation, symbolic representation and number sense. The results of One-way ANOVA analysis indicate that significant difference…

A semigroup G is a group if it has a left identity and every element has a left inverse. The purpose of this note is to weaken this condition further in two different ways. A semigroup G with an identity e is a group if every element x in G has an inverse. It is well known that this statement can be weakened. A semigroup G with a left identity e…

This report focuses on the performance of fourth-and eighth-grade students in Puerto Rico in various mathematics content areas on the 2005 National Assessment of Educational Progress (NAEP) in mathematics. The NAEP mathematics assessment was administered to public school students in Puerto Rico for the first time in 2003. Although NAEP had…