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…

Middle-to-high school transition activities improve retention and graduation rates, reduce academic challenges, and support student social development. The purpose of this study was to investigate ninth-grade algebra I and literature/composition end-of-course test performance, attendance, and discipline in relationship to transition strategies…

This document presents a summary of changes made to the 2008 Mathematics Standard for grade 8. The table presented in this document offers a summary of the: (1) Removed Performance Objectives (POs); (2) POs Moved to a Different Grade Level; (3) POs Moved within the Grade Level or from another Grade Level; and (4) New POs.

The call for "algebra for all" is not a recent phenomenon. Concerns about the inadequacy of math (and science) preparation in America's high schools have been a steady drumbeat since the 1957 launch of Sputnik; a call for raising standards and the number of math (and science) courses required for graduation has been a part of countless…

Preparing students from low-income, minority families to graduate is a challenge that begins as early as elementary school but becomes a particular concern at the secondary level. Low-income students are twice as likely as higher-income students to be poorly prepared for grade-level work and 1.3 times more likely to have learning disabilities,…

Despite widespread agreement that the activity of "reasoning-and-proving" should be central to all students' mathematical experiences, many students face serious difficulties with this activity. Mathematics textbooks can play an important role in students' opportunities to engage in reasoning-and-proving: research suggests that many decisions that…

Mathematical letter writing can be a mutually beneficial partnership between high schools and universities. Secondary school preservice teachers in methods courses require authentic experiences in focusing on students' mathematical thinking. High school students benefit from increased opportunities to engage in individualized tasks with personal…

This paper shows the basic concept of Functional Modelling in mathematics education which has become more and more important in recent years. Hence it is necessary to think about suitable graphical methods to explain the fundamental idea of a function and its influence on values and other functions. PROGRAPH diagrams are a potentially good way to…

The objective of this introduction to Colombeau algebras of generalized functions (in which distributions can be freely multiplied) is to explain in elementary terms the essential concepts necessary for their application to basic nonlinear problems in classical physics. Examples are given in hydrodynamics and electrodynamics. The problem of the…

The theory and application of second-order linear ordinary differential equations is reviewed from the standpoint of the operator factorization approach to the solution of ordinary differential equations (ODE). Using the operator factorization approach, the general second-order linear ODE is solved, exactly, in quadratures and the resulting…

This article considers research and scholarship on the use of computer algebra in mathematics education following the instrumentation and the anthropological approaches. It outlines what these approaches are, positions them with regard to other approaches, examines tensions between the two approaches and makes suggestions for how work in this…

The appendix on the centres of gravity that appears at the end of Galileo's book, "Two New Sciences", is analysed. It is shown that the method used by Galileo in this work has an interesting reasoning and also shows preliminary ideas about scaling and advances some ideas about series convergence. In addition, we note that the geometrical language…

Synthetic division is viewed as a change of basis for polynomials written under the Newton form. Then, the transition matrices obtained from a sequence of changes of basis are used to factorize the inverse of a bidiagonal matrix or a block bidiagonal matrix.

Under predetermined conditions on the roots and coefficients, necessary and sufficient conditions relating the coefficients of a given cubic equation x[cubed] + ax[squared] + bx + c = 0 can be established so that the roots possess desired properties. In this note, the condition for one root of a cubic equation to be "the negative reciprocal of…

This textbook aims to give a clear and concise exposition of the elements of algebra to be adapted to the present wants of common schools. It cannot be expected, at present, that Common Schools should pursue Algebra to the same extent as pursued in Colleges ; still they may, to good advantage, acquire the more elementary portions of this branch of…