In this note the authors investigate ways to shorten the amount of work involved in using the Rational Roots Theorem to find the rational roots of a polynomial with integral coefficients. The first result is a proof of a fact that we had long suspected, but were never able to find the statement of in any of the college algebra textbooks we had…

The author offers a simple intuition that can be exploited to derive and to help interpret some canonical results in the theory of optimal commodity taxation. He develops and explores the principle that the marginal social welfare loss per last unit of tax revenue generated be equalized across tax instruments. A simple two-consumer,…

Research has shown that certain ways of teaching can make a difference in whether students learn standards-based content. Many strategies have proven to be effective in teaching literacy, mathematics, science and social studies. These strategies have facilitated blending academic and career/technical subjects to make learning more meaningful for…

In spring 2010, Houghton Mifflin Harcourt (HMH) began planning a pilot of an application for the Apple iPad, "HMH Fuse: Algebra 1," which was then in development. The application was to be piloted in four California school districts during the 2010-2011 school year. HMH contracted with Empirical Education Inc. to conduct a one-year…

Despite the ever-increasing number of online professional development (OPD) programs, relatively few studies have been conducted to examine the efficacy of such programs for teachers and students. This manuscript presents findings from an impact study of OPD courses in fractions, algebraic thinking, and measurement on 79 fifth grade teachers'…

The constraints of a computer algebra system (CAS) generally induce limitations on its usage. Via the pedagogical features implemented in such a system, "motivating constraints" can appear, encouraging advanced theoretical learning, providing a broader mathematical knowledge and more profound mathematical understanding. We discuss this issue,…

A coin tossed onto a table often ends up rolling in such a way that the center of mass remains approximately stationary. Although this phenomenon has been studied for many years and is well-documented in the literature, it is perhaps not widely appreciated in the physics education community that the motion can be understood without the use of…

Founded in 2006 by Jonathan Osler, Math and Community Organizing teacher at El Puente Academy for Peace and Justice, a public CES high school in Brooklyn, New York, Radical Math is an organization for educators working to integrate issues of political, economic, and social justice into math education. In April 2007, Radical Math cosponsored…

In today's world, where the volume of knowledge everyone must deal with is increasing exponentially, many educators agree that schools must focus on developing skills for life-long learning. But what does that mean for an area such as algebra? Teachers' goal in school algebra should be to guide students to "work smarter" with algebraic symbols and…

In commemoration of the 100th volume of the "Mathematics Teacher," the Editorial Panel of "Teaching Children Mathematics" invited the author to read and reflect on an article published in "MT" in 1912. Her article compares the current approach to number and algebra content to that presented by Shipley. In addition, the article discusses the change…

Montgomery County Public Schools (MCPS) "Special Education at a Glance," which includes a copy of the "Guide to Planning and Assessing School-Based Special Education Programs," provides in a single document, information about the special education population at each Montgomery County (Maryland) public school, including…

The 2013 edition of the "Annual Condition of Education Report" provides a rich tapestry of information about Iowa's education system. The data presented in the report examines longitudinal trends about Iowa's students, teachers, and schools from many perspectives. Information such as demographic characteristics, assessment results,…

This report examined the implementation of Foundations of Algebra, a course designed to provide high school students with low mathematics performance an extra opportunity to review and study foundational mathematics concepts prior to enrolling in Introductory Mathematics and subsequently Algebra I. In the fall of 2009, 877 high school students…

In California, the typical college-prep course sequence in math includes Algebra I, Geometry, and Algebra II. Students advance through these courses at different rates. A number of students proceed at a quick pace, with some completing Algebra II by the end of 10th grade and a few even earlier. At the other end of the spectrum, some students…

This proceedings volume of InCoTEPD 2018 covers many ideas for handling a wide variety of challenging issues in the field of education. The outstanding ideas dealing with these issues result in innovation of the system. There are many innovation strategies resulting from recent research that are discussed in this book. These strategies will become…