In the deconstruction of the California state standards for trigonometry, linear algebra and mathematical analysis for the Cal-PASS (California Partnership for Achieving Student Success) Content Standards Deconstruction projects, it became apparent that terms were used for which no definition was given. The San Diego Central Cal-PASS Math…

This dissertation explores fifth and eighth grade students' interpretations of three kinds of mathematical representations: number lines, the Cartesian plane, and graphs of linear functions. Two studies were conducted. In Study 1, I administered the paper-and-pencil Linear Representations Assessment (LRA) to examine students'…

This is a dissertation about the beliefs that mathematics majors have about mathematics and how their beliefs are affected by the introduction of mathematics research. The mathematics research presented to the students dealt with counting regular orbits of an action. Research has shown that the beliefs that teachers hold about mathematics…

This research was designed with the primary purpose of identifying the dimensions of principal support perceived by public high school teachers in Virginia and identifying the relationship between principal support and organizational citizenship behaviors. In addition, this study also examined the relationship between principal support and student…

In this paper we articulate an approach, termed culturally-mathematically relevant pedagogy (CMRP), for fostering urban English language learners' mathematical progression. CMRP integrates three aspects, the use of (1) adaptive teaching to build on students' funds of knowledge for mathematics, (2) tasks that make sense to students given their…

As California competes for jobs in an increasingly competitive global economy, the state faces a looming shortage of highly educated workers (PPIC, 2012). For a variety of reasons, the need for individuals with degrees in science, technology, engineering, and mathematics (STEM) is of particular concern. Nowhere is this more true than in the…

In 1997, Chicago implemented a policy that required algebra for all ninth-grade students, eliminating all remedial coursework. This policy increased opportunities to take algebra for low-skill students who had previously enrolled in remedial math. However, little is known about how schools respond to the policy in terms of organizing math…

The use of the history of mathematics in teaching has long been considered a tool for enriching students' mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of…

Partial fraction decomposition is a useful technique often taught at senior secondary or undergraduate levels to handle integrations, inverse Laplace transforms or linear ordinary differential equations, etc. In recent years, an improved Heaviside's approach to partial fraction decomposition was introduced and developed by the author. An important…

This paper is based on a study which explored the conceptual understanding of Grade 11 mathematics learners of graphical functional relationships, in particular their understanding of the Cartesian plane, notation, symbols and graphical terminology. The National Curriculum Statement (NCS) for Grades 10-12 in mathematics stipulates functional…

A problem in learning to solve mathematics word problems students have been facing is to transfer the learned problem-solving knowledge from one story context to another story context. Some studies have provided evidence showing that structure facilitates transfer of learning to solve word problems. However, it is still under development for what…

Oral communication in mathematics classroom plays an essential role in the mathematics learning process, because it allows students to share ideas, refine their thoughts, reflect on their methods, and clarify their understanding (NCTM, 2000). Knowledge about teacher oral communication behaviors allows researchers and policy makers to identify and…

This paper presents a comparison of Virginia's mathematics performance expectations with the common core state standards for mathematics. The comparison focuses on number and quantity, algebra, functions, geometry, and statistics and probability. (Contains 1 footnote.)

This paper surveys the fascinating mathematics of fair division, and provides a suite of examples using basic ideas from algebra, calculus, and probability which can be used to examine and test new and sometimes complex mathematical theories and claims involving fair division. Conversely, the classical cut-and-choose and moving-knife algorithms…

Two people take turns selecting from an even number of items. Their relative preferences over the items can be described as a permutation, then tools from algebraic combinatorics can be used to answer various questions. We describe each person's optimal selection strategies including how each could make use of knowing the other's preferences. We…