Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and extension of the Spectral Theorem and is commonly used within a variety of fields, including statistics,…

This paper presents a study about using scientific simulations to enhance the process of mathematical modelling. The main component of the study is a lesson whose major objective is to have students mathematise a trajectory of a projected object and then apply the model to formulate other trajectories by using the properties of function…

To meet the growing demand for teacher learning opportunities, the educational community must create scalable professional development models and study their effectiveness. In this chapter, we argue that design-based implementation research (DBIR) is ideally suited to these efforts, and we use two research projects as illustrative cases: CSR…

"Saxon Math" is a textbook series covering grades K-12 based on incremental development and continual review of mathematical concepts to give students time to learn and practice concepts throughout the year. A distinguishing feature of "Saxon Math" is its use of a distributed approach--spreading practice and instruction for any…

Education researchers frequently seek out districts, schools, and teachers as partners for professional learning projects. They share their ambitious vision--a new model of professional learning that will support an empowered community, instructional improvement, and student achievement. The authors, along with other members of their research…

In one Colorado fifth grade classroom, math period begins with Mathematician's Chair, an activity allowing students to share their problems with entire class. Using this technique, students became adept at writing math problems, solving their own and peers' problems, using math-related writing as important medium of social discourse, and making…

The major purpose of this study was to attempt to understand some of the reasons for Mathematics perception of Taiwanese children compared to American children. The study was conducted with elementary schools in the Denver metropolitan area and Taipei, Taiwan in which fifth graders in each city (21 and 37 respectively) were selected as target…

In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (TSA); for the first time in the NAEP's history, voluntary state-by-state assessments (37 states, the District of Columbia, Guam, and the Virgin Islands) were made. The sample was designed to represent the 8th grade public school population in a state…

This handbook, which is intended for K-12 teachers in Colorado, explains how to integrate academic content standards and assessments with workplace competencies and school-to-career activities. The handbook is divided into four sections. The first presents the Colorado General Workplace Competencies, which describe the skills and knowledge…