This is the final external evaluation report prepared by SRI International for the Rural Math Excel Partnership (RMEP) project, an investing in innovation (i3) development project funded by the U.S. Department of Education. Operated by Virginia Advanced Study Strategies, Inc. (VASS), the RMEP project included six rural school districts (LEAs) in…

In this qualitative study, we initiate a discussion as to why instructors should implement numerous assessments into their mathematics courses. We describe the purpose and structure of formative and summative assessments implemented in an undergraduate two-semester sequence of abstract algebra. The evaluations included homework, exams, projects,…

Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…

We used a teaching experiment to evaluate the preparation of preservice teachers to teach early algebra concepts in the elementary school with the goal of improving their ability to generalize and justify algebraic rules when using pattern-finding tasks. Nearly all of the elementary preservice teachers generalized explicit rules using symbolic…

We present a modified version of Young's interferometer to verify experimentally the four interference laws propounded by Fresnel and Arago. Theoretical analysis is given using the complex algebra and the matrix representation for polarizers, rotators and the electromagnetic field. The advantage of the modified interferometer over other spatial…

The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…

The central ideas of postcalculus mathematics courses offered in college are difficult to introduce in middle and secondary schools, especially through the engineering and sciences examples traditionally used in algebra, geometry, and trigonometry textbooks. However, certain concepts in music theory can be used to expose students to interesting…

This article is the second in a series of two papers which suggest some practical, spreadsheet-based ideas for helping students to make appropriate connections between particular algebraic concepts. Solving equations has traditionally been taught as a pen-and-paper process. Spreadsheets, such as that of Excel, provide a contemporary, and powerful…

The common understanding within the mathematics community is that the role of the college algebra course is to prepare students for calculus. Though exceptions are emerging, the curriculum of most college algebra courses and the content of most textbooks on the market both reflect that assumption. This article calls that assumption into question…

This article explores the conceptual richness of systems of equations through a discussion of various aspects that could enhance its study. (Contains 18 figures and 1 table.)

Using the perspective of instructional conversation, we investigated how one teacher regulated student participation and conceptual reasoning in the middle-school mathematics classroom. We examined the elicitations--questions and provocative statements--made by the teacher over a four-day algebra lesson. Analyses showed how the teacher…

Do word problems and math vocabulary confuse students in your mathematics classes? Do simple keywords like "value" and "portion" seem to mislead them? Many words that students already know can have a different meaning in mathematics. To grasp that difference, students need to connect English literacy skills to math. Successful students speak,…

This study reports how 24 grade 4-6 students in one elementary and middle school interpreted formal and informal representations of variables. While interpretations for variables represented as letters (e.g., x and y) have been well established for students in algebra classes and beyond, little research into elementary school students'…

Dual enrollment (DE), an arrangement by which high school students take college courses, is becoming increasingly popular as a means of improving high school education. However, there is very little rigorous evidence on its impact on student outcomes. A particular concern in evaluating its effects is the selection bias that arises because more…

We report on our efforts to support teachers' development of mathematical knowledge for teaching through online professional development. In particular, we report on our investigation into the relationship between online interaction and teachers' development of mathematics content for teaching. Through the integration of content analysis and…