This paper offers a critical analysis of Dubinsky et al. (On Learning Fundamental Concepts of Group Theory; 1994) and proposes, as an alternative to the four axioms and the standard definitions, that permutation and symmetry may be regarded as the fundamental concepts of group theory. (Author)

This article investigates the geometry and algebra behind what happens when the definition of a parabola is changed by altering the size of the focal point.

The high school course that integrated first year algebra with an introductory environmental biology/anatomy and physiology course, in order to solve algebra problems is discussed. Lessons and activities for the course were taken by identifying the areas where mathematics and biology content intervenes may help students understand biology concepts…

Teachers use action research in order to improve their teaching and student learning. This action research will analyze students' algebraic reasoning in finding values of variables in systems of equations pictorially and algebraically. This research will look at students solving linear systems of equations without knowing the algebraic algorithms.…

The educational standards, instruction, and testing of mathematics remain a controversial subject in the United States. Given the significant and growing need for mathematics remediation, it is reasonable to question how well individual states are preparing its high school students to succeed. This evaluation examines the correlation between the…

This Parent/Student Guide explains why Algebra I is a required subject, how it helps prepare students for the future, how Algebra I fits into the student's high school math program, and what parents can do to support their student's success in learning algebra. It also explains why California policymakers require all students to take algebra and…

As a follow up to the National Council on Teacher Quality (NCTQ) national studies of how well elementary teachers are prepared to teach reading and mathematics, NCTQ looked at preparation in both subjects in all undergraduate teacher preparation programs in Wyoming. This report evaluated Wyoming's undergraduate elementary teacher preparation…

This study examines graphing calculator technology availability, characteristics of teachers who use it, teacher attitudes, and how use reflects changes to algebra curriculum and instructional practices. Algebra I and Algebra II teachers in 75 high school and junior high/middle schools in a diverse region of a northwestern state were surveyed.…

This study investigated convergent validity evidence for student growth scores with high school course grades. The Measures of Academic Progress and Educational Planning and Assessment System growth scores for approximately 1,800 ninth-grade students over 2 years were related to language, arts, and mathematics course grades for developmental,…

This study is an evaluation on whether middle-level mathematics teachers' participation in a week-long in-service course on middle-level mathematics concepts increases their understanding of this content. A secondary purpose of this study is an exploration of teacher perceptions before and after the institute via self-report surveys. Participants…

Functions are all around us, disguised as actions on concrete objects. Composition of functions, too, is all around us, because these actions can be performed in succession, the output of one serving as the input for the next. In terms of Gray and Tall's (2001) "embodied objects" or Lakoff and Nunez's (2000) "mathematical idea…

While much discussion about student success as it relates to access, equity, and underpreparedness at the collegiate level is taking place nationally and statewide, a strong and specific concern prompted some of the faculty at Pasadena City College (PCC), a large urban community college located northeast of downtown Los Angeles, to address the…