Virginia Commonwealth University B.S. in Science Degree Program

The initiation of the Virginia Commonwealth University B.S. in Science program was reported in this journal Fall 1999 as a program designed to meet the academic content major of a teacher preparation program for elementary and middle school mathematics and science teachers [1]. This paper reports the current status of the interdisciplinary B.S. in Science degree program including program enrollment data and trends. Also described are refinements in the required curriculum, which include a newly developed geometry, a mathematical computing course, and an emerging teaching technology course featuring graphing calculators, CBLs, and computer software applications

Virginia Commonwealth University\u27s Program for K-6 and 6-8 Teachers: The Interdisciplinary B.S. in Science

Virginia Commonwealth University (VCU) has very recently revised its requirements for the K-6 Certification to include a total of 21 hours in mathematics and science as well as a three credit hour methods course in mathematics and science. This requirement includes a physical science and a biological science course, each with a laboratory component, a contemporary mathematics course with extensive student projects, collaborative work and applications, a statistics course and interdisciplinary science and mathematics course. We believe that as students complete these requirements they will meet the new State K-6 licensure requirements in all areas, with the exception of geometry. We are developing a new geometry course that we hope will be required of all future teachers. The challenge of preparing middle school teachers to teach mathematics and/or science is much more difficult. VCU has been preparing very few middle school teachers of mathematics and science. We typically averaged less than one middle school science teacher and less than one middle school mathematics teacher per year. This paper provides a description of our interdisciplinary degree in mathematics and science that appears to be attracting significant numbers of students with an interest in teaching mathematics and/or science at the middle school level

Mathematics Professional Development Workshop for Middle School Teachers: Concept Versus Memorization

This article includes professional development topics for middle school mathematics and science teachers from two week-long Urban Teacher Institutes. These Institutes were held at J. Sargeant Reynolds Community College (JSRCC) and its partner institution, Virginia Commonwealth University (VCU), during the summers of 2007 and 2008, and were supported by a grant obtained by Dr. Harriet Morrison (JSRCC). Co-author Dr. Dewey Taylor directed the 2007 workshop, and both authors served as faculty leaders in both workshops. The workshops focused on teaching in an urban environment and community mapping (understanding the details of a certain locale to make the teacher more knowledgeable about the environments of both the students and the schools). The community mapping aspect of the workshops was led by Dr. Shirley Key of the University of Memphis. They featured content teaching and applications led by VCU faculty in mathematics, physics, forensics, engineering, mathematics education, and science education. This article focuses on the mathematics professional development strand in the workshop which featured conceptual learning with graphing calculator support as an alternative to the memorization of formulas

Constructions of Positive Commutative Semigroups on the Plane, II

A positive semiroup is a topological semigroup containing a subsemigroup N isomorphic to the multiplicative semigroup of nonnegative real numbers, embedded as a closed subset of E2 in such a way that 1 is an identity and 0 is a zero. Using results in Farley [1] it can be shown that positive commutative semigroups on the plane constructed by the techniques given in Farley [2] cannot contain an infinite number of two dimensional groups. In this work an example of such a semigroup will be constructed which does, however, contain an infinite number of one dimensional groups. Also, some preliminary results are given here concerning what types of semilattices of idempotent elements are possible for positive commutative semigroups on E2. In particular, we will show that there is a unique positive commutative semigroup on E2 which is the union of connected groups and which contains five idempotent elements. Also, we will show that such semigroups having nine idempotent elements are not unique by constructing an example of such a semigroup with nine idempotent elements whose semilattice of idempotent elements is not symmetric and hence which is not isomorphic to the semigroup with nine idempotent elements constructed in Farley [2]

Geochemistry of Kauai shield-stage lavas: Implications for the chemical evolution of the Hawaiian plume

We measured He, Sr, Nd, Pb, and Os isotope ratios and major and trace element concentrations in stratigraphically and paleomagnetically controlled shield-stage lavas from Kauai, Hawaii. The range of 3He/4He ratios (17–28 RA) from Kauai is similar to that reported from Loihi and thus challenges the prevailing notion that high 3He/4He ratios are restricted to the preshield stage of Hawaiian magmatism. 3He/4He ratios vary erratically with stratigraphic position, and chronostratigraphic control from paleomagnetic data indicates very rapid changes in the 3He/4He ratios (up to 8 RA in ~102 years). These variations in helium isotopic ratios are correlated with variations in radiogenic isotope ratios, suggesting rapid changes in melt composition supplying the magma reservoir. A three-component mixing model, previously proposed for Hawaiian shield lavas, does not adequately explain the isotopic data in Kauai shield lavas. The addition of a depleted-mantle (DM) component with the isotopic characteristics similar to posterosional basalts explains the isotopic variability in Kauai shield lavas. The DM component is most apparent in lavas from the Kauai shield and is present in varying proportion in other Hawaiian shield volcanoes. Shield lavas from Kauai sample a high 3He/4He end-member (Loihi component), but while lavas from western Kauai have a larger contribution from the Kea component (high 206Pb/204Pb, anomalously low 207Pb/204Pb relative to 206Pb/204Pb), lavas from eastern Kauai have a larger proportion of an enriched (Koolau) component. The systematic isotopic differences between eastern and western Kauai reflect a gradual migration of the locus of volcanism from west to east, or alternatively east and west Kauai are two distinct shield volcanoes. In the latter case, the two shield volcanoes have maintained distinct magma supply sources and plumbing systems. Our new geochemical data from Kauai are consistent with the existence of a single high 3He/4He reservoir in the Hawaiian plume and suggest that the proportion of the different mantle components in the plume have changed significantly in the past 5 Myr. The long-term evolution of the Hawaiian plume and the temporal variability recorded in Kauai lavas require more complex geochemical heterogeneities than suggested by radially zoned plume models. These complexities may arise from heterogeneities in the thermal boundary layer and through variable entrainment of ambient mantle by the upwelling plume