John L. Safko

Dynamics of a Constructivist Astronomy Course for In-service Teachers

Constructivist instructional strategies have been shown to be effective with K-16 students. Twenty-five in-service elementary and middle-school science teachers were taught astronomy using a constructivist strategy to determine its effectiveness in teacher enhancement. The teachers were monitored for changes in affective and cognitive domains during a 15-week special astronomy course. Quantitative measurement instruments and qualitative data analysis showed that the teacher-participants, who were exposed to the constructivist instructional environment, had significantly improved attitudes toward teaching astronomy and had made significant gains in knowledge of astronomy. These observations strongly suggest that using a constructivist instructional strategy in teacher-enhancement programs can create an effective learning environment for teachers that increases subject-matter knowledge and simultaneously improves attitudes, values, and interest levels.

SOME PROPERTIES OF CYLINDRICALLY SYMMETRIC EINSTEIN--MAXWELL FIELDS.

Some properties of static cylindrically symmetric universes consisting of gravitational and electromagnetic fields with a central axial mass, charge, or current density are discussed. Of three permissible distinct configurations, general solutions of the appropriate equations are given for two. The properties of the solutions of these two are then examined in greater detail. The equations of motion of test particles (both charged and uncharged) are described for some simple trajectories. The qualitative effect of the magnetic field on uncharged test particle behavior in some instances is noted as well as the qualitative distinction in the behavior of charged and uncharged test particles. The algebraically independent invariants of the Riemann tensor are calculated. A stability analysis is carried out for the two solutions when the system is subjected to radial perturbations. It turns out that both solutions are stable. The stability analysis is carried out by using the equations of the already unified fie...

Lagrange multipliers and gravitational theory

The Lagrange multiplier version of the Palatini variational principle is extended to nonlinear Lagrangians, where it is shown in the case of the quadratic Lagrangians, as expected, that this version of the Palatini approach is equivalent to the Hilbert variational method. The (nonvanishing) Lagrange multipliers for the quadratic Lagrangians are then explicitly obtained in covariant form. It is then pointed out how the Lagrange multiplier approach in the language of the (3+1) ‐formalism developed by Arnowitt, Deser, and Misner permits the recasting of the equations of motion for quadratic and general higher‐order Lagrangians into the ADM canonical formalism. In general without the Lagrange multiplier approach, the higher order ADM problem could not be solved. This is done explicitly for the simplest quadratic Lagrangian (g1/2R2) as an example.

Measurement of noncanonical variables

Abstract We consider the problems of measurements of noncanonical variables such as velocity, kinetic energy, and the electric field in the quantum domain. We show that there is an essential difference between such measurements and the measurements of canonical variables, i.e., noncanonical observables must be changed, in an uncontrollable way, while being measured. We then construct a formal theory for the measurement of noncanonical variables. We apply this theory to measurements of velocity, kinetic energy, and the electric field and show how it clarifies and simplifies previous discussions of these measurements.

Long-Term Attitude Sustainability from a Constructivist-Based Astronomy-for-Teachers Course

Twenty in-service elementary- and middle-school teachers were surveyed on attitude, value, interest, teaching confidence, and dedication to teaching in the subject area of astronomy. The teachers were surveyed immediately before and after they took a specially designed, semester-long, astronomy-for-teachers course developed with a constructivist instructional strategy. The participants reported significantly improved attitudes as measured by a Likert-scale survey. Four years later, the teacher-participants were surveyed again. Results of the second survey indicate that teacher attitudes and confidence toward teaching astronomy did not decline or worsen even after four years. The data in this study suggest that appropriately designed courses for teachers, can have long-term effectiveness.

An investigation of some of the kinematical aspects of plane symmetric space–times

A short review of the literature on plane symmetric space–times (PSSTS) is given in the Introduction. The rest of the paper concerns itself with an investigation of some of the kinematical aspects of PSSTS, i.e., properties of PSSTS which do not depend on the field equations. In particular, the existence of four special coordinate systems is considered. It is shown that the existence of these coordinate systems is not guaranteed for a general Ck (k⩽1) plane symmetric metric (PSM). For k=2, two of the coordinate systems exist in a weak sense whereas the existence of the other two is not guaranteed in any sense. A local intrinsic type classification is introduced in Sec. 3, and it is shown that the existence of an extra Killing vector is correlated to the classification. Finally, the local equivalence of two given PSSTS is considered in Sec. 4. It is shown that some algebraic equations arise from the analysis. These algebraic equations may lead directly to the solution of the problem of the local equivalenc...

A coordinate‐free derivation of a generalized geodesic deviation equation

A simple, coordinate‐free exact derivation of the geodesic deviation equation is given. This result includes the possibility of nonvanishing torsion. We then show that this form of the geodesic deviation equation can be specialized to various results given previously in the literature.

Variational methods with torsion in general relativity

Abstract It is shown that recently published field equations for the Einstein-Carton theory are basically derived from a Palatini variational approach. We then show that a Hilbert variational approach will, in general, give a different set of field equations.

Error Analysis of Straight Line Plots in the Undergraduate Physics Laboratory

A rapid error analysis of straight line plots can be performed in undergraduate laboratories by enclosing the data, in a parallelogram two of whose sides are parallel to the “best fit” line as determined by sight. Relatively little mathematical knowledge is needed for this method, so error analysis need not be ignored in elementary laboratories when straight line plots are made.

The nature of the general relativistic solution of the charged line mass

Abstract The nature of the solution of a line charge is discussed using the Already Unified Field Theory. It is shown that it is impossible to have charge without mass with this symmetry. Approximate solutions valid for either small or large mass per unit length are presented and compared with previous work. We show that, if charge is present, beyond some critical distance from the axis a neutral test body is repelled instead of attracted.