creased by 0.47 SDs under active learning (n = 158 studies), and that the odds ratio for failing was 1.95 under traditional lecturing (n = 67 studies). These results indicate that average examination scores improved by about 6% in active learning sections, and that students in classes with traditional lecturing were 1.5 times more likely to fail than were students in classes with active learning. Heterogeneity analyses indicated that both results hold across the STEM disciplines, that active learning increases scores on concept inventories more than on course examinations, and that active learning appears effective across all class sizes—although the greatest effects are in small (n ≤ 50) classes. Trim and fill analyses and fail-safe n calculations suggest that the results are not due to publication bias. The results also appear robust to variation in the methodological rigor of the included studies, based on the quality of controls over student quality and instructor identity. This is the largest and most comprehensive metaanalysis of undergraduate STEM education published to date. The results raise questions about the continued use of traditional lecturing as a control in research studies, and support active learning as the preferred, empirically validated teaching practice in regular classrooms.

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Active learning increases student performance in science, engineering, and mathematics

Extended Theories of Gravity

When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.

On Continued Gravitational Contraction

The purpose of this Resource Letter is to provide an overview of research on the learning and teaching of physics. The references have been selected to meet the needs of two groups of physicists engaged in physics education. The first is the growing number whose field of scholarly inquiry is (or might become) physics education research. The second is the much larger community of physics instructors whose primary interest is in using the results from research as a guide for improving instruction.

Resource Letter: PER-1: Physics Education Research

Many proven research-based instructional strategies have been developed for introductory college-level physics. Significant efforts to disseminate these strategies have focused on convincing individual instructors to give up their traditional practices in favor of particular research-based practices. Yet evidence suggests that the findings of educational research are, at best, only marginally incorporated into typical introductory physics courses. In this paper we present partial results of an interview study designed to generate new ideas about why proven strategies are slow to integrate in mainstream instruction. Specifically we describe the results of open-ended interviews with five physics instructors who represent likely users of educational research. We found that these instructors have conceptions about teaching and learning that are more compatible with educational research than with their self-described instructional practices. Instructors often blamed this discrepancy on situational factors that favor traditional instruction. A theoretical model is introduced to explain these findings.

Barriers to the use of research-based instructional strategies: The influence of both individual and situational characteristics

The motion of charged test particles in a Reissner-Nordstr\"om field is investigated. It is shown that naked singularities can be destroyed by shooting in suitably charged test particles to produce an event horizon around the source where none previously existed. It is also shown that existing event horizons cannot be destroyed by bombardment with charged test particles. In this manner existing naked singularities can be destroyed but not created while event horizons can be created but not destroyed. Furthermore, a simple explanation is given for radial test-particle oscillations---a phenomenon with no Newtonian analog.

Naked singularities, event horizons, and charged particles

Since 1991, we have been using Alan Van Heuvelen’s Overview, Case Study: Physics (OCS physics) methodology in introductory physics courses at New Jersey Institute of Technology (NJIT) with remarkable success. With the OCS method, physics concepts are presented first, with no mathematics. Only after the concepts are understood is math brought into the picture at the appropriate level. In addition, much of the learning is accomplished with students working together in small groups of three or four. In these collaborative settings, students actively engage each other in the learning process, working on specially designed small group problems, while the instructor acts as a facilitator of the on-going learning. We present various comparisons showing the effectiveness of OCS instruction over traditional teaching. In particular, since the introduction of OCS physics into NJIT’s summer Educational Opportunity Program (EOP), which involves mostly minority students, EOP students have significantly outperformed non-EOP students in their fall physics courses. Interviews with students and observations of videotapes suggest that “second teaching” takes place in small groups following “first teaching” by the instructor. Second teaching is interpreted on the basis of ideas developed by Vygotsky.

Concepts first—A small group approach to physics learning

We show how the Einstein-Maxwell field equations of general relativity can be used to construct a Lorentz model of an electron as an extended body consisting of pure charge and no matter. In contrast with Lorentz's approach using inertial mass, we associate the mass of the electron with its Schwarzschild gravitational mass. The Schwarzschild mass of an extended charged body as seen at infinity arises from the charge as well as the matter that the extended body possesses. The field equations for a Lorentz-type pure-charge extended electron are obtained by setting the matter terms equal to zero in the field equations for a spherically symmetric charged perfect fluid. Several explicit solutions to the pure-charge field equations are examined.

Gravitational models of a Lorentz extended electron

We develop a method for imbedding a Schwarzschild mass into a zero-curvature universe. We work with curvature coordinates ($R$,$T$), in terms of which the metric has the form $d{s}^{2}(R,T)={A}^{\ensuremath{-}1}(R,T)d{R}^{2}+{R}^{2}d{\ensuremath{\Omega}}^{2}\ensuremath{-}B(R,T)d{T}^{2}$, and coordinates ($R$,$\ensuremath{\tau}$), where $\ensuremath{\tau}$ is measured by radially moving geodesic clocks. We solve the field equations for a stress-energy tensor that corresponds to a radially moving perfect geodesic fluid outside some boundary ${R}_{b}$. Inside ${R}_{b}$ we take the stress-energy tensor to be composed of a perfect-fluid part and a Schwarzschild matter part. Specific examples of imbedding a mass into a de Sitter universe and a pressure-free Einstein---de Sitter universe are given, and we show how to extend our methods to general zero-curvature universes. A consequence of our results is that there will be spiralling of planetary orbits when a mass such as our Sun is imbedded in a universe. We relate our work to recent work done by Dirac with regard to his Large Numbers hypothesis.

Imbedding a Schwarzschild mass into cosmology

It is shown that when time is measured in a Schwarzschild field by radially falling or rising geodesic clocks, the usual Schwarzschild radial coordinate R, defined by ds/sup 2/ = dR/sup 2//(1 - 2M/R) - (1 - 2M/R) dT/sup 2/ + R/sup 2/d..cap omega../sup 2/, has the physical significance that it is a measure of proper distance between two events that occur simultaneously relative to the radially moving geodesic clocks, the two events lying on the same radial coordinate line.

Ronald Gautreau

Papers

Naked singularities, event horizons, and charged particles

Concepts first—A small group approach to physics learning

Gravitational models of a Lorentz extended electron

Imbedding a Schwarzschild mass into cosmology

The Schwarzschild radial coordinate as a measure of proper distance