Educating Gifted Students in the Regular Classroom: Efficacy, Attitudes, and Differentiation of Instruction

The purpose of this quantitative study was to determine which variable, teacher self-efficacy or teachers’ attitudes toward gifted students, better explains teachers’ willingness to differentiate instruction for gifted students. Survey data from 341third through eighth grade teachers were analyzed using multiple regression. Teachers’ attitudes toward gifted students were measured using the Survey of Practices with Students of Varying Needs (short version). The Teachers’ Sense of Efficacy Scale was used to measure teacher self-efficacy. The outcome variable, teachers’ willingness to differentiate instruction for gifted students, was measured by an instrument adapted by the researcher from an instrument developed by Heacox (2002), the Survey of Instructional Practices. Years of teaching experience was also used as control variable. Stepwise regression revealed that a total of 20% of the variance of the dependent variable can be explained by the combined effect of the two predictor variables and the control variable. The largest contribution to explaining the variance in differentiation practices for gifted students is contained within teacher efficacy with the second largest contribution being teacher attitudes. This research indicated that teacher self-efficacy is a better predictor than teachers’ attitudes toward gifted students when trying to predict teachers’ willingness to differentiate instruction for gifted students being taught in the regular classroom. While this study found statistically significant results for both of the internal factors studied, efficacy and attitude, as predictors of teachers’ willingness to differentiate instruction for gifted students, it explains only a small part of teacher’s willingness to differentiate instruction for gifted students in the regular classroom. The researcher recommends that future researchers employ the use of surveys that ask respondents to rate a list of both internal and external factors believed to influence differentiation for gifted students on how much they believe each factor influences their decisions to differentiate instruction. This method might produce a broader view of what teachers believe to be obstacles to differentiation

Sudden Gravitational Transition

We investigate the properties of a cosmological scenario which undergoes a gravitational phase transition at late times. In this scenario, the Universe evolves according to general relativity in the standard, hot big bang picture until a redshift z≲1. Nonperturbative phenomena associated with a minimally-coupled scalar field catalyzes a transition, whereby an order parameter consisting of curvature quantities such as R2, RabRab, RabcdRabcd acquires a constant expectation value. The ensuing cosmic acceleration appears driven by a dark-energy component with an equation-of-state w\u3c−1. We evaluate the constraints from type 1a supernovae, the cosmic microwave background, and other cosmological observations. We find that a range of models making a sharp transition to cosmic acceleration are consistent with observations

The K2 Mission: Characterization and Early results

The K2 mission will make use of the Kepler spacecraft and its assets to expand upon Kepler's groundbreaking discoveries in the fields of exoplanets and astrophysics through new and exciting observations. K2 will use an innovative way of operating the spacecraft to observe target fields along the ecliptic for the next 2-3 years. Early science commissioning observations have shown an estimated photometric precision near 400 ppm in a single 30 minute observation, and a 6-hour photometric precision of 80 ppm (both at V=12). The K2 mission offers long-term, simultaneous optical observation of thousands of objects at a precision far better than is achievable from ground-based telescopes. Ecliptic fields will be observed for approximately 75-days enabling a unique exoplanet survey which fills the gaps in duration and sensitivity between the Kepler and TESS missions, and offers pre-launch exoplanet target identification for JWST transit spectroscopy. Astrophysics observations with K2 will include studies of young open clusters, bright stars, galaxies, supernovae, and asteroseismology.Comment: 25 pages, 11 figures, Accepted to PAS

Quantum-limited optical time transfer for future geosynchronous links

The combination of optical time transfer and optical clocks opens up the possibility of large-scale free-space networks that connect both ground-based optical clocks and future space-based optical clocks. Such networks promise better tests of general relativity, dark matter searches, and gravitational wave detection. The ability to connect optical clocks to a distant satellite could enable space-based very long baseline interferometry (VLBI), advanced satellite navigation, clock-based geodesy, and thousand-fold improvements in intercontinental time dissemination. Thus far, only optical clocks have pushed towards quantum-limited performance. In contrast, optical time transfer has not operated at the analogous quantum limit set by the number of received photons. Here, we demonstrate time transfer with near quantum-limited acquisition and timing at 10,000 times lower received power than previous approaches. Over 300 km between mountaintops in Hawaii with launched powers as low as 40 $\mu$W, distant timescales are synchronized to 320 attoseconds. This nearly quantum-limited operation is critical for long-distance free-space links where photons are few and amplification costly -- at 4.0 mW transmit power, this approach can support 102 dB link loss, more than sufficient for future time transfer to geosynchronous orbits

Transit Timing Observations from Kepler: VI. Potentially interesting candidate systems from Fourier-based statistical tests

We analyze the deviations of transit times from a linear ephemeris for the Kepler Objects of Interest (KOI) through Quarter six (Q6) of science data. We conduct two statistical tests for all KOIs and a related statistical test for all pairs of KOIs in multi-transiting systems. These tests identify several systems which show potentially interesting transit timing variations (TTVs). Strong TTV systems have been valuable for the confirmation of planets and their mass measurements. Many of the systems identified in this study should prove fruitful for detailed TTV studies.Comment: 32 pages, 6 of text and one long table, Accepted to Ap

Validation of Kepler's Multiple Planet Candidates. III: Light Curve Analysis & Announcement of Hundreds of New Multi-planet Systems

The Kepler mission has discovered over 2500 exoplanet candidates in the first two years of spacecraft data, with approximately 40% of them in candidate multi-planet systems. The high rate of multiplicity combined with the low rate of identified false-positives indicates that the multiplanet systems contain very few false-positive signals due to other systems not gravitationally bound to the target star (Lissauer, J. J., et al., 2012, ApJ 750, 131). False positives in the multi- planet systems are identified and removed, leaving behind a residual population of candidate multi-planet transiting systems expected to have a false-positive rate less than 1%. We present a sample of 340 planetary systems that contain 851 planets that are validated to substantially better than the 99% confidence level; the vast majority of these have not been previously verified as planets. We expect ~2 unidentified false-positives making our sample of planet very reliable. We present fundamental planetary properties of our sample based on a comprehensive analysis of Kepler light curves and ground-based spectroscopy and high-resolution imaging. Since we do not require spectroscopy or high-resolution imaging for validation, some of our derived parameters for a planetary system may be systematically incorrect due to dilution from light due to additional stars in the photometric aperture. None the less, our result nearly doubles the number of verified exoplanets.Comment: 138 pages, 8 Figures, 5 Tables. Accepted for publications in the Astrophysical Journa

A Sudden Gravitational Transition

We investigate the properties of a cosmological scenario which undergoes a gravitational phase transition at late times. In this scenario, the Universe evolves according to general relativity in the standard, hot Big Bang picture until a redshift z \lesssim 1. Non-perturbative phenomena associated with a minimally-coupled scalar field catalyzes a transition, whereby an order parameter consisting of curvature quantities such as R^2, R_{ab}R^{ab}, R_{abcd}R^{abcd} acquires a constant expectation value. The ensuing cosmic acceleration appears driven by a dark-energy component with an equation-of-state w < -1. We evaluate the constraints from type 1a supernovae, the cosmic microwave background, and other cosmological observations. We find that a range of models making a sharp transition to cosmic acceleration are consistent with observations.Comment: 8 pages, 8 figures; added reference

Discovery and Validation of Kepler-452b: A 1.6-Re Super Earth Exoplanet in the Habitable Zone of a G2 Star

We report on the discovery and validation of Kepler-452b, a transiting planet identified by a search through the 4 years of data collected by NASA's Kepler Mission. This possibly rocky 1.63$^{+0.23}_{-0.20}$ R$_\oplus$ planet orbits its G2 host star every 384.843$^{+0.007}_{0.012}$ days, the longest orbital period for a small (R$_p$ < 2 R$_\oplus$) transiting exoplanet to date. The likelihood that this planet has a rocky composition lies between 49% and 62%. The star has an effective temperature of 5757$\pm$85 K and a log g of 4.32$\pm$0.09. At a mean orbital separation of 1.046$^{+0.019}_{-0.015}$ AU, this small planet is well within the optimistic habitable zone of its star (recent Venus/early Mars), experiencing only 10% more flux than Earth receives from the Sun today, and slightly outside the conservative habitable zone (runaway greenhouse/maximum greenhouse). The star is slightly larger and older than the Sun, with a present radius of 1.11$^{+0.15}_{-0.09}$ R$_\odot$ and an estimated age of 6 Gyr. Thus, Kepler-452b has likely always been in the habitable zone and should remain there for another 3 Gyr.Comment: 19 pages, 16 figure

Hectospec, the MMT's 300 Optical Fiber-Fed Spectrograph

The Hectospec is a 300 optical fiber fed spectrograph commissioned at the MMT in the spring of 2004. A pair of high-speed six-axis robots move the 300 fiber buttons between observing configurations within ~300 s and to an accuracy ~25 microns. The optical fibers run for 26 m between the MMT's focal surface and the bench spectrograph operating at R~1000-2000. Another high dispersion bench spectrograph offering R~5,000, Hectochelle, is also available. The system throughput, including all losses in the telescope optics, fibers, and spectrograph peaks at ~10% at the grating blaze in 1" FWHM seeing. Correcting for aperture losses at the 1.5" diameter fiber entrance aperture, the system throughput peaks at $\sim$17%. Hectospec has proven to be a workhorse instrument at the MMT. Hectospec and Hectochelle together were scheduled for 1/3 of the available nights since its commissioning. Hectospec has returned \~60,000 reduced spectra for 16 scientific programs during its first year of operation.Comment: 68 pages, 28 figures, to appear in December 2005 PAS

A First Comparison of Kepler Planet Candidates in Single and Multiple Systems

In this letter we present an overview of the rich population of systems with multiple candidate transiting planets found in the first four months of Kepler data. The census of multiples includes 115 targets that show 2 candidate planets, 45 with 3, 8 with 4, and 1 each with 5 and 6, for a total of 170 systems with 408 candidates. When compared to the 827 systems with only one candidate, the multiples account for 17 percent of the total number of systems, and a third of all the planet candidates. We compare the characteristics of candidates found in multiples with those found in singles. False positives due to eclipsing binaries are much less common for the multiples, as expected. Singles and multiples are both dominated by planets smaller than Neptune; 69 +2/-3 percent for singles and 86 +2/-5 percent for multiples. This result, that systems with multiple transiting planets are less likely to include a transiting giant planet, suggests that close-in giant planets tend to disrupt the orbital inclinations of small planets in flat systems, or maybe even to prevent the formation of such systems in the first place.Comment: 13 pages, 13 figures, submitted to ApJ Letter