Conceptual Limitations in Curricular Presentations of Area Measurement: One Nation’s Challenges

Research has found that elementary students face five main challenges in learning area measurement: (1) conserving area as a quantity, (2) understanding area units, (3) structuring rectangular space into composite units, (4) understanding area formulas, and (5) distinguishing area and perimeter. How well do elementary mathematics curricula address these challenges? A detailed analysis of three U.S. elementary textbook series revealed systematic deficits. Each presented area measurement in strongly procedural terms using a shared sequence of procedures across grades. Key conceptual principles were infrequently expressed and often well after related procedures were introduced. Particularly weak support was given for understanding how the multiplication of lengths produces area measures. The results suggest that the content of written curricula contributes to students’ weak learning of area measurement

The Orbit of the Companion to HD 100453A: Binary-Driven Spiral Arms in a Protoplanetary Disk

HD 100453AB is a 10+/-2 Myr old binary whose protoplanetary disk was recently revealed to host a global two-armed spiral structure. Given the relatively small projected separation of the binary (1.05", or ~108 au), gravitational perturbations by the binary seemed to be a likely driving force behind the formation of the spiral arms. However, the orbit of these stars remained poorly understood, which prevented a proper treatment of the dynamical influence of the companion on the disk. We observed HD 100453AB between 2015-2017 utilizing extreme adaptive optics systems on the Very Large Telescope and Magellan Clay Telescope. We combined the astrometry from these observations with published data to constrain the parameters of the binary's orbit to a=1.06"+/-0.09", e=0.17+/-0.07, and i=32.5+/- 6.5 degrees. We utilized publicly available ALMA CO data to constrain the inclination of the disk to i~28 degrees, which is relatively co-planar with the orbit of the companion and consistent with previous estimates from scattered light images. Finally, we input these constraints into hydrodynamical and radiative transfer simulations to model the structural evolution of the disk. We find that the spiral structure and truncation of the circumprimary disk in HD 100453 are consistent with a companion-dirven origin. Furthermore, we find that the primary star's rotation, its outer disk, and the companion exhibit roughly the same direction of angular momentum, and thus the system likely formed from the same parent body of material.Comment: 28 pages, 11 figures, Accepted to Ap

Curricular Treatments of Length Measurement in the United States: Do They Address Known Learning Challenges?

Extensive research has shown that elementary students struggle to learn the basic principles of length measurement. However, where patterns of errors have been documented, the origins of students’ difficulties have not been identified. This study investigated the hypothesis that written elementary mathematics curricula contribute to the problem of learning length measurement. We analyzed all instances of length measurement in three mathematics curricula (grades K–3) and found a shared focus on procedures. Attention to conceptual principles was limited overall and particularly for central ideas; conceptual principles were often presented after students were asked to use procedures that depended on them; and students often did not have direct access to conceptual principles. We also report five groupings of procedures that appeared sequentially in all three curricula, the conceptual principles that underlie those procedures, and the conventional knowledge that receives substantial attention by grade 3

New Extinction and Mass Estimates of the Low-mass Companion 1RXS 1609 B with the Magellan AO System: Evidence of an Inclined Dust Disk

We used the Magellan adaptive optics system to image the 11 Myr substellar companion 1RXS 1609 B at the bluest wavelengths to date (z' and Ys). Comparison with synthetic spectra yields a higher temperature than previous studies of $T_\mathrm{eff}=2000\pm100\mathrm{K}$ and significant dust extinction of $A_V=4.5^{+0.5}_{-0.7}$ mag. Mass estimates based on the DUSTY tracks gives 0.012-0.015 Msun, making the companion likely a low-mass brown dwarf surrounded by a dusty disk. Our study suggests that 1RXS 1609 B is one of the 25% of Upper Scorpius low-mass members harboring disks, and it may have formed like a star and not a planet out at 320 AU.Comment: 5 pages, 4 figures; accepted to ApJ

The Multiplicity of M-Dwarfs in Young Moving Groups

We image 104 newly identified low-mass (mostly M-dwarf) pre-main sequence members of nearby young moving groups with Magellan Adaptive Optics (MagAO) and identify 27 binaries with instantaneous projected separation as small as 40 mas. 15 were previously unknown. The total number of multiple systems in this sample including spectroscopic and visual binaries from the literature is 36, giving a raw multiplicity rate of at least $35^{+5}_{-4}\%$ for this population. In the separation range of roughly 1 - 300 AU in which infrared AO imaging is most sensitive, the raw multiplicity rate is at least $24^{+5}_{-4}\%$ for binaries resolved by the MagAO infrared camera (Clio). The M-star sub-sample of 87 stars yields a raw multiplicity of at least $30^{+5}_{-4}\%$ over all separations, $21^{+5}_{-4}\%$ for secondary companions resolved by Clio from 1 to 300 AU ($23^{+5}_{-4}\%$ for all known binaries in this separation range). A combined analysis with binaries discovered by the Search for Associations Containing Young stars shows that multiplicity fraction as a function of mass and age over the range of 0.2 to 1.2 $M_\odot$ and 10 - 200 Myr appears to be linearly flat in both parameters and across YMGs. This suggests that multiplicity rates are largely set by 100 Myr without appreciable evolution thereafter. After bias corrections are applied, the multiplicity fraction of low-mass YMG members ($< 0.6 M_\odot$) is in excess of the field.Comment: 25 page

Introducing a basic psychological performance demand model for sport and organisations

This study presents the development of a basic psychological performance demand model (PDM) for sport and organisations, adopting a process view of performance underpinned by reversal theory (Apter [2001] An introduction to reversal theory. In M. J. Apter (Ed.), Motivational styles in everyday life: A guide to reversal theory (pp. 3-36⁠). Washington, DC: American Psychological Association). Six elite coaches with extensive coaching experience at European, Commonwealth, Olympic and Paralympic Games were interviewed. Their interview statements were analysed using a combination of deductive and inductive analysis procedures for qualitative data. In conjunction with the interviewer, coaches developed PDMs for their specific sports. Analysis of interview data and coaches’ specific PDMs identified four main cross-sport themes or fundamental psychological capabilities required for meeting performance demands. These were: Mastery motivation, Decision making, Execution, and Teamship. The PDM offers a starting framework for a new basic performance model that is novel and pragmatic with potential applicability across sports and organisations. The model is useful in its existing form, but needs further testing, extended practical application and reflection by coaches, athletes, and sport psychologists. It has potential for use in other coaching contexts beyond sport, such as business, leadership development, education, and health