Understanding linear measure

This article provides strategies for enhancing tasks to offer students better opportunities to develop conceptual understanding of length measurement. Teachers are offered strategies that help move instruction beyond procedures

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

Affect graphing: leveraging graphical representations in the study of students’ affect in mathematics

Affect (e.g., beliefs, attitudes, emotions) plays a crucial role in mathematics learning, but reliance on verbal and written responses (from surveys, interviews, etc.) limits students’ expression of their affective states. As a complement to existing methods that rely on verbal reports, we explore how graphing can be used to study affect during mathematical experiences. We analyze three studies that used graphing to represent, stimulate recall, and reflect on affect. In each, students were asked to draw their perception of an affective construct, such as confidence or intensity of emotion, against time. The studies differed in participant populations, target affect, timescales of participant experience, and structural features of the graphs. The affordances of graphing include reduced dependence on verbal data, temporal ordering of participants’ recollections, explicit representation of change over time, and the creation of objects (the graph) for discussion. These studies as examples show that well-structured graphing can productively supplement existing methods for studying affect in mathematics education, as a different medium through which students can communicate their experience

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

Young Clusters in the Nuclear Starburst of M 83

We present a photometric catalog of 45 massive star clusters in the nuclear starburst of M 83 (NGC 5236), observed with the Hubble Space Telescope WFPC2, in both broad-band (F300W, F547M, and F814W) and narrow-band (F656N and F487N) filters. By comparing the photometry to theoretical population synthesis models, we estimate the age and mass of each cluster. We find that over 75% of the star clusters more massive than 2*10^4 Msun in the central 300 pc of M 83 are less than 10 Myr old. Among the clusters younger than 10 Myr and more massive than 5*10^3 Msun, 70% are between 5 and 7 Myr old. We list an additional 330 clusters that are detected in our F300W images, but not in the shallower F547M and F814W images. The clusters are distributed throughout a semicircular annulus that identifies the active region in the galaxy core, between 50 and 130 pc from the optical center of M 83. Clusters younger than 5 Myr are preferentially found along the perimeter of the semicircular annulus. We suggest that the 5-7 Myr population has evacuated much of the interstellar material from the active ringlet region, and that star formation is continuing along the edges of the region.Comment: 40 pages, 13 figures, accepted to ApJ

HexPak and GradPak: variable-pitch dual-head IFUs for the WIYN 3.5m Telescope Bench Spectrograph

We describe the design, construction, and expected performance of two new fiber integral field units (IFUs) --- HexPak and GradPak --- for the WIYN 3.5m Telescope Nasmyth focus and Bench Spectrograph. These are the first IFUs to provide formatted fiber integral field spectroscopy with simultaneous sampling of varying angular scales. HexPak and GradPak are in a single cable with a dual-head design, permitting easy switching between the two different IFU heads on the telescope without changing the spectrograph feed: the two heads feed a variable-width double-slit. Each IFU head is comprised of a fixed arrangement of fibers with a range of fiber diameters. The layout and diameters of the fibers within each array are scientifically-driven for observations of galaxies: HexPak is designed to observe face-on spiral or spheroidal galaxies while GradPak is optimized for edge-on studies of galaxy disks. HexPak is a hexagonal array of 2.9 arcsec fibers subtending a 40.9 arcsec diameter, with a high-resolution circular core of 0.94 arcsec fibers subtending 6 arcsec diameter. GradPak is a 39 by 55 arcsec rectangular array with rows of fibers of increasing diameter from angular scales of 1.9 arcsec to 5.6 arcsec across the array. The variable pitch of these IFU heads allows for adequate sampling of light profile gradients while maintaining the photon limit at different scales.Comment: 10 pages, 4 figures, presented at SPIE, Astronomical Telescopes and Instrumentation, 1 - 6 July 2012, Amsterdam, Netherland

Regulation of Peroxisome Proliferator-Activated Receptors by E6-Associated Protein

Peroxisome proliferator-activated receptors (PPARs) are nuclear receptors (NRs) that regulate genes involved in lipid and glucose metabolism. PPAR activity is regulated by interactions with cofactors and of interest are cofactors with ubiquitin ligase activity. The E6-associated protein (E6-AP) is an E3 ubiquitin ligase that affects the activity of other NRs, although its effects on PPARs have not been examined. E6-AP inhibited the ligand-independent transcriptional activity of PPARα and PPARβ, with marginal effects on PPARγ, and decreased basal mRNA levels of PPARα target genes. Inhibition of PPARα activity required the ubiquitin ligase function of E6-AP, but occurred in a proteasome-independent manner. PPARα interacted with E6-AP, and in mice treated with PPARα agonist clofibrate, mRNA and protein levels of E6-AP were increased in wildtype, but not in PPARα null mice, indicating a PPARα-dependent regulation. These studies suggest coordinate regulation of E6-AP and PPARα, and contribute to our understanding of the role of PPARs in cellular metabolism

Collapsing Spaces, Colliding Places: Leveraging Constructs from Humanistic Geography to Explore Mathematics Classes

Humanistic geographers distinguish between space and place: “What begins as undifferentiated space becomes place as we get to know it better and endow it with value” (Tuan, 1977, page 6). In this essay, we seek to demonstrate how mathematics education researchers and mathematics instructors may find space and place illuminating for understanding important aspects of students’ learning experiences during the coronavirus pandemic—and possibly beyond. Specifically, after introducing the terms and relating them to the context of a university mathematics class, we exemplify how home and class places collided for three undergraduate mathematics students forced to deal with the abrupt transition to online education. We conclude by discussing implications of attending to space and place for designers and researchers of (pandemic) online instruction and make connections to how the pandemic and attending to space and place can serve as a catalyst for reshaping undergraduate mathematics education

Radiocaesium transfer and radiation exposure of frogs in Fukushima Prefecture

The International Commission on Radiological Protection has proposed an environmental assessment framework. This includes ionising radiation exposure assessment for different frog life-stages, but radiocaesium transfer parameters are unavailable. We collate data from the Fukushima Prefecture (contaminated by the Fukushima accident) and estimate radiocaesium concentration ratio (CR ) values for tadpoles and adult frogs, presenting the largest available amphibian CR dataset. In total, 513 adult frogs and 2540 tadpoles were analysed in 62 and 59 composite samples respectively. Results suggest that equilibrium was reached between water and amphibian radiocaesium activity concentrations circa one-year after the accident. Radiocaesium transfer to tadpoles was higher than to adult frogs. Dose rates were estimated for different life-stages and species in both the aquatic and terrestrial environment. Estimated dose rates to adults and tadpoles were typically similar because external exposure dominated for both organisms; frogspawn dose rates were estimated to be orders of magnitude lower than other life-stages. For the two sites assessed, which were outside of the most contaminated areas of the Fukushima Prefecture, estimated dose rates were below those anticipated to present a risk to wildlife populations; it is likely that dose rates in more contaminated areas were in excess of some effects benchmark values

Mortality Rates in a Diverse Cohort of Mechanically Ventilated Patients With Novel Coronavirus in the Urban Midwest

Objectives: Differences in mortality rates previously reported in critically ill patients with coronavirus disease 2019 have increased the need for additional data on mortality and risk factors for death. We conducted this study to describe length of stay, mortality, and risk factors associated with in-hospital mortality in mechanically ventilated patients with coronavirus disease 2019. Design: Observational study. Setting: Two urban, academic referral hospitals in Indianapolis, Indiana. Patients or Subjects: Participants were critically ill patients 18 years old and older, admitted with coronavirus disease 2019 between March 1, 2020, and April 27, 2020. Interventions: None. Measurements and Main Results: Outcomes included in-hospital mortality, duration of mechanical ventilation, and length of stay. A total of 242 patients were included with mean age of 59.6 years (sd, 15.5 yr), 41.7% female and 45% African American. Mortality in the overall cohort was 19.8% and 20.5% in the mechanically ventilated subset. Patients who died were older compared with those that survived (deceased: mean age, 72.8 yr [sd, 10.6 yr] vs patients discharged alive: 54.3 yr [sd, 14.8 yr]; p < 0.001 vs still hospitalized: 59.5 yr [sd, 14.4 yr]; p < 0.001) and had more comorbidities compared with those that survived (deceased: 2 [0.5–3] vs survived: 1 [interquartile range, 0–1]; p = 0.001 vs still hospitalized: 1 [interquartile range, 0–2]; p = 0.015). Older age and end-stage renal disease were associated with increased hazard of in-hospital mortality: age 65–74 years (hazard ratio, 3.1 yr; 95% CI, 1.2–7.9 yr), age 75+ (hazard ratio, 4.1 yr; 95% CI, 1.6–10.5 yr), and end-stage renal disease (hazard ratio, 5.9 yr; 95% CI, 1.3–26.9 yr). The overall median duration of mechanical ventilation was 9.3 days (interquartile range, 5.7–13.7 d), and median ICU length of stay in those that died was 8.7 days (interquartile range, 4.0–14.9 d), compared with 9.2 days (interquartile range, 4.0–14.0 d) in those discharged alive, and 12.7 days (interquartile range, 7.2–20.3 d) in those still remaining hospitalized. Conclusions: We found mortality rates in mechanically ventilated patients with coronavirus disease 2019 to be lower than some previously reported with longer lengths of stay.Drs. Perkins, Gao, and Khan are supported through National Institutes of Health (NIH)-National Institute on Aging (NIA) R01 AG 055391, R01 AG 052493, and National Heart, Lung, and Blood Institute R01 HL131730. Dr. Twigg is supported through NIH-NIA U01 AG060900. The remaining authors have disclosed that they do not have any potential conflicts of interest