Woo-Hoo! The Mathematics and Education of the D’oh-Nut A Review of Simon Singh’s The Simpsons and Their Mathematical Secrets

I am a mathematics educator working in a Faculty of Education, at a mid-sized university. I have degrees in mathematics, teaching, and education related to the teaching and learning of mathematics. I also have twenty years of experience with school boards as a secondary school mathematics teacher and department head. It is from these experiences, knowledge, and professional practice that I approached this book review—from a place of how I see the world around me and work to understand it. I love thinking about and working to understand teachers’ beliefs, problem solving, and professional learning in problem solving contexts, and thus my secondary school teacher ‘self’, or identity, is quite interconnected to my mathematics education researcher ‘self, or identity

Exploration de la nature et de l’objectif des rétroactions données lors du visionnement de vidéos dans le cadre d’un cours sur la laparoscopie en gynécologie

Background: Feedback about intraoperative performance remains a cornerstone of surgical training. Video playback offers one potential method for more effective feedback to surgical residents. More research is needed to better understand this method. This study explores the nature of instructional interactions and feedback in the operating room (OR) and when using video playback during post-operative review in obstetrics and gynecology (OBGYN) training. Method: This case study occurred between September 2016 and February 2017. Three OBGYN residents and five OBGYN supervising surgeons were involved in six laparoscopic cases. Intraoperative and video playback dialogues were recorded and analysed, the former deductively using codes identified from published literature, and the latter both deductively, using the same codes, and inductively, with codes that emerged from the data during analysis. Results: 1090 intraoperative interactions were identified within 376 minutes of dialogue. Most interactions were didactic, instructing the resident how to use an instrument to perform a task. Deductive analysis of postoperative video playback review identified 146 interactions within 155 minutes. While the most common interaction type remained didactic, a teaching component was included more often. It became apparent that deductive analysis using the intraoperative codes did not adequately capture the nature and focus of feedback during video playback. Hermeneutic phenomenological analysis identified more dialogic video playback sessions with more resident-initiated questions and reflection. Conclusions: This study demonstrates that the nature of feedback during video playback is fundamentally different from that in the OR, offering a greater potential for collaborative and improved learning.Contexte : La rétroaction sur la performance peropératoire demeure la pierre angulaire de la formation chirurgicale. Le visionnement de vidéos est un moyen d’offrir une rétroaction plus efficace aux résidents en chirurgie. Des recherches supplémentaires sont nécessaires pour mieux cerner cette méthode. La présente étude explore la nature des interactions pédagogiques et de la rétroaction donnée en salle d’opération et lors du visionnement de vidéos au cours de l’analyse postopératoire dans le cadre de la formation en obstétrique et gynécologie. Méthode : Cette étude de cas a été réalisée entre septembre 2016 et février 2017. Trois résidents et cinq chirurgiens superviseurs en obstétrique et gynécologie ont participé à six interventions laparoscopiques. Les dialogues peropératoires et les échanges qui ont eu lieu lors du visionnement des vidéos ont été enregistrés et analysés, les premiers de manière déductive en utilisant les codes tirés de la littérature, et les seconds à la fois de manière déductive, en utilisant les mêmes codes, et inductive, à l’aide de codes dégagés des données pendant l'analyse. Résultats : Les interactions peropératoires recensées au cours des 376 minutes de dialogue sont au nombre de 1090. La plupart des rétroactions étaient didactiques, visant à expliquer au résident comment utiliser un instrument pour effectuer une tâche. L'analyse déductive des vidéos postopératoires a permis le repérage de 146 interactions au cours d’une période de 155 minutes. Si la plupart de ces interactions demeuraient didactiques, elles comprenaient plus souvent une composante d’enseignement. Il s’est avéré que l'analyse déductive à l’aide des codes peropératoires ne rendait pas compte de manière adéquate de la nature et de l'objectif de la rétroaction offerte pendant le visionnement des vidéos. L'analyse phénoménologique herméneutique a permis d'identifier des séances de visionnement qui étaient plus dialogiques, comprenant davantage de questions et de réflexions provenant des résidents. Conclusion : La présente étude montre que la rétroaction donnée pendant le visionnement des vidéos et celle donnée en salle d'opération sont fondamentalement différentes, et que la première favorise davantage que la seconde l’apprentissage collaboratif et son efficacité

Surprising variations in the rotation of the chemically peculiar stars CU Virginis and V901 Orionis

CU Vir and V901 Ori belong among these few magnetic chemically peculiar stars whose rotation periods vary on timescales of decades. We aim to study the stability of the periods in CU Vir and V901 Ori using all accessible observational data containing phase information. We collected all available relevant archived observations supplemented with our new measurements of these stars and analysed the period variations of the stars using a novel method that allows for the combination of data of diverse sorts. We found that the shapes of their phase curves were constant, while the periods were changing. Both stars exhibit alternating intervals of rotational braking and acceleration. The rotation period of CU Vir was gradually shortening until the year 1968, when it reached its local minimum of 0.52067198 d. The period then started increasing, reaching its local maximum of 0.5207163 d in the year 2005. Since that time the rotation has begun to accelerate again. We also found much smaller period changes in CU Vir on a timescale of several years. The rotation period of V901 Ori was increasing for the past quarter-century, reaching a maximum of 1.538771 d in the year 2003, when the rotation period began to decrease. A theoretically unexpected alternating variability of rotation periods in these stars would remove the spin-down time paradox and brings a new insight into structure and evolution of magnetic upper-main-sequence stars.Comment: 5 pages, 3 figure

The radio lighthouse CU Virginis: the spindown of a single main sequence star

The fast rotating star CU Virginis is a magnetic chemically peculiar star with an oblique dipolar magnetic field. The continuum radio emission has been interpreted as gyrosyncrotron emission arising from a thin magnetospheric layer. Previous radio observations at 1.4 GHz showed that a 100% circular polarized and highly directive emission component overlaps to the continuum emission two times per rotation, when the magnetic axis lies in the plane of the sky. This sort of radio lighthouse has been proposed to be due to cyclotron maser emission generated above the magnetic pole and propagating perpendicularly to the magnetic axis. Observations carried out with the Australia Telescope Compact Array at 1.4 and 2.5 GHz one year after this discovery show that this radio emission is still present, meaning that the phenomenon responsible for this process is steady on a timescale of years. The emitted radiation spans at least 1 GHz, being observed from 1.4 to 2.5 GHz. On the light of recent results on the physics of the magnetosphere of this star, the possibility of plasma radiation is ruled out. The characteristics of this radio lighthouse provides us a good marker of the rotation period, since the peaks are visible at particular rotational phases. After one year, they show a delay of about 15 minutes. This is interpreted as a new abrupt spinning down of the star. Among several possibilities, a quick emptying of the equatorial magnetic belt after reaching the maximum density can account for the magnitude of the breaking. The study of the coherent emission in stars like CU Vir, as well as in pre main sequence stars, can give important insight into the angular momentum evolution in young stars. This is a promising field of investigation that high sensitivity radio interferometers such as SKA can exploit.Comment: Accepted to MNRAS, 8 pages, 7 figures, updated versio

A Tight Upper Limit on Oscillations in the Ap star Epsilon Ursae Majoris from WIRE Photometry

Observations of Epsilon UMa obtained with the star tracker on the Wide Field Infrared Explorer (WIRE) satellite during a month in mid-2000 are analyzed. This is one of the most precise photometry of an Ap star. The amplitude spectrum is used to set an upper limit of 75 parts per million for the amplitude of stellar pulsations in this star unless it accidentally oscillates with a single mode at the satellite orbit, its harmonics or their one day aliases. This is the tightest limit put on the amplitude of oscillations in an Ap star. As the rotation period of Epsilon UMa is relatively short (5.1 d), it cannot be argued that the observations were made at a wrong rotational phase. Our results thus support the idea that some Ap stars do not pulsate at all.Comment: 4 pages, 4 figures, 2 style files, accepted for publication in ApJ

Hospital usage of TOXBASE in Great Britain:Temporal trends in accesses 2008 to 2015

Aim: Examining temporal trends in accesses to the UK's National Poison Information Service's TOXBASE database in Britain. Methods: Generalised additive models were used to examine trends in daily numbers of accesses to TOXBASE from British emergency departments between January 2008 and December 2015. Day-of-the-week, seasonality and long term trends were analysed at national and regional levels (Wales, Scotland and the 9 English Government Office Regions). Results: The long-term trend in daily accesses increases from 2.8 (95% CI:2.6, 3.0) per user on 1st January 2008 to 4.6 (95% CI:4.3, 4.9) on 31st December 2015, with small but significant differences in population-corrected accesses by region (p<0.001). There are statistically significant seasonal and day of the week patterns (p<0.001) across all regions. Accesses are 18 % (95% CI:14%, 22%) higher in summer than in January and at the weekend compared to weekdays in all regions; there is a 7.5% (95% CI:6.1%, 8.9%) increase between Friday and Sunday. Conclusions: There are consistent in-year patterns in access to TOXBASE indicating potential seasonal patterns in poisonings in Britain, with location-dependant rates of usage. This novel descriptive work lays the basis for future work on the interaction of TOXBASE use with emergency admission of patients into hospital

Emergence of Bulk CsCl Structure in (CsCl)nCs+ Cluster Ions

The emergence of CsCl bulk structure in (CsCl)nCs+ cluster ions is investigated using a mixed quantum-mechanical/semiempirical theoretical approach. We find that rhombic dodecahedral fragments (with bulk CsCl symmetry) are more stable than rock-salt fragments after the completion of the fifth rhombic dodecahedral atomic shell. From this size (n=184) on, a new set of magic numbers should appear in the experimental mass spectra. We also propose another experimental test for this transition, which explicitely involves the electronic structure of the cluster. Finally, we perform more detailed calculations in the size range n=31--33, where recent experimental investigations have found indications of the presence of rhombic dodecahedral (CsCl)32Cs+ isomers in the cluster beams.Comment: LaTeX file. 6 pages and 4 pictures. Accepted for publication in Phys. Rev.