The process of modelling-related problem posing – A case study with preservice teachers

In real life, problems emerge from situations and often need to be posed before they can be solved. Despite the ongoing emphasis on the processes involved in solving modelling problems, little is known about the process of problem posing. To help fill this gap, the current study examined (1) what activities are involved in modelling-related problem posing and (2) the sequence in which they occur. For this purpose, we invited seven preservice teachers to pose a problem based on given real-world situations and analyzed their problem-posing activities. We identified the five most frequent activities that occurred in the sequence: understanding–exploring–generating–problem solving–evaluating. These results contribute to the uncovering of important activities and contribute to theories of modelling and problem posing

A novel method quantifying caries following orthodontic treatment

This retrospective pilot study used a newly developed evaluation tool to assess the prevalence and incidence of White Spot Lesions (WSL) before and after multibracket appliance (MB) therapy. Digital photographs of 121 adolescent patients (63 ♂, 58 ♀) with metal brackets were analyzed retrospectively before and after MB therapy. The labial surfaces of anterior teeth, canine teeth, and premolars in the upper (UJ) and lower jaws (LJ) were evaluated using the Enamel Decalcification Index (EDI) by Banks and Richmond (Eur J Orthod, 16(1):19–25, 1994, levels 0–3) and a specially developed digitally scaled graticule with concentric circles to quantify the extent of WSL (in %). The statistical data analysis was based on crosstabulations and logistic regression. Before MB, 69.4% of the patients presented at least one WSL and 97.5% after, an increase of 28.1%. Before MB, 18.4% of the tooth surfaces (TS) showed an EDI level of 1–3. After MB, 51.8% of the TS featured WSL. 18.2% of the TS showed a WSL to the extent of ≥ 20–100% before and 52.3% after MB. The incidence in the UJ (71–79%) as well as the LJ (64–76%) was highest for the first and second premolars and lowest for LJ incisors (22–35%). The probability for developing a new distal WSL is higher than developing gingival, mesial or occlusal WSL. Labial MB therapy drastically increases the risk of developing WSL. We verified a concise quantification of the extent of labial WSL with the evaluation index

How can we model subsurface stormflow at the catchment scale if we cannot measure it?

Subsurface stormflow (SSF) can be a dominant run‐off generation process in humid mountainous catchments (e.g., Bachmair & Weiler, 2011; Blume & van Meerveld, 2015; Chifflard, Didszun, & Zepp, 2008). Generally, SSF develops in structured soils where bedrock or a less permeable soil layer is overlaid by a more permeable soil layer and vertically percolating water is deflected, at least partially, in a lateral downslope direction due to the slope inclination. SSF can also occur when groundwater levels rise into more permeable soil layers and water flows laterally through the more permeable layers to the stream (“transmissivity feedback mechanism”; Bishop, Grip, & O'Neill, 1990). The different existing terms for SSF in the hydrological literature such as shallow subsurface run‐off, interflow, lateral flow, or soil water flow reflects the different underlying process concepts developed in various experimental studies in different environments by using different experimental approaches at different spatial and temporal scales (Weiler, McDonnell, Tromp‐van Meerveld, & Uchida, 2005). Intersite comparisons and the extraction of general rules for SSF generation and its controlling factors are still lacking, which hampers the development of appropriate approaches for modelling SSF. But appropriate prediction of SSF is essential due to its clear influence on run‐off generation at the catchment scale (e.g., Chifflard et al., 2010; Zillgens, Merz, Kirnbauer, & Tilch, 2005), on the formation of floods (e.g., Markart et al., 2013, 2015) and on the transport of nutrients or pollutants from the hillslopes into surface water bodies (Zhao, Tang, Zhao, Wang, & Tang, 2013). However, a precise simulation of SSF in models requires an accurate process understanding including, knowledge about water pathways, residence times, magnitude of water fluxes, or the spatial origin of SSF within a given catchment because such factors determine the transport of subsurface water and solutes to the stream. But due to its occurrence in the subsurface and its spatial and temporal variability, determining and quantifying the processes generating SSF is a challenging task as they cannot be observed directly. Therefore, it is logical to ask whether we can really model SSF correctly if we cannot measure it well enough on the scale of interest (Figure 1). This commentary reflects critically on whether current experimental concepts and modelling approaches are sufficient to predict the contribution of SSF to the run‐off at the catchment scale. This applies in particular to the underlying processes, controlling factors, modelling approaches, research gaps, and innovative strategies to trace SSF across different scales

Modellieren beim Problem Posing – Modellierungsaktivitäten beim Problem Posing zu realweltlichen Situationen

Das Lösen von mathematischen Problemen ist eine zentrale Grundlage für das Betreiben von Mathematik. Außerhalb des Schulunterrichts liegen diese Probleme jedoch nur selten vorgefertigt vor und müssen zunächst entwickelt werden. Die Entwicklung eigener Probleme (Problem Posing) hat in den letzten Jahren in der mathematikdidaktischen Forschung stark an Bedeutung gewonnen. Insbesondere gilt das Problem Posing als ein gewinnbringender Ansatz zur Förderung des Problemlösens, da die Entwicklung eigener Probleme wichtige Problemlöseprozesse anspricht (Cai & Leikin, 2020). Das Modellieren kann als Problemlösen realweltlicher Probleme charakterisiert werden. Demnach ist es möglich, dass Problem Posing zu gegebenen realweltlichen Situationen (modellierungsbezogenes Problem Posing) auch zur Förderung des mathematischen Modellierens gewinnbringend eingesetzt werden kann. Bisher existiert nur wenig Forschung zum Problem Posing aus Modellierungsperspektive. Um das Potential des Problem Posings für das Modellieren zu untersuchen, soll die Verbindung zwischen den Problem Posing und Modellierungsprozessen aus einer kognitiven Perspektive analysiert werden

The Distance to NGC 2264

We determine the distance to the open cluster NGC 2264 using a statistical analysis of cluster member inclinations. We derive distance-dependent values of sin i (where i is the inclination angle) for 97 stars in NGC 2264 from the rotation periods, luminosities, effective temperatures, and projected equatorial rotation velocities, v sin i, measured for these stars. We have measured 96 of the v sin i values in our sample by analyzing high-resolution spectra with a cross-correlation technique. We model the observed distribution of sin i for the cluster by assuming that member stars have random axial orientations and by adopting prescriptions for the measurement errors in our sample. By adjusting the distance assumed in the observed sin i distribution until it matches the modeled distribution, we obtain a best-fit distance for the cluster. We find the data to be consistent with a distance to NGC 2264 of 913 pc. Quantitative tests of our analysis reveals uncertainties of 40 and 110 pc due to sampling and systematic effects, respectively. This distance estimate suggests a revised age for the cluster of 1.5 Myrs, although more detailed investigations of the full cluster membership are required to draw strong conclusions.Comment: 12 pages, 11 figure

CSI 2264: Characterizing Accretion-Burst Dominated Light Curves for Young Stars in NGC 2264

Based on more than four weeks of continuous high cadence photometric monitoring of several hundred members of the young cluster NGC 2264 with two space telescopes, NASA's Spitzer and the CNES CoRoT (Convection, Rotation, and planetary Transits), we provide high quality, multi-wavelength light curves for young stellar objects (YSOs) whose optical variability is dominated by short duration flux bursts, which we infer are due to enhanced mass accretion rates. These light curves show many brief -- several hour to one day -- brightenings at optical and near-infrared (IR) wavelengths with amplitudes generally in the range 5-50% of the quiescent value. Typically, a dozen or more of these bursts occur in a thirty day period. We demonstrate that stars exhibiting this type of variability have large ultraviolet (UV) excesses and dominate the portion of the u-g vs. g-r color-color diagram with the largest UV excesses. These stars also have large Halpha equivalent widths, and either centrally peaked, lumpy Halpha emission profiles or profiles with blue-shifted absorption dips associated with disk or stellar winds. Light curves of this type have been predicted for stars whose accretion is dominated by Rayleigh-Taylor instabilities at the boundary between their magnetosphere and inner circumstellar disk, or where magneto-rotational instabilities modulate the accretion rate from the inner disk. Amongst the stars with the largest UV excesses or largest Halpha equivalent widths, light curves with this type of variability greatly outnumber light curves with relatively smooth sinusoidal variations associated with long-lived hot spots. We provide quantitative statistics for the average duration and strength of the accretion bursts and for the fraction of the accretion luminosity associated with these bursts.Comment: Accepted for publication in AJ. 39 pages; 6 tables; 25 figures, many of which are highly degraded to meet size limits. Please download the regular resolution version at http://web.ipac.caltech.edu/staff/amc/staufferetal2014.pd

A text mining tool to support reading and authorial writing

Este artigo apresenta um estudo sobre o potencial de uma ferramenta de mineração de texto para auxiliar no processo de leitura e escrita autoral. No mundo letrado, a leitura e escrita estão diretamente ligadas aos processos de aprendizagem, favorecendo a formação do pensamento crítico e argumentativo. Dados estatísticos mostram que em países em desenvolvimento, como o Brasil, os estudantes demonstram grande dificuldade em escrever ou interpretar textos. Visando minimizar tais dificuldades, este estudo apresenta uma proposta que alia práticas pedagógicas e recursos tecnológicos para contribuir com os processos de leitura e escrita. O artigo apresenta um estudo envolvendo 22 estudantes que participaram de atividades de leitura e escrita em um curso semi-presencial de 30 horas. Os resultados do estudo, realizado por uma perspectiva qualitativa, permitiram concluir que as ferramentas e estratégias propostas contribuíram para o desenvolvimento de uma escrita autoral pelos participantes.This article presents a study on the potential of a text mining tool to assist students in reading and writing. In the literate world, reading and writing are directly linked to learning processes, favoring the development of critical and argumentative thinking. Statistics show that in developing countries, such as Brazil, students show great difficulty writing or interpreting texts. In order to minimize these difficulties, this study presents a proposal that combines teaching practices and technology to contribute to the processes of reading and writing. The article presents a study in which 22 students participated in reading and writing activities, in a 30 hours course. The results of the study, based on a qualitative perspective, allowed us to conclude that the tools and strategies proposed contributed to the development of an authorial presence in their writing