Mathematics teachers’ ideas about mathematical models: a diverse landscape

This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers’ ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers’ written responses to three open-ended questions through content analysis. A varied landscape of ideas was identified. Teachers referred to different entities as constituting models, expressed different ideas about whether data points can be part of models, and whether models convey more information than data. Interesting differences according to educational background were identified, especially between teachers with and without mathematics backgrounds

Mathematics teachers’ ideas about mathematical models: A diverse landscape

This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers’ ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers’ written responses to three open-ended questions through content analysis. A varied landscape of ideas was identified. Teachers referred to different entities as constituting models, expressed different ideas about whether data points can be part of models, and whether models convey more information than data. Interesting differences according to educational background were identified, especially between teachers with and without mathematics backgrounds.Ideas de profesores de matemáticas sobre modelos matemáticos: un panorama diversoEste artículo describe las ideas que tienen profesores de matemáticas (grados 5-9) acerca de los modelos matemáticos de fenómenos del mundo real y explora cómo esas ideas difieren dependiendo de la formación académica de los profesores. Analizamos las respuestas de 56 profesores en ejercicio estadounidenses a tres preguntas abiertas, mediante un análisis de contenido. Identificamos un panorama variado de ideas sobre las entidades que constituyen el modelo matemático, sobre si los datos pertenecen o no al modelo, y sobre si el modelo es más o menos informativo que los datos. Encontramos diferencias interesantes entre profesores con y sin formación matemática.Handle:  http://hdl.handle.net/10481/3323

Mathematics teachers’ ideas about mathematical models: A diverse landscape

This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers’ ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers’ written responses to three open-ended questions through content analysis. A varied landscape of ideas was identified. Teachers referred to different entities as constituting models, expressed different ideas about whether data points can be part of models, and whether models convey more information than data. Interesting differences according to educational background were identified, especially between teachers with and without mathematics backgrounds.Ideas de profesores de matemáticas sobre modelos matemáticos: un panorama diversoEste artículo describe las ideas que tienen profesores de matemáticas (grados 5-9) acerca de los modelos matemáticos de fenómenos del mundo real y explora cómo esas ideas difieren dependiendo de la formación académica de los profesores. Analizamos las respuestas de 56 profesores en ejercicio estadounidenses a tres preguntas abiertas, mediante un análisis de contenido. Identificamos un panorama variado de ideas sobre las entidades que constituyen el modelo matemático, sobre si los datos pertenecen o no al modelo, y sobre si el modelo es más o menos informativo que los datos. Encontramos diferencias interesantes entre profesores con y sin formación matemática.Handle:  http://hdl.handle.net/10481/3323

Ideas de profesores de matemáticas sobre modelos matemáticos: un panorama diverso

This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers’ ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers’ written responses to three open-ended questions through content analysis. A varied landscape of ideas was identified. Teachers referred to different entities as constituting models, expressed different ideas about whether data points can be part of models, and whether models convey more information than data. Interesting differences according to educational background were identified, especially between teachers with and without mathematics backgrounds.Este artículo describe las ideas que tienen profesores de matemáticas (grados 5-9) acerca de los modelos matemáticos de fenómenos del mundo real y explora cómo esas ideas difieren dependiendo de la formación académica de los profesores. Analizamos las respuestas de 56 profesores en ejercicio estadounidenses a tres preguntas abiertas, mediante un análisis de contenido. Identificamos un panorama variado de ideas sobre las entidades que constituyen el modelo matemático, sobre si los datos pertenecen o no al modelo, y sobre si el modelo es más o menos informativo que los datos. Encontramos diferencias interesantes entre profesores con y sin formación matemática.This study was funded by the National Science Foundation (NSF), Grant # DUE- 0962863, “The Poincaré Institute: A Partnership for Mathematics Education.” The ideas expressed herein are those of the authors and do not necessarily reflect the ideas of the funding agency

SILICON CARBIDE MICRO-DEVICES FOR COMBUSTION GAS SENSING UNDER HARSH CONDITIONS

A sensor based on the wide bandgap semiconductor, silicon carbide (SiC), has been developed for the detection of combustion products in power plant environments. The sensor is a catalytic gate field effect device that can detect hydrogen containing species in chemically reactive, high temperature environments. For these capacitive sensors we have determined that the optimum sensor operating point in terms of sensor lifetime and response time is at midgap. Detailed measurements of the oxide leakage current as a function of temperature were performed to investigate the high temperature reliability of the devices. In addition, robust metallization and electrical contacting techniques have been developed for device operation at elevated temperatures. To characterize the time response of the sensor responses in the millisecond range, a conceptually new apparatus has been built. Using laser induced fluorescence imaging techniques we have shown that the gas underneath the sensor can be completely exchanged with a time constant under 1 millisecond. Ultrahigh vacuum studies of the surface chemistry of the platinum gate have shown that sensor deactivation by adsorbed sulfur is a possible problem. Investigations on the chemical removal of sulfur by catalytic oxidation or reduction are continuing

Comprehensive transcriptome analysis of the highly complex Pisum sativum genome using next generation sequencing

<p>Abstract</p> <p>Background</p> <p>The garden pea, <it>Pisum sativum</it>, is among the best-investigated legume plants and of significant agro-commercial relevance. <it>Pisum sativum </it>has a large and complex genome and accordingly few comprehensive genomic resources exist.</p> <p>Results</p> <p>We analyzed the pea transcriptome at the highest possible amount of accuracy by current technology. We used next generation sequencing with the Roche/454 platform and evaluated and compared a variety of approaches, including diverse tissue libraries, normalization, alternative sequencing technologies, saturation estimation and diverse assembly strategies. We generated libraries from flowers, leaves, cotyledons, epi- and hypocotyl, and etiolated and light treated etiolated seedlings, comprising a total of 450 megabases. Libraries were assembled into 324,428 unigenes in a first pass assembly.</p> <p>A second pass assembly reduced the amount to 81,449 unigenes but caused a significant number of chimeras. Analyses of the assemblies identified the assembly step as a major possibility for improvement. By recording frequencies of Arabidopsis orthologs hit by randomly drawn reads and fitting parameters of the saturation curve we concluded that sequencing was exhaustive. For leaf libraries we found normalization allows partial recovery of expression strength aside the desired effect of increased coverage. Based on theoretical and biological considerations we concluded that the sequence reads in the database tagged the vast majority of transcripts in the aerial tissues. A pathway representation analysis showed the merits of sampling multiple aerial tissues to increase the number of tagged genes. All results have been made available as a fully annotated database in fasta format.</p> <p>Conclusions</p> <p>We conclude that the approach taken resulted in a high quality - dataset which serves well as a first comprehensive reference set for the model legume pea. We suggest future deep sequencing transcriptome projects of species lacking a genomics backbone will need to concentrate mainly on resolving the issues of redundancy and paralogy during transcriptome assembly.</p

Exome-wide analysis of rare coding variation identifies novel associations with COPD and airflow limitation in MOCS3, IFIT3 and SERPINA12.

Several regions of the genome have shown to be associated with COPD in genome-wide association studies of common variants.To determine rare and potentially functional single nucleotide polymorphisms (SNPs) associated with the risk of COPD and severity of airflow limitation.3226 current or former smokers of European ancestry with lung function measures indicative of Global Initiative for Chronic Obstructive Lung Disease (GOLD) 2 COPD or worse were genotyped using an exome array. An analysis of risk of COPD was carried out using ever smoking controls (n=4784). Associations with %predicted FEV1 were tested in cases. We followed-up signals of interest (p<10(-5)) in independent samples from a subset of the UK Biobank population and also undertook a more powerful discovery study by meta-analysing the exome array data and UK Biobank data for variants represented on both arrays.Among the associated variants were two in regions previously unreported for COPD; a low frequency non-synonymous SNP in MOCS3 (rs7269297, pdiscovery=3.08×10(-6), preplication=0.019) and a rare SNP in IFIT3, which emerged in the meta-analysis (rs140549288, pmeta=8.56×10(-6)). In the meta-analysis of % predicted FEV1 in cases, the strongest association was shown for a splice variant in a previously unreported region, SERPINA12 (rs140198372, pmeta=5.72×10(-6)). We also confirmed previously reported associations with COPD risk at MMP12, HHIP, GPR126 and CHRNA5. No associations in novel regions reached a stringent exome-wide significance threshold (p<3.7×10(-7)).This study identified several associations with the risk of COPD and severity of airflow limitation, including novel regions MOCS3, IFIT3 and SERPINA12, which warrant further study