Studies on isocyanides: synthesis of tetrazolyl-isoindolinones via tandem Ugi four-component condensation/intramolecular amidation

The Ugi four-component condensation between methyl o-formylbenzoates 1, anilines 2a-c, isocyanides 3, and trimethylsilyl azide (4) afforded the expected Ugi adducts 5a-d, which were cyclized to the title compounds 6a-d upon treatment with sodium ethoxide in ethanol. Starting from aralkyl- or alkylamines 2d-g the Ugi adducts underwent a spontaneous cyclization to tetrazolyl-isoindolinones 6e-j.     

Isolation of three new naturally occurring compounds from the culture of Micromonospora sp. P1068

Bioassay guided isolation of an antibacterial extract prepared from the fermentation broth of a Micromonospora sp. P1068 led to the isolation of eight compounds identified as (3R) 3,4',7-trihydroxy-isoflavanone (1), 3-hydroxydehydrodaidzein, daidzein (2), 3-methyl-1H-indole-2-carboxylic acid (3), 1H-indole-3-carboxaldehyde (4), 3-(p-hydroxyphenyl)-N-methylpropionamide, N-methylphloretamide (5), phenyl acetic acid (6), 2-hydroxy phenyl acetic acid (7) and 4-hydroxy-5-methoxy-benzoic acid (8). Compounds 1 and 5 were found to be novel chemical entities while 3 was isolated from a natural source for the first time. All compounds were evaluated for their antimicrobial activities against a panel of clinically significant microorganisms. Compound 4 was active against Staphylococcus aureus (MIC, 32 microg/ml), Enterococcus faecium (MIC, 32 microg/ml) and Escherichia coli (MIC, 64 microg/ml).     

Crutch or Catalyst: Teachers' Beliefs and Practices Regarding Calculator use in Mathematics Instruction

This study investigated K‐12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction. A survey was administered to more than 800 elementary, middle and high school teachers in a large metropolitan area to address the following questions: (a) what are the beliefs and practices of mathematics teachers regarding calculator use? and (b) how do these beliefs and practices differ among teachers in three grade bands? Factor analysis of 20 Likert scale items revealed four factors that accounted for 54% of the variance in the ratings. These factors were named Catalyst Beliefs, Teacher Knowledge, Crutch Beliefs, and Teacher Practices. Compared to elementary teachers, high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction. However, the higher the grade level of the teacher, the higher the mean score on the perception that calculator use may be a way of getting answers without understanding mathematical processes. The mean scores for teachers in all three grade bands indicated agreement that students can learn mathematics through calculator use and using calculators in instruction will lead to better student understanding and make mathematics more interesting. The survey results shed light on teachers' self reported beliefs, knowledge, and practices in regard to consistency with elements of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) technology principle and the NCTM use of technology position paper (2003). This study extended previous research on teachers' beliefs regarding calculator use in classrooms by examining and comparing the results of teacher surveys across three grade bands.     

Future teachers’ professional knowledge on argumentation and proof: a case study from universities in three countries

In this paper, qualitative results of a case study about the professional knowledge in the area of argumentation and proof of future teachers from universities in three countries are described. Based on results of open questionnaires, data about the competencies these future teachers have in the areas of mathematical knowledge and knowledge of mathematics pedagogy are presented. The study shows that the majority of the future teachers at the participating universities situated in Germany, Hong Kong and Australia, were not able to execute formal proofs, requiring only lower secondary mathematical content, in an adequate and mathematically correct way. In contrast, in all samples there was evidence of at least average competencies of pedagogical content reflection about formal and pre-formal proving in mathematics teaching. However, it appears that possessing a mathematical background as mandated for teaching and having a high affinity with proving in mathematics teaching at the lower secondary level are not a sufficient preparation for teaching proof.     

Reduction in the Resonance Error in Numerical Homogenization II: Correctors and Extrapolation

This paper is the follow-up of Gloria (Math Models Methods Appl Sci 21(8):1601–1630, 2011). One common drawback among numerical homogenization methods is the presence of the so-called resonance error, which roughly speaking is a function of the ratio \(\frac{\varepsilon }{\rho }\), where \(\rho \) is a typical macroscopic lengthscale and \(\varepsilon \) is the typical size of the heterogeneities. In the present work, we make a systematic use of regularization and extrapolation to reduce this resonance error at the level of the approximation of homogenized coefficients and correctors for general non-necessarily symmetric stationary ergodic coefficients. We quantify this reduction for the class of periodic coefficients, for the Kozlov subclass of almost-periodic coefficients, and for the subclass of random coefficients that satisfy a spectral gap estimate (e.g., Poisson random inclusions). We also report on a systematic numerical study in dimension 2, which demonstrates the efficiency of the method and the sharpness of the analysis. Last, we combine this approach to numerical homogenization methods, prove the asymptotic consistency in the case of locally stationary ergodic coefficients, and give quantitative estimates in the case of periodic coefficients.     

A Survey of Calculator Usage in High Schools

This survey investigated the current status of calculator use in classrooms and schools. The results indicated that the prevailing policy in the sample of high schools is to allow the use of calculators during classroom learning activities and tests. Scientific calculators are more frequently used than graphing calculators in algebra I and geometry; whereas, graphing calculators are more frequently used in algebra II and precalculus/trigonometry. At the time of this survey, school policies regarding the use of graphing calculators with symbolic algebra capabilities were still not determined.     

Ugi four-component condensation with two cleavable components: the easiest synthesis of 2,N-diarylglycines

The Ugi four-component condensation between anilines, aromatic aldehydes, isocyanides, and α-oxoacids afforded the expected adducts which were cleaved in mild conditions to give 2,N-diarylglycines in high yields.