Examination of Lower Secondary Mathematics Teachers’ Content Knowledge and Its Connection to Students’ Performance

© 2015, Ministry of Science and Technology, Taiwan.This mixed methods study examined an association between cognitive types of teachers’ mathematical content knowledge and students’ performance in lower secondary schools (grades 5 through 9). Teachers (N = 90) completed the Teacher Content Knowledge Survey (TCKS), which consisted of items measuring different cognitive types of teacher knowledge. The first cognitive type (T1) assessed participants’ knowledge of basic facts and procedures. The second cognitive type (T2) measured teachers’ understanding of concepts and connections. The third cognitive type (T3) gauged teachers’ knowledge of mathematical models and generalizations. The study comprised two levels of quantitative data analysis. First, we explored each cognitive type of teachers’ content knowledge and the overall TCKS score as they related to student performance. Second, we studied the correlation between each cognitive type of teacher content knowledge to deepen the understanding of content associations. Results of the study show a statistically significant correlation between cognitive types T1 and T2 of teacher content knowledge and student performance (p < .05). The correlation between cognitive type T3 and student performance was not significant (p = .0678). The most substantial finding was the correlation between teachers’ total score on the TCKS and student performance (Pearson’s r = .2903, p = .0055 < .01). These results suggest that teachers’ content knowledge plays an important role in student performance at the lower secondary school. The qualitative phase included structured interviews with two of the teacher participants in order to further elaborate on the nature of the quantitative results of the study

Examination of Lower Secondary Mathematics Teachers’ Content Knowledge and Its Connection to Students’ Performance

© 2015 Ministry of Science and Technology, Taiwan This mixed methods study examined an association between cognitive types of teachers’ mathematical content knowledge and students’ performance in lower secondary schools (grades 5 through 9). Teachers (N = 90) completed the Teacher Content Knowledge Survey (TCKS), which consisted of items measuring different cognitive types of teacher knowledge. The first cognitive type (T1) assessed participants’ knowledge of basic facts and procedures. The second cognitive type (T2) measured teachers’ understanding of concepts and connections. The third cognitive type (T3) gauged teachers’ knowledge of mathematical models and generalizations. The study comprised two levels of quantitative data analysis. First, we explored each cognitive type of teachers’ content knowledge and the overall TCKS score as they related to student performance. Second, we studied the correlation between each cognitive type of teacher content knowledge to deepen the understanding of content associations. Results of the study show a statistically significant correlation between cognitive types T1 and T2 of teacher content knowledge and student performance (p < .05). The correlation between cognitive type T3 and student performance was not significant (p = .0678). The most substantial finding was the correlation between teachers’ total score on the TCKS and student performance (Pearson’s r = .2903, p = .0055 < .01). These results suggest that teachers’ content knowledge plays an important role in student performance at the lower secondary school. The qualitative phase included structured interviews with two of the teacher participants in order to further elaborate on the nature of the quantitative results of the study

Influence of territorial ecological load factors on social and economic well-being of population: Methodology development and econometric model construction

The article provides insights into the methodological approaches to the complex evaluation of the people quality of life associated with the analysis of the interaction between social and economic well-being and environmental quality. The study offers the results of the mathematical calculations which demonstrate the relation between the level of well-being of the population and the level of the ecological environment's development based on the cases of the municipal areas of the Republic Tatarstan, Russia. The key policy recommendations aiming at the improvement of the people quality of life vis-à-vis the features of the municipal development are postulated. © IDOSI Publications, 2013

Solvent effect on the enthalpy of solution and partial molar volume of the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate

Enthalpies of solution and partial molar volumes of the ionic liquid 1-butyl-3- methylimidazolium tetrafluoroborate were determined in 15 solvents of different polarity. Very large differences of the enthalpies of solution (Δ ΔsolHIL = 38.9 kJ·mol -1) and partial molar volumes (ΔVIL = 43 cm 3·mol -1) are nearly the same as observed for lithium perchlorate solutions. These results clearly indicate that the low values of the macroscopic polarity parameters of [bmim]BF 4 do not correspond with the large differences of the intermolecular interactions in IL solutions. The values of the partial molar volume of the cation, V [bmim]+, were estimated for the first time. The changes of the partial molar volumes, V IL, reflect mainly the changes of anion volume, V BF4. The rate of the Diels-Alder reaction of 9,10- dimethylanthracene with maleic anhydride in the [bmim]BF 4 medium was nearly the same as in common molecular solvents. © Springer Science+Business Media, LLC 2012

Enthalpies of solution and partial molar volumes of magnesium perchlorate in alcohols and salt effect of acceleration of the Diels-Alder reaction

Densities and enthalpies of solution at 25°C were measured for dilute solutions of magnesium perchlorate (MP) in some alcohols using the Anton Paar DSA 5000M vibrating tube densimeter and differential calorimetric measurements. In all studied solvents the solution of MP was highly exothermic and large solvent volume contraction was observed. Maximum effect was obtained in methanol and ethanol solutions. Acceleration effect of the Diels-Alder reaction of 9,10-dimethylanthracene with acrylonitrile (in medium of acrylonitrile) in the presence of salts LiClO4, Mg(ClO4)2 and GaCl3 was as 18:160:59,000. © 2011 Elsevier B.V

Homo-Diels-Alder reaction of a very inactive diene, bicyclo[2,2,1]hepta-2, 5-diene, with the most active dienophile, 4-phenyl-1,2,4-triazolin-3,5-dione. Solvent, temperature, and high pressure influence on the reaction rate

Solvent, temperature, and high pressure influence on the rate constant of homo-Diels-Alder cycloaddition reactions of the very active hetero-dienophile, 4-phenyl-1,2,4-triazolin-3,5-dione (1), with the very inactive unconjugated diene, bicyclo[2,2,1]hepta-2,5-diene (2), and of 1 with some substituted anthracenes have been studied. The rate constants change amounts to about seven orders of magnitude: from 3.95.10-3 for reaction (1+2) to 12200 L mol-1 s-1 for reaction of 1 with 9,10-dimethylanthracene (4e) in toluene solution at 298 K. A comparison of the reactivity (ln k2) and the heat of reactions (r-nH) of maleic anhydride, tetracyanoethylene and of 1 with several dienes has been performed. The heat of reaction (1+2) is -218 ± 2 kJ mol-1, of 1 with 9,10-dimethylanthracene -117.8 ± 0.7 kJ mol-1, and of 1 with 9,10-dimethoxyanthracene -91.6 ±0.2 kJ mol-1. From these data, it follows that the exothermicity of reaction (1+2) is higher than that with 1,3-butadiene. However, the heat of reaction of 9,10- dimethylanthracene with 1 (-117.8 kJ mol-1) is nearly the same as that found for the reaction with the structural C=C counterpart, N-phenylmaleimide (-117.0 kJ mol-1). Since the energy of the N=N bond is considerably lower (418 kJ/bond) than that of the C=C bond (611 kJ/bond), it was proposed that this difference in the bond energy can generate a lower barrier of activation in the Diels-Alder cycloaddition reaction with 1. Linear correlation (R = 0.94) of the solvent effect on the rate constants of reaction (1+2) and on the heat of solution of 1 has been observed. The ratio of the volume of activation (V≠) and the volume of reaction (V r-n) of the homo-Diels-Alder reaction (1+2) is considered as "normal": V≠/Vr-n = -25.1/-30.95 = 0.81. Copyright © 2012 John Wiley & Sons, Ltd

Anomalies in the change of volumetric parameters of the Diels-Alder reaction in solution

In this article negative values of the activation volume in retro-Diels-Alder reactions are interpreted in terms of the different possibilities of penetration of the solvent molecules into the sterically branched structures of the adduct and activated complex. Empty spaces, inaccessible to penetration of solvent molecules, lead to increases of the molar volume of the screened adducts in solution and, consequently, to a less negative value of the Diels-Alder reaction volume. The values of partial molar volumes of anthracene, maleic anhydride and the adducts cyclopentadiene-maleic anhydride, anthracene-maleic anhydride and anthracene-tetracyanoethylene, in several solvents, were calculated from the solution density data. © Springer Science+Business Media, LLC 2012