Investigating secondary students beliefs about mathematical problem-solving

Many studies over the past 30 years have highlighted the important role of students’ beliefs for successful problem-solving in mathematics. Given the recent emphasis afforded to problem-solving on the reformed Irish secondary school mathematics curriculum, the main aim of this study was to identify Irish students’ (n = 975) beliefs about the field. A quantitative measure of these beliefs was attained through the use of the Indiana Mathematical Belief Scale, an existing 30-item (five-scale) self-report questionnaire. A statistical analysis of the data revealed that students who were further through their secondary education had a stronger belief that not all problems could be solved by applying routine procedures. In contrast, the same students held less positive beliefs than their younger counterparts that they could solve time-consuming problems and that conceptual understanding was important. The analysis also indicated that gender had a significant impact on three of the five belief scales.     

An improved method for generating the centralizer of an involution

In this paper we describe a new method for finding generators of a centralizer of an involution. This technique works well in practice and can cope with cases when the existing method fails. As an application, we show how we can use our method to obtain a presentation of 2^{2 £} U₆(2).     

A Simplified Model for the Etch Rate of Novolac-Based Photoresist

The novolac-based resins used as positive-tone photoresists are frequently etched in an oxygen plasma. It is desirable to have a predictive model of the photoresist etch rate but, for process improvement, control, and analysis, the development of a rigorous mechanistic model is impractical. Instead, a simplified mechanistic model is derived, here, according to the method proposed by Hougen and Watson for the study of fluid–solid interactions. This model derivation method is employed in order to arrive at a functional form that represents chemical etching of the resist by oxygen radicals, assisted by the plasma ion flux. Values for model parameters are determined from process data by nonlinear regression. The quality of the model fit to the data is tested statistically.     

Aluminium

Ohne Zusammenfassung     

A structural interpretation of B10 and B11 NMR spectra in sodium borate glasses

It is shown that the B¹⁰ spectra for sodium borate glasses are sensitive to the different structural groups in the glasses. Five boron sites are inferred from the data: two 4-coordinated sites and three 3-coordinated sites. The two 4-coordinated boron sites are identified as BO₄ units connected to all BO₃ units, and BO₄ units connected to one BO₄ unit and three BO₃ units. The three 3-coordinated boron sites are identified as BO₃ units connected to: (1) all BO₃ units; (2) a mixture of BO₃ and BO₄ units; and (3) all BO₄ units. These five sites can be interpreted in terms of Krogh-Moe's structural model of alkali borate glasses, wherein the fraction of each structural group can be determined for eight sodium borate glasses spanning the compositional range from 0 to 35 mol% Na₂O. The resulting fractions are consistent with Krogh-Moe's structural model.