Mathematics achievement and interest in mathematics from a differential perspective

In this article, we present results of an empirical study with 500 German students of grades 7 and 8. The study focussed on students' mathematics achievement and their interest in mathematics as well as on the relation between these two constructs. In particular, the results show that the development of an individual student's achievement between grade 7 and grade 8 depends on the achievement level of the specific classroom and therefore on the specific mathematics instruction Interest in mathematics could be regarded a predictor for mathematics achievement Moreover, our findings suggest that the students show hardly any fear of mathematics independent of their achievement level.     

Exact Scaling Functions for One-Dimensional Stationary KPZ Growth

We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a Riemann–Hilbert problem related to the Painlevé II equation. We solve these equations numerically with very high precision and compare our, up to numerical rounding exact, result with the prediction of Colaiori and Moore⁽¹⁾ obtained from the mode coupling approximation.     

Adsorption of dicarboxylates on nano-sized gibbsite particles: effects of ligand structure on bonding mechanisms

The adsorption of the dicarboxylates o-phthalate, maleate, fumarate, malonate, and oxalate (representing ligands with the general composition ⁻O₂C---C_n---CO₂⁻; n=0, 1, or 2) on gibbsite were studied by means of quantitative batch adsorption experiments and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy. The interpretations of ATR-FTIR spectra were aided by comparison with IR spectra of solution species and by results from theoretical frequency calculations. The main objectives of the study were to identify the molecular level bonding mechanisms of the dicarboxylates to gibbsite, and to investigate how these were influenced by the composition and structure of the ligands. Carboxylates with n=2 formed predominantly outer sphere complexes, whereas the importance of inner sphere complexes progressively increased for n=1 and 0. The inner sphere structures were identified as mononuclear chelates with one oxygen from each carboxylate group bonded to Al(III) at the surface. This showed the importance of chelate ring structure for the formation of inner sphere surface complexes, with stabilities of the complexes increasing in the order seven-membered ring less than six-membered ring less than five-membered ring. For ligands with n=2 only small variations in surface speciation were observed as a function of steric factors; irrespective of the relative positions of the carboxylate groups and bulkiness of the ligands outer sphere bonding is the dominating adsorption mode. Adsorption experiments were also conducted with gibbsite particles exhibiting differences in shape and surface roughness. These experiments showed that inner sphere complexes were favored on the less well-developed and more irregular gibbsite particles.     

Limits of Functions as They Developed Through Time and as Students Learn Them Today

This article compares first-year university students' development of the concept of limits to mathematicians' historical development of the concept. The aim was to find out if students perceive the notion as mathematicians of the past did, as understandings of the concept evolved. The results imply that there are some similarities—for example, the struggle with rigor and attainability. Knowledge of such critical areas can be used to improve students' opportunities of learning limits of functions. Some teaching aspects related to the study are also discussed.     

Development and characterisation of a new interface for coupling capillary LC with collision-cell ICP–MS and its application for phosphorylation profiling of tryptic protein digests

A comparison of different nebulisers for direct hyphenation of capillary and nano liquid chromatography (Cap-LC, Nano-LC) and quadrupole-based collision cell inductively coupled plasma mass spectrometry (CC-ICP–MS) for phosphorylation profiling of tryptic protein digests is described. Helium was used as cell gas and specially tuned instrumental conditions were used to achieve background minimisation at the mass of phosphorus, because of kinetic energy discrimination of the interfering polyatomic ions. The proposed set-up is based on a modified capillary electrophoresis interface and a home-made 4 mL spray chamber. It enables the use of gradient conditions with a highly concentrated organic mobile phase as often used in protein phosphorylation analysis, without the need to apply membrane desolvation for removal of the organic phase or further background minimisation. No significant signal suppression or other negative effects caused by the organic mobile phase occur, because of the low flow rates used in Cap-LC and the robust plasma conditions of the CC-ICP–MS instrument. A tryptic digest of beta-casein was investigated as model compound to demonstrate the applicability of the proposed set-up for phosphorylation profiling in protein analysis using quadrupole based collision-cell ICP–MS as phosphorus-specific detector. Detection limits for phosphorylated peptides down to the sub picomole level were obtained. As a complementary technique, electrospray ionisation tandem mass spectrometry (ESI–MS–MS) with data base searching was used for further characterisation of the phosphorylated peptides detected.