A model for developing students’ example space: the key role of the teacher

Our research addresses the role of examples to foster the students’ development of the mathematical concepts, and of their mathematical ways of thinking. We consider the notion of example space introduced by Watson and Mason (Mathematics as a constructive activity: learners generating examples, 2005), particularly when it is not formed by a simple juxtaposition of examples, rather it is endowed by a certain structure. Such a structure is provided by the semiotic actions and by the theoretic and logical dimensions of the mathematical activities. However, the formation of structured example spaces is far from being an automatic process. In this paper, we focus on the genesis of examples and on the role of the teacher in helping the students to structure their examples spaces through the so-called cognitive apprenticeship method. We point out that the genesis of examples is often accomplished within a complex cyclic dynamics, the “cycle of examples production and modification”. We illustrate it by means of two emblematic episodes from a classroom discussion. We show that the teacher’s intervention can be crucial in helping the students to modify a wrong example, to generate the right one for the task and to start the long-term process of building up the structure of their own space of examples.     

Biocatalytic Modification of Naturally Occurring Iron Porphyrin

Hematin, a hydroxyferriprotoporphyrin, is the stable, oxidized form of heme. Heme has been reported to be the active catalytic center of naturally occurring peroxidases such as horseradish peroxidase (HRP). While there have been reports on the use of hematin as a catalyst for oxidative polymerization reactions, these reactions could be carried out only at high pH conditions due to limited aqueous solubility of hematin at lower pH conditions. We report here the biocatalytic modification of hematin using a lipase, Novozyme-435. Hematin has been modified by tethering monomethoxy polyethylene glycol (mPEG) chains which provide aqueous solubility over a fairly wide range of pH conditions. This pegylated Hematin (PEG-Hematin) is synthesized via a one-step solventless reaction and the products formed can be isolated with minimal purification. The PEG-Hematin synthesized serves as a robust alternative to HRP for the polymerization of aniline and phenol.     

Networking strategies and methods for connecting theoretical approaches: first steps towards a conceptual framework

The article contributes to the ongoing discussion on ways to deal with the diversity of theories in mathematics education research. It introduces and systematizes a collection of case studies using different strategies and methods for networking theoretical approaches which all frame (qualitative) empirical research. The term ‘networking strategies’ is used to conceptualize those connecting strategies, which aim at reducing the number of unconnected theoretical approaches while respecting their specificity. The article starts with some clarifications on the character and role of theories in general, before proposing first steps towards a conceptual framework for networking strategies. Their application by different methods as well as their contribution to the development of theories in mathematics education are discussed with respect to the case studies in the ZDM-issue.     

Optimal information structure in a simple economic system

In a highly simplified version of a common economic model, the planner can choose among alternative time-varying designs for the information structure in order to steer the system to a target state in an optimal way. The resulting problem is imbedded into a more general one with bilinear dynamics, that is, linear in the control and the state variables but not in both. The existence of a feasible decentralized information structure is studies and designs are found which make the system optimal, given a performance function assigning losses to deviations froma target state. The conditions under which a decentralized structure is optimal are also studied and a numerical case is considered.     

Dynamic modelling in development plannin

In this paper a dynamic regional model is proposed, aimed at understanding and forecasting the dynamic response of the population to many different investment policies in the agricultural, services and industrial sectors. In spite of its generality, the model has been conceived in order to be applied to underdeveloped regions. Particularly, from the demographic point of view, attention has been focused on migration phenomena; from the economic point of view, attention has been focused mainly on the rate of growth of the capital stock.

Modularity is another feature of the proposed model; it is made of seven submodels which describe in a very aggregated form the evolution of the regional socio-economic system. The outputs of the submodels are then spatially distributed using a set of ‘spatial operators’ which take into account many social and economic factors relevant to the sub-areas into which the region can be divided.     

Structural defects and device electrical behaviour in AlGaN/GaN heterostructures grown on 8° off-axis 4H-SiC

This paper reports on the influence of material defects on the electrical behaviour of AlGaN/GaN heterostructures grown onto off-axis 4H-SiC. A structural characterization revealed the presence of near-surface V-shaped defects, mostly oriented along the miscut direction [11-20]. High electron mobility transistors with the channel oriented along this direction showed a preferential conduction, while a significant reduction of the drain current occurred only along the orthogonal direction. An electrical analysis allowed us to demonstrate the anisotropy of the mobility of the two-dimensional electron gas.     

Hyperconjugation and the increasing bulk of OCOCX3 substituents in trans-1,4-disubstituted cyclohexanes destabilize the diequatorial conformer

The trans diesters of 1,4-cyclohexanediol with a number of acetic acid analogues, CX3COOH, of varying steric hindrance and polarity (CX3 = Me, Et, iso-Pr, tert-Bu, CF3, CH2Cl, CHCl2, CCl3, CH2Br, CHBr2, CBr3) were synthesized, and the axial,axial/equatorial,equatorial conformational equilibria were studied by low-temperature 1H NMR spectroscopy in CD2Cl2. The structures and relative energies of the axial,axial and equatorial,equatorial conformers were calculated at both the MP2/6-311G* and the MP2/6-311+G* levels of theory, and it was only by including diffuse functions that a good correlation of deltaG(o)calcd vs deltaG(o)exptl could be obtained. Both the structures and the energy differences of the axial,axial and equatorial,equatorial conformers are discussed with respect to the established models of conformational analysis, viz., steric 1,3-diaxial and hyperconjugative interactions. Interestingly, the hyperconjugative interactions sigma(C-C)/sigma(C-H) --> sigma*(C-O), together with a steric effect which also destabilizes the equatorial,equatorial conformers on increasing bulk of the substituents, proved to dominate the position of the conformational equilibria. In addition, the preference of the axial,axial conformers with respect to their equatorial,equatorial analogues was greater than expected from the conformational energies of the corresponding substituents in the monosubstituted cyclohexyl esters. The reason for this very interesting and unexpected result is also discussed.