Re-sourcing curriculum materials: in search of appropriate frameworks for researching the enacted mathematics curriculum

This article provides a commentary to the eight papers of this issue of ZDM entitled “Researching the enacted mathematics curriculum.” It is structured around three main questions concerning (1) the layers of the curriculum addressed in the eight papers; (2) an identification of the main theoretical framework used, and an appreciation of this as compared to another European framework; and (3) challenges for future research on the enacted mathematics curriculum. The author outlines her views derived from a particular European perspective.     

AN INVESTIGATION OF MATHEMATICS TEXTBOOKS IN ENGLAND,FRANCE AND GERMANY: SOME CHALLENGES FOR ENGLAND

This paper reports on an analysis of mathematics textbooks used in lower secondary classrooms in England, France and Germany. The examination was carried out using an analysis schedule based on existing literature on textbooks. In this paper we look first at the development of the analysis schedule and then at the how particular textbooks treat the topic of angle. From this we conclude that learners in the different countries are offered different mathematics. In particular, learners in England are offered few challenges in the mathematics they are offered compared with their French and German counterparts.     

Investigating textbooks as crucial interfaces between culture, policy and teacher curricular practice: two contrasted case studies in France and Norway

This paper reports on an investigation of mathematics curriculum documents, commonly used textbooks and teacher ‘curricular practice’ with respect to educational traditions in France and Norway. The study has helped to develop a deeper understanding of (1) educational traditions in France and Norway; (2) the ways the educational traditions permeate the system, from policy documents through textbooks into the classroom; and (3) the connections between the worlds of policy, textbooks and teacher curricular practice in mathematics. Results show that French and Norwegian curricular documents and practices were influenced by egalitarian values, albeit differently interpreted and ‘lived’ in each country. In terms of mathematics, using a focus on grade 6 geometric transformations has shown that French textbooks and teacher curricular practices emphasized theoretical properties and mathematical reasoning, whereas the Norwegian counterparts stressed practical and inquiry-based activities. It is argued that mathematics textbooks can be regarded as a crucial interface between culture, policy and curricular practice, and as a pivotal resource in teachers’ resource system for curricular practice, even in times of digitization.     

Meson spectrum in a relativistic harmonic model with instanton-induced interaction

On the basis of the phenomenological relativistic harmonic model for quarks, we have obtained the ground-state masses of the light pseudo-scalar and vector mesons. The full Hamiltonian used in the investigation has Lorentz scalar + vector confinement potential, along with one-gluon-exchange potential (OGEP) and the instanton-induced quark-antiquark interaction. A good agreement is obtained with the experimental masses. The respective role of instanton-induced interaction and OGEP for the determination of the meson masses is discussed.Received: 18 October 2002, Revised: 13 January 2003, Published online: 23 December 2003PACS: 12.39.Ki Relativistic quark model - 12.39.Pn Potential models - 14.40.Aq , K, and mesonsS. Pepin: Present address: rue de Sluse 13, B-4000 Liége, Belgium     

Micro-motor with screen-printed rotor magnets

The feasibility to develop mini- and micro-magnetic electro-mechanical systems (MEMS) has been evaluated by prototyping of a single-phase stepper motor. The main targeted application of such device is the watch industry needing micro-motors in huge quantities at low cost. The motor part that required the greatest efforts has been the magnet, which cannot yet be found in film layer. The screen-printing technology has been used for the production of NdFeB-based magnets whose properties have been characterised. The thick film magnets have been integrated in the stepper motor specially designed for this purpose. The whole motor has been characterised and conclusions are drawn on the possibility of producing thick film magnets for magnetic MEMS.     

Subsolidus phase relations in the systems CeO2RE2O3 (RE2O3 = C-type rare earth sesquioxide)

The systems CeO₂RE₂O₃ (RE₂O₃ = C-type rare earth sesquioxide) were studied to: (1) investigate the claims of several workers for the existence of a complete solid solution series between CeO₂ and RE₂O₃ and (2) to characterize the weak C-type X-ray diffraction peaks reported by others from samples in the single-phase fluorite solid solution region. It is shown that a complete solid solution series does not exist, and an explanation for the observations of others reporting such is tendered. It is also shown that the observation of C-type reflections in the supposed single-phase fluorite field can be attributed to the partial reduction of Ce⁴⁺ to Ce³⁺ at the firing temperature, resulting in the movement of the bulk composition into a two-phase field of the CeO₂RE₂O₃Ce₂O₃ phase diagram, rather than the formation of a domain structure due to ordering.     

Modeling the Evolution and Rupture of Pendular Liquid Bridges in the Presence of Large Wetting Hysteresis

A model has been developed to predict the shape evolution, rupture distance and postrupture liquid distribution of a pendular liquid bridge between two unequally sized spherical particles in the presence of wetting hysteresis. Two different simplifications of the bridge geometry were considered: a toroidal and a parabolic approximation. The liquid bridge was assumed to rupture through its thinnest neck leaving liquid distributed on each sphere. Experimental measurements showed that the rupture distance was well predicted by both profile approximations by assuming that rupture occurred when the liquid-vapor interfacial area of the bridge and the postrupture droplets was equal. Both bridge profile approximations only correctly predicted the evolution of the apparent contact angle and the extent of postrupture liquid distribution when the solid-liquid interfacial area measured throughout the separation was included in the calculations. This is because during the pendular liquid bridge elongation, the three-phase contact line usually begins to slip on at least one of the spheres. The parabolic profile approximation was slightly more accurate than the toroidal one. The toroidal approximation is more difficult to use because one of the parameters passes through infinity as the bridge changes from convex to concave in shape. In some cases the toroidal approximation was also unable to generate a solution. Copyright 2000 Academic Press.     

Modeling the triggering of streamers in air by ultrashort laserpulses

The physical processes involved in the triggering of ionization waves (streamers) by ultrashort laser pulses, focused in air at 350 Torr and in a uniform electric field, are investigated by means of a one-dimensional (1-D) numerical model. The model describes the interaction of the laser pulse with air and takes into account many of the reactions in the laser-created plasma as well as the radial expansion of the plasma. Consequences of the model are that the threshold electric field for the appearance of streamers is an increasing function of the delay between the laser pulse and the electric field pulse and a decreasing function of the laser energy. Also, it appears that the electron temperature, the plasma density and radius, and the conduction of heat across the plasma boundaries play major roles in the capacity of the laser-created plasma to trigger streamers. The results of the model are compared with the available experimental data     

Combining UV photodissociation with electron transfer for peptide structure analysis

The combination of near‐UV photodissociation with electron transfer and collisional activation provides a new tool for structure investigation of isolated peptide ions and reactive intermediates. Two new types of pulse experiments are reported. In the first one called UV/Vis photodissociation–electron transfer dissociation (UVPD‐ETD), diazirine‐labeled peptide ions are shown to undergo photodissociation in the gas phase to form new covalent bonds, guided by the ion conformation, and the products are analyzed by electron transfer dissociation. In the second experiment, called ETD‐UVPD wherein synthetic labels are not necessary, electron transfer forms new cation–peptide radical chromophores that absorb at 355 nm and undergo specific backbone photodissociation reactions. The new method is applied to distinguish isomeric ions produced by ETD of arginine containing peptides. Copyright © 2015 John Wiley & Sons, Ltd.     

Re-sourcing teachers’ work and interactions: a collective perspective on resources, their use and transformation

This paper reviews the literature on the theme of mathematics teachers’ work and interactions with resources, taking a particular perspective, the so-called ‘collective perspective’ on resources, their use and transformation. The review is presented under three headings: (1) theoretical frameworks commonly used in this area of research; (2) teachers’ interactions with resources in terms of their design and use; and (3) teachers’ interactions with resources in terms of teacher learning and professional development. From the literature, and the collection of papers in this issue, we argue that the collective dimensions play an important role in mathematics teachers’ work with resources and in their professional learning/development. Further empirical investigations are likely to be needed on: how teachers may work in collectives and with resources, and in which ways ‘productive’ collectives may form and work together; which roles particular resources can play in these delicate constellations and how particular resources may support teachers in their work and learning; and which kinds of resources offer opportunities for community building.