Prospective elementary school teachers' ways of making sense of mathematical problem posing. 'Modos en que futuros profesores de primaria dan sentido a la invención de problemas matemáticos'.

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Hybrid tasks : promoting statistical thinking and critical thinking through the same mathematical activities

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Mathematics teachers' ideas about mathematical models : a diverse landscape

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Application of cognitive diagnosis models to competency-based situational judgment tests

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Forms of generalization in students experiencing mathematical learning difficulties

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Lessons from PISA 2012 about mathematical literacy : an illustrated essay

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Construction and modification of the autonomy of school mathematical knowledge in Portugal

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Mathematical and electrical analysis of pulsed tones

This paper discusses a study conducted to perform a mathematical analysis and an electrical analysis of pulsed tones to determine which type of pulsed tone is most suitable.

Recommendations for a mathematical curriculum to be used in conjunction with an oral deaf education program

Students who are deaf or hard of hearing have typically had difficulty in mathematics; however, this problem often is overlooked because of difficulties in language and reading abilities. This study aims to identify the most appropriate mathematics curriculum for deaf or hard of hearing students in an oral deaf education program.

The counter-propagating Rossby-wave perspective on baroclinic instability. I: Mathematical basis

It is shown that Bretherton's view of baroclinic instability as the interaction of two counter-propagating Rossby waves (CRWs) can be extended to a general zonal flow and to a general dynamical system based on material conservation of potential vorticity (PV). The two CRWs have zero tilt with both altitude and latitude and are constructed from a pair of growing and decaying normal modes. One CRW has generally large amplitude in regions of positive meridional PV gradient and propagates westwards relative to the flow in such regions. Conversely, the other CRW has large amplitude in regions of negative PV gradient and propagates eastward relative to the zonal flow there. Two methods of construction are described. In the first, more heuristic, method a ‘home-base’ is chosen for each CRW and the other CRW is defined to have zero PV there. Consideration of the PV equation at the two home-bases gives ‘CRW equations’ quantifying the evolution of the amplitudes and phases of both CRWs. They involve only three coefficients describing the mutual interaction of the waves and their self-propagation speeds. These coefficients relate to PV anomalies formed by meridional fluid displacements and the wind induced by these anomalies at the home-bases. In the second method, the CRWs are defined by orthogonality constraints with respect to wave activity and energy growth, avoiding the subjective choice of home-bases. Using these constraints, the same form of CRW equations are obtained from global integrals of the PV equation, but the three coefficients are global integrals that are not so readily described by ‘PV-thinking’ arguments. Each CRW could not continue to exist alone, but together they can describe the time development of any flow whose initial conditions can be described by the pair of growing and decaying normal modes, including the possibility of a super-modal growth rate for a short period. A phase-locking configuration (and normal-mode growth) is possible only if the PV gradient takes opposite signs and the mean zonal wind and the PV gradient are positively correlated in the two distinct regions where the wave activity of each CRW is concentrated. These are easily interpreted local versions of the integral conditions for instability given by Charney and Stern and by Fjørtoft.

An ontological approach to competency management

Competency management is a very important part of a well-functioning organisation. Unfortunately competency descriptions are not uniformly specified nor defined across borders: National, sectorial or organisational, leading to an opaque competency description market with a multitude of competency frameworks and competency benchmarks. An ontology is a formalised description of a domain, which enables automated reasoning engines to be built which by utilising the interrelations between entities can make “intelligent” choices in different situations within the domain. Introducing formalised competency ontologies automated tools, such as skill gap analysis, training suggestion generation, job search and recruitment, can be developed, which compare and contrast different competency descriptions on the semantic level. The major problem with defining a common formalised ontology for competencies is that there are so many viewpoints of competencies and competency frameworks. Work within the TRACE project has focused on finding common trends within different competency frameworks in order to allow an intermediate competency description to be made, which other frameworks can reference. This research has shown that competencies can be divided up into “knowledge”, “skills” and what we call “others”. An ontology has been created based on this with a simple structure of different “kinds” of “knowledges” and “skills” using semantic interrelations to define the basic semantic structure of the ontology. A prototype tool for analysing a skill gap analysis has been developed. Personal profiles can be produced using the tool and a skill gap analysis is performed on a desired competency profile by using an ontologically based inference engine, which is able to list closest fit and possible proficiency gaps