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'.

Resumen basado en el de la publicación

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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Forms of generalization in students experiencing mathematical learning difficulties

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Competencies in understanding statistical information in primary and secondary school levels : an inter-cultural empirical study in Germany and Colombian students

Resumen en espa??ol, portugu??s y franc??s

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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Museum Studies Borderlands: negotiating curriculum and competencies

Given ICTOP‘s work on revising the curriculum guide using the competencies approach (2000-2008), the author asks whether it is possible to reflect some of the issues and conceptual underpinnings that are at play in the discourse of museology/museum studies as a field of study and pedagogy when designing curriculum when taking the competencies approach. Until we address this question, ICTOP‘s work will have little relevance for the design of syllabi/curriculum by post-secondary institutions. This presentation lays out some of the professional issues underlying and the role for critical reflexive professionalism which can bridge theory and practice, competencies and epistemological knowledge and s how a way forward. Then it moves to address some of the territories where critical discussion is at work that would extend the curriculum discussions of ICTOP, while pointing to some developments that offer a museology of possibilities.

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.