Use and abuse of calculators: implications for mathematics education

Fostering mathematical understanding and sense for numbers is an objective for current mathematics education. This paper presents a historical vision of the use of numbers and of calculation processes and reflects about the current need of electronic calculators. The coexistence of two different mathematical systems, one based on the Greek axiomatic mathematics and another, the floating point system, used in electronic calculators, can lead to some confusions that which affects the teaching of mathematics, especially in the numerical sense development. The paper also presents common mistakes caused by the missing verification of the results from calculations or lack of awareness about the limitations of calculators. Finally, the implications those elements have on the mathematical education are presented together with some conclusions

Analysis of Nonlinear Noisy Integrate\&Fire Neuron Models: blow-up and steady states

Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network and the noise. We analyse several aspects of the NNLIF model: the number of steady states, a priori estimates, blow-up issues and convergence toward equilibrium in the linear case. In particular, for excitatory networks, blow-up always occurs for initial data concentrated close to the firing potential. These results show how critical is the balance between noise and excitatory/inhibitory interactions to the connectivity parameter

El modelo BGK con potencial confinante: existencia, comportamiento asintótico y equilibrios Maxwellianos periódicos en tiempo

Un modelo aproximado de la ecuaci´on de Boltzmann en presencia de un potencial externo, que mantiene su no linealidad y sus propiedades cualitativas, es la ecuación de Boltzmann-BGK con potencial externo. Para esta ecuación estudiamos la existencia de solución, la estabilidad de sus estados estacionarios y la convergencia a los estados de equilibrio. Para un dato inicial con masa, entropía y energía total acotadas probamos existencia de solución y convergencia fuerte en L1 hacia los estados de equilibrio Maxwellianos, mediante argumentos de compacidad. Un caso especialmente interesante es el que se plantea cuando se considera un potencial externo armónico, ya que aparece toda una familia de estados estacionarios dependientes del tiempo de forma periódica. Este fenómeno es compartido con la ecuación de Boltzmann y con algunos otros modelos cinéticos. Para todos estos modelos probamos la multiestabilidad de dichos estados y ofrecemos condiciones para identificar el estado de equilibrio

La enseñanza y el aprendizaje del patrimonio en los museos : la perspectiva de los gestores

En este artículo se analizan las concepciones de los gestores patrimoniales respecto al concepto de patrimonio y a su enseñanza aprendizaje en los ámbitos educativos no formales. Así, tomando como muestra de estudio 43 gestores de museos y centros de interpretación patrimonial de las provincias de Huelva, Sevilla y Cádiz, se presentan los obstáculos conceptuales detectados para el desarrollo, por parte de este colectivo, de propuestas didácticas de carácter holístico, identitario, innovador y sociocrítico. Para ello, se diseñan dos instrumentos de investigación: un cuestionario para la obtención de datos y un sistema de categorías para el análisis de la información obtenida. Como resultado, se puede destacar la alta especialización de los gestores patrimoniales respecto al concepto de patrimonio frente a su escasa formación, conceptualización e incluso interés hacia la educación patrimonial.This article analyses the notions of patrimonial managers in terms of the concept of heritage and its teaching and learning in non-formal educational areas. So, taking 43 managers of museums and patrimonial interpretation centres of the provinces of Huelva, Seville and Cadiz as our study sample, we present the conceptual obstacles detected to the development by this group of didactic proposals of a holistic, identitarian, innovating and socio-critical nature. To this end, two research instruments were designed: a data gathering questionnaire and a system of categories for analysis of the information obtained. As a result, the high degree of specialisation of the patrimonial managers is notable in terms of the concept of heritage compared with their scant training, conceptualisation and even interest in patrimonial education

An attempt to identify the issues underlying the lack of consistent conceptualisations in the field of student mathematics-related beliefs

This paper aims to clarify the inconsistencies present in the field of student mathematics-related beliefs. Despite the general agreement about the important role that beliefs play in the learning of mathematics, the study of student mathematics-related beliefs has resulted in a body of uncoordinated research. The lack of consensus on defining and classifying beliefs has generated much confusing terminology, preventing a consistent conceptualization of the phenomenon. To identify the problem underlying existing inconsistencies, we have undertaken a systematic review of the literature to analyse the belief conceptualisations proposed by the most cited authors in this field of research. Our analysis suggests that authors often fail to conceptualise beliefs in four important ways: existing theories related to the phenomenon under research are normally not considered; definitions are often too broad and do not clearly confine the construct under evaluation; and existing beliefs sub-constructs are rarely defined and thus not explicitly distinguished. Our study has also revealed that some of the scales developed to measure the belief constructs lack of content and internal validity. We believe that these findings open new lines of research that may help to clarify the field of student mathematics-related beliefs.This work was supported by Horizon 2020 (710577), Ministerio de Ciencia e Innovación (EDU2017-84979-R), Erasmus+ (2017-1-ES01-KA203-038491) and (2019-1-CZ01-KA201-061377), Ministerio de Ciencia e Innovación (PGC2018-100758-B-I00), RED8-Educación matemática y formación de profesores (EDU2016-81994-REDT) and Junta de Castilla y León (Q3718001E)S

Suspended sediment transport and beach dynamics induced by monochromatic conditions, long waves and wave groups

This study presents the analysis of the water surface elevation, velocity and suspended sediment concentration measurements obtained at a large wave flume under mobile bed conditions. The wave reproduced erosive and accretive conditions, and included monochromatic, short waves perturbed with a free long wave, bichromatic and random conditions. Each tested condition started from a handmade 1/15 slope and lasted for an approximate time period of 2.4 h (6 runs of the selected wave condition), to compare the different beach profile developments and, in particular, the events that control sediment transport in the swash and surf zones. All erosive tested conditions produced a shoreline retreat and a bar at the breaking area whose development in time is directly correlated to the length of the breaking area. On the other hand, not all accretive conditions present a shoreward transport, and random conditions do not seem to alter the initial profile. The processed data show the suspended sediment event control produced by the existence or absence of wave–backwash interactions in the swash zone. The existence of these interactions, and their number within the wave group, will be a key parameter in controlling the sediment stirring, water velocity magnitudes and, therefore, the suspended sediment fluxes in the inner surf and outer swash.This work has been supported by the European Community's 6th Framework Programme through the grant to the budget of the Integrating Activity HYDRALAB III (Contract no. 022441). The first author also acknowledges the economical funding and support received from the MINECO and FEDER who founded the Plan-Wave project (Ref. CTM2013-45141-R), and the Secretaria d'Universitats i Recerca del Dpt. d'Economia i Coneixement de la Generalitat de Catalunya (Ref 2014SGR1253).Peer ReviewedPostprint (author's final draft