Primary school teacher’s noticing of students’ mathematical thinking in problem solving

Professional noticing of students’ mathematical thinking in problem solving involves the identification of noteworthy mathematical ideas of students’ mathematical thinking and its interpretation to make decisions in the teaching of mathematics. The goal of this study is to begin to characterize pre-service primary school teachers’ noticing of students’ mathematical thinking when students solve tasks that involve proportional and non-proportional reasoning. From the analysis of how pre-service primary school teachers notice students’ mathematical thinking, we have identified an initial framework with four levels of development. This framework indicates a possible trajectory in the development of primary teachers’ professional noticing.

Self-heating function of carbon nanofiber cement pastes

The viability of carbon nanofiber (CNF) composites in cement matrices as a self-heating material is reported in this paper. This functional application would allow the use of CNF cement composites as a heating element in buildings, or for deicing pavements of civil engineering transport infrastructures, such as highways or airport runways. Cement pastes with the addition of different CNF dosages (from 0 to 5% by cement mass) have been prepared. Afterwards, tests were run at different fixed voltages (50, 100 and 150V), and the temperature of the specimens was registered. Also the possibility of using a casting method like shotcrete, instead of just pouring the fresh mix into the mild (with no system’s efficiency loss expected) was studied. Temperatures up to 138 °C were registered during shotcrete-5% CNF cement paste tests (showing initial 10 °C/min heating rates). However a minimum voltage was required in order to achieve a proper system functioning.

Incidencia de las infraestructuras aeroportuarias en la expansión urbana española durante las últimas décadas: la ampliación del aeropuerto de Málaga como estudio de caso

La presente comunicación pretende abordar, desde un punto de vista integrador centrado en el análisis de la dinámica económica y territorial con la que se relaciona, el proceso de ampliación del aeropuerto de Málaga, poniendo en relación las necesidades arrastradas de tiempos pasados, con los beneficios e impactos derivados más inmediatos. Un estudio de caso significativo debido al rol que el aeropuerto desempeña como destino turístico internacional de primer orden y, asimismo, incentivo adicional y pieza clave en el proceso urbanizador contemporáneo en la costa mediterránea andaluza.