Different moments in the participatory stage of the secondary students’ abstraction of mathematical conceptions

This study provides support to the characteristics of participatory and anticipatory stages in secondary school pupils’ abstraction of mathematical conceptions. We carried out clinical task-based interviews with 71 secondary-school pupils to obtain evidence of the different constructed mathematical conceptions (Participatory Stage) and how they were used (Anticipatory Stage). We distinguish two moments in the Participatory Stage based on the coordination of information from particular cases by activity-effect reflection which, in some cases, lead to a change of focus enabling secondary-school pupils to achieve a reorganization of their knowledge. We argue that (a) the capacity of perceiving regularities in sets of particular cases is a characteristic of activity-effect reflection in the abstraction of mathematical conceptions in secondary school, and (b) the coordination of information by pupils provides opportunities for changing the attention-focus from the particular results to the structure of properties.

Conditional Order-m Efficiency of Wastewater Treatment Plants: The Role of Environmental Factors

The growing economic and environmental importance of managing water resources at a global level also entails greater efforts and interest in improving the functioning and efficiency of the increasingly more numerous wastewater treatment plants (WWTPs). In this context, this study analyzes the efficiency of a uniform sample of plants of this type located in the region of Valencia (Spain). The type of efficiency measure used for this (conditional order-m efficiency) allows continuous and discrete contextual variables to be directly involved in the analysis and enables the assessment of their statistical significance and effect (positive or negative). The main findings of the study showed that the quality of the influent water and also the size and age of the plants had a significant influence on their efficiency levels. In particular, as regards the effect of such variables, the findings pointed to the existence of an inverse relationship between the quality of the influent water and the efficiency of the WWTPs. Also, a lower annual volume of treated water and more modern installations showed a positive influence. Additionally, the average efficiency levels observed turned out to be higher than those reported in previous studies.

Semantic change and intersubjectification: The origin of reprise evidential conditional in Old Catalan

The reprise evidential conditional (REC) is nowadays not very usual in Catalan: it is restricted to journalistic language and to some very formal genres (such as academic or legal language), it is not present in spontaneous discourse. On the one hand, it has been described among the rather new modality values of the conditional. On the other, the normative tradition tended to reject it for being a gallicism, or to describe it as an unsuitable neologism. Thanks to the extraction from text corpora, we surprisingly find this REC in Catalan from the beginning of the fourteenth century to the contemporary age, with semantic and pragmatic nuances and different evidence of grammaticalization. Due to the current interest in evidentiality, the REC has been widely studied in French, Italian and Portuguese, focusing mainly on its contemporary uses and not so intensively on the diachronic process that could explain the origin of this value. In line with this research, that we initiated studying the epistemic and evidential future in Catalan, our aim is to describe: a) the pragmatic context that could have been the initial point of the REC in the thirteenth century, before we find indisputable attestations of this use; b) the path of semantic change followed by the conditional from a ‘future in the past’ tense to the acquisition of epistemic and evidential values; and c) the role played by invited inferences, subjectification and intersubjectification in this change.