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.

Psychometric properties of the School Anxiety Inventory-Short Version in Spanish secondary education students

Background: The School Anxiety Inventory (SAI) can be applied in different fields of psychology. However, due to the inventory’s administration time, it may not be useful in certain situations. To address this concern, the present study developed a short version of the SAI (the SAI-SV). Method: This study examined the reliability and validity evidence drawn from the scores of the School Anxiety Inventory-Short Version (SAI-SV) using a sample of 2,367 (47.91% boys) Spanish secondary school students, ranging from 12 to 18 years of age. To analyze the dimensional structure of the SAI-SV, exploratory and confirmatory factor analyses were applied. Internal consistency and test-retest reliability were calculated for SAISV scores. Results: A correlated three-factor structure related to school situations (Anxiety about Aggression, Anxiety about Social Evaluation, and Anxiety about Academic Failure) and a three-factor structure related to the response systems of anxiety (Physiological Anxiety, Cognitive Anxiety, and Behavioral Anxiety) were identified and supported. The internal consistency and test-retest reliability were determined to be appropriate. Conclusions: The reliability and validity evidence based on the internal structure of SAI-SV scores was satisfactory.

Structure and mechanical properties of sodium and calcium caseinate edible active films with carvacrol

Edible active films based on sodium caseinate (SC) and calcium caseinate (CC) plasticized with glycerol (G) at three different concentrations and carvacrol (CRV) as active agent were prepared by solvent casting. Transparent films were obtained and their surfaces were analysed by optical microscopy and scanning electron microscopy (SEM). The influence of the addition of three different plasticizer concentrations was studied by determining tensile properties, while Fourier transformed infrared spectroscopy (FTIR) and thermogravimetric analysis (TGA) were used to evaluate the structural and thermal behavior of such films. The addition of glycerol resulted in a reduction in the elastic modulus and tensile strength, while some increase in the elongation at break was observed. In general terms, SC films showed flexibility higher than the corresponding CC counterparts. In addition, the presence of carvacrol caused further improvements in ductile properties suggesting the presence of stronger interactions between the protein matrix and glycerol, as it was also observed in thermal degradation studies. FTIR spectra of all films showed the characteristic bands and peaks corresponding to proteins as well as to primary and secondary alcohols. In summary, the best results regarding mechanical and structural properties for caseinates-based films containing carvacrol were found for the formulations with high glycerol concentrations.