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.

Successional stage after land abandonment modulates fire severity and post-fire recovery in a Mediterranean mountain landscape

This study analyses the effect of successional stage after farmland terrace abandonment on post-fire plant recovery in a Mediterranean landscape. Specific objectives of the study were to (1) compare fuel characteristics and fire severity in three successional stages after farmland abandonment – dry grassland, dense shrubland and pine stands; (2) analyse the effect of pre-fire successional stage and fire severity on vegetation recovery and (3) analyse the relative vulnerability (i.e. potential for ecosystem shift and soil degradation) to wildfires of the successional stages. We assessed 30 abandoned terraces (15 unburned and 15 burned), with diverse successional stages, on the Xortà Range (south-east Spain). Post-fire recovery was measured 1, 4 and 7 years after fire. The successional stages varied in aboveground biomass, litter amount, vertical structure and continuity of plant cover, and flammability. Dry grassland showed the lowest fire severity, whereas no differences in severity were found between shrubland and pine stands. One year after fire, plant cover was inversely related to fire severity; this relationship attenuated with time after fire. Post-fire recovery of pine stands and shrubland led in both cases to shrublands, contributing to landscape homogenisation. The pine stands showed the largest changes in composition due to fire and the lowest post-fire plant recovery – a sign of high vulnerability to fire.