Fractions as the Coordination of Multiplicatively Related Quantities: A Cross-Sectional Study of Children's Thinking

Although equal sharing problems appear to support the development of fractions as multiplicative structures, very little work has examined how children's informal solutions reflect this possibility. The primary goal of this study was to analyze children's coordination of two quantities (number of people sharing and number of things being shared) in their solutions to equal sharing problems and to see to what extent this coordination was multiplicative. A secondary goal was to document children's solutions for equal sharing problems in which the quantities had a common factor (other than 1). Data consisted of problem-solving interviews with students in 1st, 3rd, 4th, and 5th grades (n=112). We found two major categories of strategies: (a) Parts Quantities strategies and (b) Ratio Quantities strategies. Parts quantities involved children's partitions of continuous units expressed in terms of the number of pieces that would be created. Ratio quantities involved children's creation of associated sets of discrete quantities. Within these strategies, children drew upon a range of relationships among fractions, ratio, multiplication, and division to mentally or physically manipulate quantities of sharers and things to produce exhaustive and equal partitions of the items. Additionally, we observed that problems that included number combinations with common factors elicited a wider range of whole-number knowledge and operations in children's strategies and therefore appeared to support richer interconnections than problems with relatively prime or more basic number combinations.     

Acute kinematics changes in marathon runners using different footwear

The effects of running with or without shoes on injury prevention have been extensively studied, and several investigations have assessed biomechanical differences between them. However, findings are not consensual and further insights on biomechanical load associated with differently shod or barefoot conditions may be needed. This study aimed to observe if habitually shod marathon runners show acute alterations when running barefoot or with minimalist shoes, and to determine whether the running kinematical adaptations of wearing minimalist shoes were similar to barefoot running. Twelve male marathon runners ran on the treadmill at their average marathon pace in different footwear conditions: habitual running shoes, minimalist shoes, and barefoot. High-resolution infrared cameras and visual 3D software were used to assess kinematic data. The following parameters were studied: foot strike angle, cycle time, stance time, normalized stride length, hip, knee, and ankle angular position at initial contact, and their respective range-of-motion (ROM) during stance phase. Contrary to the expectations, it was found that highly trained habitually shod elite marathon runners changed their lower limb kinematic pattern both when running barefoot or wearing minimalist shoes. Minimalist shoes showed a trend towards intermediate biomechanical effects between running with and without shoes.     

Relationship between exchange block time in swim starts and final performance in relay races in international championships

Abstract

The purpose of this study was to investigate the association between relay exchange block time and final performance in 4 × 100-m and 4 × 200-m freestyle and 4 × 100-m medley relays as a function of sex (men and women) and classification (medallists and non-medallists) in international competitions. Nineteen international competitions covering a 13-year period (2000–2012) were analysed retrospectively. The data corresponded to a total of 827 team relay histories (407 men, 420 women). Kruskal–Wallis and Mann–Whitney tests were performed to determine any differences by sex, classification, and event. Similarly, the relationship between the exchange block times and final performance was examined by means of a Pearson correlation analysis. In the three events, the men’s exchange block times were shorter than those of the women (η² = 0.049–0.109; P < 0.001). The exchange block time was especially relevant for the women’s relay medallists in the 4 × 100-m freestyle (r = 0.306, P = 0.021) and 4 × 100-m medley (r = 0.385, P = 0.011), while for men the relationship was clearer for the non-medallists. These results suggest that the exchange block time should be considered as one of the performance parameters of swimming relay starts, and thus should be included explicitly as part of training. In particular, the coach could design training targeted at standardising an optimal exchange block time equal to or less than that expected for other teams in the competition.     

“The Hardest Task”—Peer Review and the Evaluation of Technological Activities

Minerva - Technology development and innovation are fundamentally different from scientific research. However, in many circumstances, they are evaluated jointly and by the same processes. In these...     

Relational engagement: Proportional reasoning with bilingual Latino/a students

In this paper, we explored how engagement developed over time during a proportional reasoning unit for a group of US bilingual Latino/a students, with particular attention to aspects of social and cultural activity that supported students’ engagement. Our findings suggest that student mathematical engagement developed primarily as a relational process characterized by students’ social relations across time, their understandings about their relationships with mathematics, and the important relations emerging across proportional reasoning ideas.     

Preventive Conservation Applied to Wallpaintings in a Desert Environment in Mexico

ABSTRACT

The church of San Diego de Alcalá, located in Pitiquito, Sonora , in Mexico, lies on a missionary road founded by the Jesuit Eusebio F. Kino, which, with the expulsion of the Jesuit order in 1767, passed into the care of the Franciscans. It contains wallpaintings which presented deterioration problems whose cause was not easy to determine, since the damage appeared to be inconsistent with the techniques used and the environmental conditions. With an interdisciplinary team, a methodology was designed for a combined study of the environment of the church and its wallpaintings. Thermal imaging of the exterior and interior walls indicated that the building was made up of different materials, and the junctions between them explained the different deterioration pathologies between one zone and another. Hydrological maps for groundwater in the locality were studied, to elucidate the presence of water in a desert zone; abundant sources of water in the subsoil were identified, which, because of overexploitation of the land, have been diminishing over time. This allowed the elaboration of a plan for site management, through the identification of those deterioration factors that can be mitigated by simple maintenance actions that are inherent to the environment and the materials, which enabled a scheduled maintenance scheme to be implemented. This improved the condition of the building and its wallpaintings, while reducing the resource invested to achieve this goal.