It is a challenge for mathematics teachers to provide activities for their students at a high level of cognitive demand. In this article, we explore the possibilities that history of mathematics has to offer to meet this challenge. History of mathematics can be applied in mathematics education in different ways. We offer a framework for describing the appearances of history of mathematics in curriculum materials. This framework consists of four formats that are entitled speck, stamp, snippet, and story. Characteristic properties are named for each format, in terms of size, content, location, and function. The formats are related to four ascending levels of cognitive demand. We describe how these formats, together with design principles that are also derived from the history of mathematics, can be used to raise the cognitive level of existing tasks and design new tasks. The combination of formats, cognitive demand levels, and design principles is called the 4S-model. Finally, we advocate that this 4S-model can play a role in mathematics teacher training to enable prospective teachers to reach higher cognitive levels in their mathematics classrooms.
For long flights, the cruise is the longest phase and where the largest amount of fuel is consumed. An in-cruise optimization method has been implemented to calculate the optimal trajectory that reduces the flight cost. A three-dimensional grid has been created, coupling lateral navigation and vertical navigation profiles. With a dynamic analysis of the wind, the aircraft can perform a horizontal deviation or change altitudes via step climbs to reduce fuel consumption. As the number of waypoints and possible step climbs is increased, the number of flight trajectories increases exponentially; thus, a genetic algorithm has been implemented to reduce the total number of calculated trajectories compared to an exhaustive search. The aircraft’s model has been obtained from a performance database, which is currently used in the commercial flight management system studied in this paper. A 5% average flight cost reduction has been obtained.
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Heritable Connective Tissue Disorders (HCTD) show an overlap in the physical features that can evolve in childhood. It is unclear to what extent children with HCTD experience burden of disease. This study aims to quantify fatigue, pain, disability and general health with standardized validated questionnaires.METHODS: This observational, multicenter study included 107 children, aged 4-18 years, with Marfan syndrome (MFS), 58%; Loeys-Dietz syndrome (LDS), 7%; Ehlers-Danlos syndromes (EDS), 8%; and hypermobile Ehlers-Danlos syndrome (hEDS), 27%. The assessments included PROMIS Fatigue Parent-Proxy and Pediatric self-report, pain and general health Visual-Analogue-Scales (VAS) and a Childhood Health Assessment Questionnaire (CHAQ).RESULTS: Compared to normative data, the total HCTD-group showed significantly higher parent-rated fatigue T-scores (M = 53 (SD = 12), p = 0.004, d = 0.3), pain VAS scores (M = 2.8 (SD = 3.1), p < 0.001, d = 1.27), general health VAS scores (M = 2.5 (SD = 1.8), p < 0.001, d = 2.04) and CHAQ disability index scores (M = 0.9 (SD = 0.7), p < 0.001, d = 1.23). HCTD-subgroups showed similar results. The most adverse sequels were reported in children with hEDS, whereas the least were reported in those with MFS. Disability showed significant relationships with fatigue (p < 0.001, rs = 0.68), pain (p < 0.001, rs = 0.64) and general health (p < 0.001, rs = 0.59).CONCLUSIONS: Compared to normative data, children and adolescents with HCTD reported increased fatigue, pain, disability and decreased general health, with most differences translating into very large-sized effects. This new knowledge calls for systematic monitoring with standardized validated questionnaires, physical assessments and tailored interventions in clinical care.
