Modelling Mathematical Reasoning in Physics Education

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

Chemistry and Chemical Education Through Text and Image: Analysis of Twentieth Century Textbooks Used in Brazilian Context

Assuming that textbooks give literary expression to cultural and ideological values of a nation or group, we propose the analysis of chemistry textbooks used in Brazilian universities throughout the twentieth century. We analyzed iconographic and textual aspects of 31 textbooks which had significant diffusion in the context of Brazilian universities at that period. As a result of the iconographic analysis, nine categories of images were proposed: (1) laboratory and experimentation, (2) industry and production, (3) graphs and diagrams, (4) illustrations related to daily life, (5) models, (6) illustrations related to the history of science, (7) pictures or diagrams of animal, vegetable or mineral samples, (8) analogies and (9) concepts of physics. The distribution of images among the categories showed a different emphasis in the presentation of chemical content due to a commitment to different conceptions of chemistry over the period. So, we started with chemistry as an experimental science in the early twentieth century, with an emphasis change to the principles of chemistry from the 1950s, culminating in a chemistry of undeniable technological influence. Results showed that reflections not only on the history of science, but on the history of science education, may be useful for the improvement of science education.

Multiple Quaternary Refugia in the Eastern Guiana Shield Revealed by Comparative Phylogeography of 12 Frog Species

The Guiana Shield (GS) is one of the most pristine regions of Amazonia and biologically one of the richest areas on Earth. How and when this massive diversity arose remains the subject of considerable debate. The prevailing hypothesis of Quaternary glacial refugia suggests that a part of the eastern GS, among other areas in Amazonia, served as stable forested refugia during periods of aridity. However, the recently proposed disturbance-vicariance hypothesis proposes that fluctuations in temperature on orbital timescales, with some associated aridity, have driven Neotropical diversification. The expectations of the temporal and spatial organization of biodiversity differ between these two hypotheses. Here, we compare the genetic structure of 12 leaf-litter inhabiting frog species from the GS lowlands using a combination of mitochondrial and nuclear sequences in an integrative analytical approach that includes phylogenetic reconstructions, molecular dating, and Geographic Information System methods. This comparative and integrated approach overcomes the well-known limitations of phylogeographic inference based on single species and single loci. All of the focal species exhibit distinct phylogeographic patterns highlighting taxon-specific historical distributions, ecological tolerances to climatic disturbance, and dispersal abilities. Nevertheless, all but one species exhibit a history of fragmentation/isolation within the eastern GS during the Quaternary with spatial and temporal concordance among species. The signature of isolation in northern French Guiana (FG) during the early Pleistocene is particularly clear. Approximate Bayesian Computation supports the synchrony of the divergence between northern FG and other GS lineages. Substructure observed throughout the GS suggests further Quaternary fragmentation and a role for rivers. Our findings support fragmentation of moist tropical forest in the eastern GS during this period when the refuge hypothesis would have the region serving as a contiguous wet-forest refuge.

Vorapaxar in the Secondary Prevention of Atherothrombotic Events

BACKGROUND Thrombin potently activates platelets through the protease-activated receptor PAR-1. Vorapaxar is a novel antiplatelet agent that selectively inhibits the cellular actions of thrombin through antagonism of PAR-1. METHODS We randomly assigned 26,449 patients who had a history of myocardial infarction, ischemic stroke, or peripheral arterial disease to receive vorapaxar (2.5 mg daily) or matching placebo and followed them for a median of 30 months. The primary efficacy end point was the composite of death from cardiovascular causes, myocardial infarction, or stroke. After 2 years, the data and safety monitoring board recommended discontinuation of the study treatment in patients with a history of stroke owing to the risk of intracranial hemorrhage. RESULTS At 3 years, the primary end point had occurred in 1028 patients (9.3%) in the vorapaxar group and in 1176 patients (10.5%) in the placebo group (hazard ratio for the vorapaxar group, 0.87; 95% confidence interval [CI], 0.80 to 0.94; P<0.001). Cardiovascular death, myocardial infarction, stroke, or recurrent ischemia leading to revascularization occurred in 1259 patients (11.2%) in the vorapaxar group and 1417 patients (12.4%) in the placebo group (hazard ratio, 0.88; 95% CI, 0.82 to 0.95; P=0.001). Moderate or severe bleeding occurred in 4.2% of patients who received vorapaxar and 2.5% of those who received placebo (hazard ratio, 1.66; 95% CI, 1.43 to 1.93; P<0.001). There was an increase in the rate of intracranial hemorrhage in the vorapaxar group (1.0%, vs. 0.5% in the placebo group; P<0.001). CONCLUSIONS Inhibition of PAR-1 with vorapaxar reduced the risk of cardiovascular death or ischemic events in patients with stable atherosclerosis who were receiving standard therapy. However, it increased the risk of moderate or severe bleeding, including intracranial hemorrhage. (Funded by Merck; TRA 2P-TIMI 50 ClinicalTrials.gov number, NCT00526474.)

History and Epistemology of Science in the Classroom: The Synthesis of Quinine as a Proposal

The history of the quinine synthesis can be used as a case study to emphasize that science is influenced by social and historical processes. The first efforts toward the synthesis of this substance, which until recently was the only treatment for malaria, were by Perkin in 1856 when, trying to obtain quinine,,. he synthesized mauveine. Since then, the quest for the total synthesis of quinine involved several characters in a web of controversies. A major step in this process was made in 1918 by Rabe and Kindler, who proposed the synthesis of quinine from quinotoxine. Twenty-six years later, after obtaining the total synthesis of quinotoxine, Woodward and Doering announced the total synthesis of quinine. However, the lack of experimental details about Rabe and Kindler's process, associated with Woodward and Doering's failure to reproduce it, raised a series of doubts about the synthesis. Stork and colleagues questioned the veracity of the experimental data and even the scientific reputation of the involved researchers. Doubts remained alive until 2008, when Williams and Smith reported, not without reservations, the reproducibility of Rabe and Kindler's protocol. The scientific knowledge as a social and historical development, its legitimating process, and the absence of neutrality in science constitute aspects that can be discussed from this case study, providing significant contributions to science education, in particular, to the initial or continued training of chemistry teachers.