Didactic Sequence for Teaching Exponential Function

This paper presents a methodological proposal for the teaching of exponential function, resulting from the application of a didactic sequence involving exponential function, where evidence of learning and the consolidation and application of mathematical concepts in problem solving were identified and analyzed. The Didactic Engineering of Michèle Artigue (1988) was used as a research methodology. As theoretical contributions that guided and enabled the development of the research, we chose the use of Mathematical Investigation in the classroom; Didactic Sequence in the conception of Zabala (1999); the Articulated Units of Conceptual Reconstruction proposed by Cabral (2017) and assumptions of Vygotsky\u27s theory. A didactic sequence composed of five UARC\u27s was elaborated to work the exponential function, with a view to minimizing the difficulties naturally imposed by the content to be explained. Microgenetic analysis of verbal interactions between teacher and students was used to analyze the results of the application. The results show that the students participating in the experiment showed evidence of learning, recorded during the process, and began to have a good understanding of the concepts and properties related to the topic, in addition to a good performance in carrying out the activities, facts that corroborate the potential of the didactic sequence proposed herein

How much leaf area do insects eat? A data set of insect herbivory sampled globally with a standardized protocol

Herbivory is ubiquitous. Despite being a potential driver of plant distribution and performance, herbivory remains largely undocumented. Some early attempts have been made to review, globally, how much leaf area is removed through insect feeding. Kozlov et al., in one of the most comprehensive reviews regarding global patterns of herbivory, have compiled published studies regarding foliar removal and sampled data on global herbivory levels using a standardized protocol. However, in the review by Kozlov et al., only 15 sampling sites, comprising 33 plant species, were evaluated in tropical areas around the globe. In Brazil, which ranks first in terms of plant biodiversity, with a total of 46,097 species, almost half (43%) being endemic, a single data point was sampled, covering only two plant species. In an attempt to increase knowledge regarding herbivory in tropical plant species and to provide the raw data needed to test general hypotheses related to plant–herbivore interactions across large spatial scales, we proposed a joint, collaborative network to evaluate tropical herbivory. This network allowed us to update and expand the data on insect herbivory in tropical and temperate plant species. Our data set, collected with a standardized protocol, covers 45 sampling sites from nine countries and includes leaf herbivory measurements of 57,239 leaves from 209 species of vascular plants belonging to 65 families from tropical and temperate regions. They expand previous data sets by including a total of 32 sampling sites from tropical areas around the globe, comprising 152 species, 146 of them being sampled in Brazil. For temperate areas, it includes 13 sampling sites, comprising 59 species

Canagliflozin and renal outcomes in type 2 diabetes and nephropathy

BACKGROUND Type 2 diabetes mellitus is the leading cause of kidney failure worldwide, but few effective long-term treatments are available. In cardiovascular trials of inhibitors of sodium–glucose cotransporter 2 (SGLT2), exploratory results have suggested that such drugs may improve renal outcomes in patients with type 2 diabetes. METHODS In this double-blind, randomized trial, we assigned patients with type 2 diabetes and albuminuric chronic kidney disease to receive canagliflozin, an oral SGLT2 inhibitor, at a dose of 100 mg daily or placebo. All the patients had an estimated glomerular filtration rate (GFR) of 30 to <90 ml per minute per 1.73 m2 of body-surface area and albuminuria (ratio of albumin [mg] to creatinine [g], >300 to 5000) and were treated with renin–angiotensin system blockade. The primary outcome was a composite of end-stage kidney disease (dialysis, transplantation, or a sustained estimated GFR of <15 ml per minute per 1.73 m2), a doubling of the serum creatinine level, or death from renal or cardiovascular causes. Prespecified secondary outcomes were tested hierarchically. RESULTS The trial was stopped early after a planned interim analysis on the recommendation of the data and safety monitoring committee. At that time, 4401 patients had undergone randomization, with a median follow-up of 2.62 years. The relative risk of the primary outcome was 30% lower in the canagliflozin group than in the placebo group, with event rates of 43.2 and 61.2 per 1000 patient-years, respectively (hazard ratio, 0.70; 95% confidence interval [CI], 0.59 to 0.82; P=0.00001). The relative risk of the renal-specific composite of end-stage kidney disease, a doubling of the creatinine level, or death from renal causes was lower by 34% (hazard ratio, 0.66; 95% CI, 0.53 to 0.81; P<0.001), and the relative risk of end-stage kidney disease was lower by 32% (hazard ratio, 0.68; 95% CI, 0.54 to 0.86; P=0.002). The canagliflozin group also had a lower risk of cardiovascular death, myocardial infarction, or stroke (hazard ratio, 0.80; 95% CI, 0.67 to 0.95; P=0.01) and hospitalization for heart failure (hazard ratio, 0.61; 95% CI, 0.47 to 0.80; P<0.001). There were no significant differences in rates of amputation or fracture. CONCLUSIONS In patients with type 2 diabetes and kidney disease, the risk of kidney failure and cardiovascular events was lower in the canagliflozin group than in the placebo group at a median follow-up of 2.62 years