Alternative Tasks for the Teaching and the Learning of functions: analysis of an intervention in the High School

In this paper we focus on the application of two mathematical alternative tasks to the teaching and learning of functions with high school students. The tasks were elaborated according to the following methodological approach: (i) Problem Solving and/or mathematics investigation and (ii) a pedagogical proposal, which defends that mathematical knowledge is developed by means of a balance between logic and intuition. We employed a qualitative research approach (characterized as a case study) aimed at analyzing the didactic pedagogical potential of this type of methodology in high school. We found that tasks such as those presented and discussed in this paper provide a more significant learning for the students, allowing a better conceptual understanding, becoming still more powerful when one considers the social-cultural context of the students.

Molecular evolution of a malaria resistance gene (DARC) in primates

Genes involved in host-pathogen interactions are often strongly affected by positive natural selection. The Duffy antigen, coded by the Duffy antigen receptor for chemokines (DARC) gene, serves as a receptor for Plasmodium vivax in humans and for Plasmodium knowlesi in some nonhuman primates. In the majority of sub-Saharan Africans, a nucleic acid variant in GATA-1 of the gene promoter is responsible for the nonexpression of the Duffy antigen on red blood cells and consequently resistance to invasion by P. vivax. The Duffy antigen also acts as a receptor for chemokines and is expressed in red blood cells and many other tissues of the body. Because of this dual role, we sequenced a 3,000-bp region encompassing the entire DARC gene as well as part of its 5' and 3' flanking regions in a phylogenetic sample of primates and used statistical methods to evaluate the nature of selection pressures acting on the gene during its evolution. We analyzed both coding and regulatory regions of the DARC gene. The regulatory analysis showed accelerated rates of substitution at several sites near known motifs. Our tests of positive selection in the coding region using maximum likelihood by branch sites and maximum likelihood by codon sites did not yield statistically significant evidence for the action of positive selection. However, the maximum likelihood test in which the gene was subdivided into different structural regions showed that the known binding region for P. vivax/P. knowlesi is under very different selective pressures than the remainder of the gene. In fact, most of the gene appears to be under strong purifying selection, but this is not evident in the binding region. We suggest that the binding region is under the influence of two opposing selective pressures, positive selection possibly exerted by the parasite and purifying selection exerted by chemokines.