Using blogs to enhance the capacity of mathematical communication in High School

The aim of this investigation is to analyze the use of the blog as an educational resource for the development of the mathematical communication in secondary education. With this aim, four aspects are analyzed: organization of mathematical thinking through communication; communication of mathematical thinking; analysis and evaluation of the strategies and mathematical thought of others; and expression of mathematical ideas using mathematical language. The research was conducted from a qualitative approach on an exploratory level, with the case study method of 4 classrooms of second grade of secondary education in a private school in Lima. The observational technique of 20 publications in the blog of the math class was applied; a study of a focal group with a sample of 9 students with different levels of academic performance; and an interview with the academic coordinator of the school was conducted. The results show that the organization of mathematical thinking through communication is carried out in the blog in a written, graphical and oral way through explanations, schemes and videos. Regarding communication of mathematical thinking, the blog is used to describe concepts, arguments and mathematical procedures with words and examples of the students. The analysis and evaluation of the strategies and mathematical thinking is performed through comments and debates about the publications. It was also noted that the blog does not facilitate the use of mathematical language to express mathematical ideas, since it does not allow direct writing of symbols nor graphic representation.

GIS technologies and spatial organization patterns among hunter-gatherers: an archaeological case study from Southern Patagonia (southern South America)

This paper discusses some aspects of hunter-gatherer spatial organization in southern South Patagonia, in later times to 10,000 cal yr BP. Various methods of spatial analysis, elaborated with a Geographic Information System (GIS) were applied to the distributional pattern of archaeological sites with radiocarbon dates. The shift in the distributional pattern of chronological information was assessed in conjunction with other lines of evidence within a biogeographic framework. Accordingly, the varying degrees of occupation and integration of coastal and interior spaces in human spatial organization are explained in association with the adaptive strategies hunter-gatherers have used over time. Both are part of the same human response to changes in risk and uncertainty variability in the region in terms of resource availability and environmental dynamics.

Of Marx and Makers: an Historical Perspective on Generative Justice

In Marxist frameworks “distributive justice” depends on extracting value through a centralized state. Many new social movements—peer to peer economy, maker activism, community agriculture, queer ecology, etc.—take the opposite approach, keeping value in its unalienated form and allowing it to freely circulate from the bottom up. Unlike Marxism, there is no general theory for bottom-up, unalienated value circulation. This paper examines the concept of “generative justice” through an historical contrast between Marx’s writings and the indigenous cultures that he drew upon. Marx erroneously concluded that while indigenous cultures had unalienated forms of production, only centralized value extraction could allow the productivity needed for a high quality of life. To the contrary, indigenous cultures now provide a robust model for the “gift economy” that underpins open source technological production, agroecology, and restorative approaches to civil rights. Expanding Marx’s concept of unalienated labor value to include unalienated ecological (nonhuman) value, as well as the domain of freedom in speech, sexual orientation, spirituality and other forms of “expressive” value, we arrive at an historically informed perspective for generative justice.