Cultural Processes in Elementary Mathematics: Studies in a Remote Papua New Guinea Community

The algorithmic origins of counting

“…Eventually, they learn algebra, geometry, and calculus; some learn how to solve arbitrary puzzles with mathematical structure, like a Rubik's cube or Sudoku. Children in some cultures use a body counting system (Saxe, 2012) where they acquire algorithms for arithmetic which are fundamentally unlike our culture's algorithms. Some even learn abacus as a visual system where they mentally picture images of beads and manipulate them with corresponding algorithms in order to solve arithmetic problems (Frank & Barner, 2012; Hatano et al., 1977, 1987; Hishitani, 1990; Miller & Stigler, 1991; Stigler, 1984; Stigler et al., 1986).…”

Tracing culture in children’s thinking: a socioecological framework in understanding nature (Rastreando la cultura en el pensamiento infantil: una socioecología para comprender la naturaleza)

“…First, neo-Vygotskian traditions have been instrumental in studying the role of culture in conceptual development (e.g., Cole, 1996;Enfield & Levinson, 2006;Nelson, 1996;Rogoff, 2003;Olson & Cole, 2006;Saxe, 2012;Saxe et al, 1987; see Gauvain et al, 2011 for a review). In this approach, culture, rooted in experienced cultural members, practices, institutions and artefacts, is viewed as a species-specific medium of ontogenetic development (e.g., Cole, 1996).…”

“…Research from the Vygotskian tradition is an example of this approach. From this view, child development is mediated by more experienced members of their culture and by their practices, institutions and cultural artefacts (e.g., Cole, 1996;Enfield & Levinson, 2006;Nelson, 1996;Olson & Cole, 2006;Rogoff, 2003;Saxe, 2012;Saxe, Guberman, & Gearhart, 1987; see Gauvain, Beebe, & Zhao, 2011 for a review). Other work has focused on identifying what early emerging developmental capacities are shared across cultures, and how these become shaped by the particular cultures in which children are immersed (e.g., Astuti, Solomon, & Carey, 2004;Gelman & Legare, 2011;Unsworth et al, 2012;Waxman, Medin, & Ross, 2007;Winkler-Rhoades, Medin, Waxman, Woodring, & Ross, 2010).…”

The invisible quantity: time intervals in early algebra / La cantidad invisible: los intervalos de tiempo en el álgebra temprana

“…Las representaciones convencionales y sus normas no las han inventado los estudiantes, que no siempre las comprenden en un sentido matemático convencional. Los más jóvenes suelen tener dificultades con este tipo de significados en el contexto de actividades discursivas y sociales (Saxe, 2012;Sfard, 2007;Vygotsky, 1978). Con una actividad de este tipo, los objetos utilizados como representación matemática sirven a modo de herramientas para organizar y analizar conceptos matemáticos emergentes que en último término facilitan el acceso a las propiedades estructurales de la representación, necesarias para realizar inferencias y que de otro modo hubiesen permanecido ocultas.…”

“…Conventional representations and their rules are not invented by students; nor do students immediately understand them in the mathematically conventional sense. Students come to grapple with such meaning in the context of discourse and social activity (Saxe, 2012;Sfard, 2007;Vygotsky, 1978). Through such activity, mathematical objects of a representation come to serve as mediating tools to organize and analyse emerging mathematical ideas such that, eventually, one may draw upon structural properties of a representation to make inferences that may otherwise remain hidden.…”