The discourse of mathematization: bilingual students reinventing mathematics and themselves as mathematical thinkers

In this paper, students' bilingualism and multicultural experiences are examined as cognitive resources for mathematization. Capitalizing on the view of language as action, and on students' familiarity with certain experiences through direct participation, the study includes a conceptual framework, never used with bilingual mathematics learners, to investigate how bilingual students organize and coordinate actions to solve mathematical problems about familiar and unfamiliar experiences in English and Spanish. The study used a research methodology to investigate two questions: (a) How do bilingual students' mathematize familiar experience problems and unfamiliar experience problems in Spanish and English? (b) What do differences and similarities in bilingual students' mathematization across problems and languages reveal about experience and bilingualism as cognitive resources? Findings show important differences. In problems about familiar experiences, students generated more productive actions, more reflective actions, and less unproductive actions than in problems about unfamiliar experience. As for the bilingualism, students used Spanish and English differently. When solving problems in Spanish, they framed actions more socially by including partners or sharing the action with partners, whereas in English they framed actions more individually, more depersonalized, excluding partners and instead relying on words in problems to justify their individual actions. This suggests that reinventing mathematics and themselves as mathematical thinkers is part of using their bilingualism and experiences as cognitive tools, and attention to how they use each language for each type of problem can reveal substantial knowledge about how bilinguals learn mathematics.