Dr. Eliane Keane, Miami Dade College, U.S.A. [email protected] Joaquín G. Martínez, Carlos Albizu University, U.S.A. [email protected]: Oral PresentationMain theme: Learning CommunitiesSecondary theme: Interdisciplinary Curriculum: Foreign Language and Fractal GeometryFlying Tetrahedral Kites in FrenchDr. Eliane Keane, Miami Dade College, U.S.A. [email protected] Joaquín G. Martínez, Carlos Albizu University, U.S.A. [email protected] this paper, we provide an overview of successful educational practices used in French-Mathematical Learning Communities (LC) and discuss the rationale for future integration of mathematics into ESL classrooms in community colleges. We framed our teaching techniques on both Krashen’s theories and constructivist approaches to education, facilitated collaboration, and found that a major learning outcome was retention of student knowledge. Students in the LC explored complex geometrical concepts while these concepts were infused into a foreign language course. Through this unique exploratory activity linking humanities, language acquisition, and mathematics, students engaged in solving complex geometrical problems, linkedproblem solving to a foreign language, and learned to perceive the study of mathematics in association with another academic discipline. Although the French-mathematical LC provided anactive learning experience for students, we claim that ESL students may especially benefit from similar learning communities.IntroductionResearch in mathematics education, language acquisition, cognitive learning, and generalpedagogy highlights the importance of collaborative learning and teaching to achieve student success (Piaget, 1926; Vygotsky, 1978; Schoenfield, 1992; Pappas, 1993; Menezes, 1997; Bransford, 2000). Further, learning processes in mathematics and foreign languages are alike, in the sense that context, total immersion, and cognitive learning play a significant role in comprehension, thus knowledge retention. Accordingly, the belief that students need to understand mathematics in context and to apply complex concepts to meaningful real world situations is based on that preliminary premise. Therefore, the idea of a learning community linking French and Mathematics was born.Mathematics educators have been aware that many processes associated with student learning, the development of critical thinking, discovery learning, and student engagement in “doing” mathematics are facilitated when mathematics is integrated across different areas of the curriculum (Pappas, 1994; NCTM, 1989; Papert & Harell, 1991; Webb , 1991; Paas, & Merrienboer, 1994; Rosenthal, 1995). In this paper, we discuss successful educational practices - 1 -in a French-Mathematical learning community, where educators integrate Krashen’s (1985) notions of the input hypothesis as a theoretical framework for student success in learning the beginnings of fractal geometry, fractals, platonic solids, and French.ArgumentOur students experienced success comprehending complex geometrical concepts while immersed in a foreign language environment. Krashen (1985) stresses the notion of comprehensible input (i+1) as a pivotal aspect of language acquisition. Building on the notion that languages should not be taught in a vacuum (Edelhoff & van Bommel, 1980), this learning community established a relationship of mutual reinforcement between the second language (L2)outcomes and the intended mathematical objectives. Further, our students faced an additional level of cognition as they attempted to master new mathematical concepts in the L2. Aside from learning the second language, the students also had to make additional connections to understandgeometrical concepts of self-similarity, fractals, and platonic solids by processing knowledge through the additional filter (L2). We claim that the additional cognitive process contributed to the effective retention of both skills; they relied on the assimilation of one as a prerequisite for mastery of the other. The teachers assumed the role of monitors in this learning community and defined both extremes, from actual to potential development, allowing students the opportunity to define their own zone of proximal development (Vygotsky, 1978). Krashen’s notion of +1 was used to facilitate growth in both mathematics and in the target language (French), whereby the “mathematical knowledge +1” and the “French knowledge +1” were generated by both the teachers and by those students operating at the higher levels of their potential development zone (Vygotzky, 1978). As monitors of a dynamic classroom environment, the teachers also adopted amethodology advocated in the Van Hiele model which recognized a hierarchy in levels of geometrical thinking (Teppo, 1991). The cohesive sense of community supporting the learning environment, the meaningful interaction between students, and the pertinence of the content area knowledge facilitated the learning experience; students successfully acquired knowledge of French applied vocabulary, culture, and some concepts associated with fractal geometry while processing other mathematical concepts at a higher level of cognition (Cummings, 1979; Bloom, 1984; Larsen-Freeman, 1997).The Learning Community ModelStudents enrolled in Geometry and French courses. They were engaged in a series of collaborative activities between the two disciplines under the auspices of both the Mathematics and French professors. In the geometry classroom environment as well as in the French classroom, the professors exposed students to a variety of strategies commonly used in content-centered second language instruction: cooperative learning and group strategies, multi-tasks based on experiential learning, whole language strategies (Goodman, 1986; Crandall, 1992), and the Natural Approach (Krashen & Terrell, 1983).For example, in the Geometry class the students built tetrahedral kites while they learned about fractals ( Mendelbrot, 2002). We promoted cooperative learning and students worked in groups of four to build the kites. Each team member was assigned a specific responsibility during the building phase of the kites. For instance, in one of the teams, one student was - 2 -assigned to record new vocabulary and the geometrical concept associated with the word, another student did research on additional uses and applications of these new