Linking Home and School: A Bridge to the Many Faces of Mathematics

Final report Executive Summary Principal Investigators: Marta Civil – University of Arizona Rosi Andrade – University of Arizona Norma González – University of Utah Introduction Mathematics in school and mathematics outside school are different and often unconnected to one another. For example, people may be competent in dealing with mathematical tasks that they view as personally relevant, but this contrasts dramatically with their low performance in school-like situations. What is the gap between one and the other, and what can be done to bridge it? This study (referred to as BRIDGE-- Linking Home and School: A Bridge to the Many Faces of Mathematics) examined such questions as they applied to language and cultural minority students. This study emphasized mathematics teaching that stressed students' own construction of meaning and connections to their world outside school, in the home. This approach to teaching, we claim, is important for all students, but in particular for economically underprivileged and language / culture minority students, since they are still being left behind in the academic journey, and more specifically in mathematics. Over the course of the project, the study took us to six elementary and two middle schools, within two major school districts in Tucson, Arizona. One of the schools was in a working-class to middle-class neighborhood; all the other schools were in working-class neighborhoods. The general population of students that the project worked with were 75% Latino, 5% Native American, 10% African American, and 10% European American. Overall, 17 teachers took part in the project. In terms of students impacted, this is harder to assess but, for example, in one given year, the three teachers we had in the middle school developed curriculum projects that involved approximately 170 students. Research Design This study investigated four questions:1) What are the effects of mathematical study groups on teachers' professional development and pedagogical practices? 2) What is the mathematical potential of students' households and activities outside school? 3) How do we take familial knowledge to an abstract level with potential for academic use? 4) What is the role of parents in changing teaching practices? To address these questions we relied on a four-component model: a) Household Ethnographic Analysis; b) Teacher-Researcher Study Groups; c) Classroom Implementation; d) Parents as Intellectual Resources. Our research design is essentially qualitative with a strong ethnographic component (see pp. 3-4). This summary presents implications of the study within the framework of each of the four components. Household Ethnographic Analysis Despite our better sense to do otherwise, somewhere, sometime during formal and informal education, myths and stereotypes about parents and especially language minority and working class families are woven and reinforced time and time again. The very nature of the ethnographic experience and later analysis of the data collected, coupled with the ongoing teacher-researcher study groups, served to challenge and transform counterproductive and misguided perceptions which have otherwise served to limit the ebb and flow of knowledge and experiences between home and classroom. Teachers received ethnographic training along similar lines as in the Funds of Knowledge for Teaching Project. They then went into the homes as learners, with a specific focus on the mathematical potential in the households. We include here a brief glimpse at an example of how powerful this experience was for one of the teachers. During a study group meeting this teacher vividly described her home visit. She shared that though the family was materially speaking not wealthy, there was a wealth of love, respect and discipline. This, suggested the teacher, was a family for us all to learn from — this family had taught her a great deal about respecting families and about a family's own resilience during difficult periods. This is the nature of experiences that are shared by teacher-researchers following household visits; other household knowledge and experiences begin to build on this foundation. We have learned that before we can begin discussing the academic potential for household knowledge, it is necessary to cull out, like this teacher did, the social, cultural and historical contexts of each family in order to appreciate the struggles they face. At the same time, in sharing the stories of a family, it is inevitable to bring one's own experiences and knowledge to the table, and in this way, teachers themselves are exploring their own funds of knowledge. (See pp. 4-6) Teacher-Researcher Study Groups Every two to three weeks, we came together to "play with mathematics," address pedagogical issues, debrief household visits, and read and discuss relevant articles. The significance of the study-group is that it is first a forum for the process of consciousness about pedagogy, curriculum and knowledge in the teaching and learning of mathematics, then a vehicle for forging the links between home and school knowledge and experience in the creation of innovative curriculum and pedagogy in mathematics. It would be all too easy to answer some of the questions raised within the Study Group sessions by quickly dismissing what some do as mathematics by validating formal application over informal practices. But, we have the burden to understand the social and cultural practices in which mathematics is embedded. We do, however, agree that mathematics often serves as a gatekeeper. In doing so, we have begun to realize the ways in which we often measure others' knowledge of mathematics to the yardstick of testing, which values certain knowledge and experiences as superior, while qualifying as inferior other less palpable expressions of mathematical knowledge. Interestingly, but not surprisingly, for example, we have also found that some of these perceptions were closely related to gender and class specific knowledge and experiences of individuals. That mathematics is not gender or culturally or socially neutral as a subject should be of no surprise, but we are usually taught that it is not and presented with it as a neutral subject. This was an area that we continued to explore and delve into as we pursued the activities of the study group. (See pp. 6-7) Classroom Implementation The knowledge gained from the household visits was to serve as a building block towards the development of curriculum themes that would link home mathematics and school mathematics. Thus, for example, one of the teachers used his household visits and his informal interviewing of many of this middle school students to develop a sophisticated curriculum plan around the idea of "build your dream home." Through this project, students learned many of the required mathematical skills and concepts in a familiar context–that of house construction. Furthermore, several of their family members were involved in the final projects, the making of a model for their dream home. Another teacher, knowing that her students' families were quite knowledgeable about gardening, developed a theme centered on this topic. This theme allowed her to explore in depth topics in measurement, geometry, and graphing, that while they are grade-appropriate, they are often barely touched on. This is one key aspect we want to point out. By providing teachers with a supportive yet challenging environment to become learners of mathematics, they, in turn, expanded the array of topics and pedagogical approaches in their own teaching of mathematics. (See pp. 7-9) Parents as Intellectual Resources In our continuous challenge of the deficit view towards working class and language minority families, in this project we pushed forward the idea of parents as intellectual resources. The knowledge gained from the household visits was a step in this direction. But, a stronger step, we think, was the development of mathematics workshops for a core group of mothers. With these Mexican immigrant women we began a two-way dialogue that encompassed explorations of mathematics as adult learners as well as conversations about educational issues, in particular those related to the teaching and learning of mathematics in schools. These workshops centered on the premise that we were all learners. The content of the workshops was jointly negotiated and, as in the teachers' study group sessions, often brought to light the social and cultural aspects of mathematics instruction and how our values color our perceptions. We firmly believe that if we wish to have parents involved in different and meaningful ways in the education of their children, then we should facilitate that transition as we do for teachers, through workshops and other opportunities for their professional development. (See pp. 9-11) Conclusions Of the many implications from our work (see pp. 11-14), some have direct application to how schools are structured and the roles of teachers and parents within the current framework of home-school collaborations. We believe in the importance of this work, however, there are limitations to how we can extend our findings if schools as institutions, and preservice teacher training and teacher professional development, continue to look to the individual as the problem without reforming their own ranks and institutions. When we choose to engage teachers in meaningful reflective practice, and parents as intellectuals interested in the pursuit of knowledge and activities that extend beyond home activities, then we can begin the work of integrating these pursuits in authentic collaboration for the benefit of students. As the Funds of Knowledge concept has evolved in our work, the approach to ethnographic training has shifted as we have learned more about what works and what does not. What works is that the more the participants can engage and identify with the topic matter, the more interest and motivation are generated. What does not work is a top/down classroom style approach, for example, in which teacher-researcher participants can learn methodological techniques, but which strips away the multidimensionality of a personal ethnographic encounter. In other words, we learn ethnography by doing ethnography. Similarly, we learn mathematics by doing mathematics. It is this engagement of the teachers and the parents (and of the children in the teachers' classrooms) as active doers of mathematics, and the supported reflection that goes along with the activity, that hold promise in the work towards establishing bridges between everyday experiences and school mathematics.