Teaching and Learning Creatively: Using Children's Narratives
Cicero, Ana Maria Lo, De La Cruz, Yolanda, Fuson, Karen C., Teaching Children Mathematics
The Children's Math Worlds project seeks to integrate students' social, emotional, and cultural experiences into classroom mathematics. For seven years, we have been developing in classrooms a conceptually challenging research-based mathematics curriculum called Children's Math Worlds (CMW) for kindergarten through grade 3. We build on the individual experiences, interests, and practical mathematics knowledge that diverse children bring to our classrooms. Our collaborative research project has been, and is being, carried out in urban schools of underrepresented minorities, mostly Latino English-speaking and Latino Spanish-speaking children, and in English-speaking upper-middle-class schools to ensure that our work crosses socioeconomic boundaries. The CMW family component was described in De La Cruz (1999). See that article for data concerning the excellent comparative performance of CMW children.
In this article, we focus on two central, related activities of CMW: (1) linking mathematical activities in the classroom to children's mathematical experiences outside of school and (2) creating a rich and sustained environment for learning to write, solve, and explain ways of solving word problems. Solving word problems has traditionally been difficult for many children, especially those for whom English is a second language. Word problems are often neglected and not assigned to these children. We have found that centering our classes on such problems, using problems of increasing difficulty, and supporting language use by children enable them to solve word problems readily. For more details, see Fuson et al. (1997). In our following description, we weave in voices of some of our classroom teachers to comment on various aspects of teaching using children's lives.
Theoretical Underpinnings of the Curriculum
Our project uses a Vygotskian model for unfolding, formulating, and solving mathematics problems from children's experience. This model describes one way in which teachers build on children's prior knowledge about various situations to facilitate students' construction of understandings of formal mathematical concepts, symbolism, and problems (see Fuson et al.  for more details). The unfolding multiple narratives of different children's experiences provide a framework that is co-constructed by the teacher and children and within which teachers relate new mathematical ideas to children's lives.
This building on children's knowledge is balanced by the other vital Vygotskian aspect of our approach: teaching within the "zone of proximal development" (ZPD). The ZPD, or learning zone, is what children can accomplish with assistance. The teacher leads children from a starting point to more advanced mathematical knowledge. This knowledge includes being better at listening, explaining and helping one another understand; learning more advanced, efficient, and accurate solution methods; and learning mathematical symbolism, language, and new ideas. The teacher, and eventually other children, help students progress in all these ways. The teacher is guided by an ambitious vision of the growth in children's knowledge by the end of the year and is supported by the CMW curriculum.
Getting Started: Eliciting and Using Children's Stories
Some children are eager and ready to share their stories. Others are initially too shy to relate their stories to the class, so they draw or write their stories. Eventually all children participate. Asking children to bring photographs from home either about a trip or any other subject can produce intriguing stories and can give teachers insights into the children's lives. Children enjoy listening to one another's stories. Since each story gives some insight into that child's life, children believe that they are a part of a dynamic class. Stories can be told at other times of the day and told again during mathematics class, perhaps by another child, to emphasize listening and remembering. …