Research

I am interested in the everyday activities and interactions that constitute the environments in which children learn and develop. In my research, I examine the interplay of social, cultural, and cognitive processes in children’s intellectual growth, building on ideas in cultural psychology, to understand how environments take shape, are transformed by participants, and have consequences for participants' learning and development. I use these notions to investigate everyday activities as cultural contexts in which children construct knowledge as they participate in the meaningful practices of their communities. This conceptual framework, combined with a developmental perspective on individual change, leads me to investigate the sociocultural organization of children’s everyday activities and the knowledge children bring to and acquire from participating in them. I am interested in how learning and problem solving outside of school differ from the same processes in school, and how such research can promote children’s school achievement and well-being.

To address these issues, I have focused on the areas of mathematics and, more recently, science. Mathematical and scientific reasoning are increasingly viewed as cultural processes, and I have studied mathematical practices among Latin American, Korean American, Brazilian, and working- and middle-class Euro-American children from preschool through adolescence. Because mathematical and scientific knowledge are learned and used in many contexts, my research has addressed learning in parent-child play, shopping and household activities, games, and museums. Finally, recent reform efforts in mathematics and science education provide a bridge for asking questions about how studies of learning and problem solving outside the classroom can inform our understanding of schooling.

The Development of Everyday Arithmetic Among Brazilian Children
In one study, I examined the development of mathematical knowledge in poor Brazilian children with little formal school instruction. Virtually all children in the communities where I collected my data were sent frequently to local stands to make purchases, an activity that often entailed mathematical reasoning in the exchange of money for goods. Interviews with parents revealed that the responsibilities assigned to children of different ages varied and, as a result, older children encountered more complex arithmetic in their commercial transactions than did younger children. Moreover, the complexity of children’s commercial transactions was related to their performance on arithmetic tasks, a relationship that extended beyond the influence of age or schooling. The results provided evidence that children acquire mathematical skill as they participate in everyday activities, and that shifts in children’s cognitive achievements are supported by parallel shifts in the complexity of their assigned activities. The study highlighted the importance of cultural artifacts - in this case, money - for cognitive development, a central aspect of sociohistorical approaches to understanding development.

Ethnic Differences in Children’s Arithmetical Activities and Achievements
In this study, I examined the impact of cultural artifacts on children’s mathematics in a comparative study of Latin American and Korean American children attending the same elementary school. The comparison was intriguing because, as groups, Korean American children tend to do much better in school mathematics than do Latin American children. I found that children's mathematical tasks outside of school varied across ethnic groups, and participation in out-of-school activities was related to children's performance on mathematical tasks that differed in their representation of quantity: each group performed best on tasks that most resembled their out-of-school activities. Although the findings point to mathematical problem solving as situated within particular contexts, some knowledge forms may be more flexibly applied across contexts: Korean American children were more likely to apply similar problem-solving strategies across varied problem types. In this work, I view children’s activities as mediators between, on the one hand, cultural factors, including forms of social interaction, artifacts, educational experiences, values, and attitudes, and, on the other hand, children’s cognitive achievements. In addition, the findings show that children, including those traditionally at risk for school failure, bring with them to school considerable mathematical understanding that often is ignored but could be used as a foundation for school instruction.

How Children Structure and Transform Mathematical Environments in Game Play
Studies of children’s learning from the perspective of cultural psychology often are criticized for emphasizing the role of adults and ignoring children’s own contributions to their development. In response to this criticism, I worked with two graduate students (Debra Menk and Jrene Rahm) to look at how children structure mathematical environments while engaged in a common cultural activity—playing a board game. We examined the mathematical problems that emerged in games played by children of different ages and mathematical ability. We found that players’ goals, conventions about play, and forms of social interaction varied as a function of players' age and ability. Of special interest was how social interactions led to opportunities for children to engage in mathematical problem solving beyond their current level of understanding-opportunities to construct new mathematical understanding.

I also have applied insights from investigations of children’s learning in cultural practices to classroom instruction. Geoffrey Saxe and I created a classroom activity in the form of a board game that third and fourth grade children from an inner city school played for ten weeks. We found that players' problem-solving strategies on a posttest varied as a result of the types of social interaction in which they had participated during game play. Our findings led us to question the generality of developmental sequences (at least with regard to the mathematical concepts we studied) and pointed to the role of social interaction in shaping diverse mathematical outcomes.

Learning in Museums
Two museum studies extend my previous research in significant ways: I have added learning about science to my prior focus on mathematics, and I am studying discourse for evidence of how children construct scientific knowledge through social interaction. In a study funded by the Spencer Foundation, a graduate student (Kenneth Emo) and I recorded conversations between parents and children as they explored an exhibition in the Denver Museum of Nature and Science. In several preliminary reports, we used ideas from the Russian linguists Bakhtin and Lotman to discuss how parents helped children understand exhibits, and noted that parents who viewed science as the gradual development of theories about the world were more likely to engage their children in interpreting and questioning the information presented in the museum compared to parents who viewed science as an unchanging body of facts. In another museum-related project, supported by a fellowship from the National Academy of Education, I have been examining how children work together to construct scientific understanding as they explore hands-on exhibits in a science discovery center. A central issue of this research is to understand the kinds of information (e.g., exhibit text, everyday experience, school-based learning) children use to make sense of scientific phenomena. In papers based on these data, I discussed the conditions that led children to seek (or not seek) further information as they interacted with exhibits.