The development of spatial thinking, emergent geometric concepts and architectural principles in the everyday context.

다국어 초록 (Multilingual Abstract)

This study investigated four- and five-year-old children's spontaneous spatial and geometric behavior and underlying architectural principles (SPAGAR) in the everyday context. The following research questions were investigated: What types of spatial and geometric thinking do young children employ during free play? What architectural principles underlie young children's block constructions? Which aspects of spatial, geometric, and architectural thinking are most prominent in young children's play? Are there age, gender, or socioeconomic class differences in SPAGAR activity? What physical, social, environmental, or cultural conditions are related to SPAGAR activity?.
A total of 90 children from five preschools participated. The method of naturalistic observation (Ginsburg, Pappas, & Seo, in press) was employed. A target child was videotaped for 15 minutes during free play regardless of activity or location. Thirteen SPAGAR codes were identified: line symmetry, plane symmetry, rotational symmetry, patterning, figure identification, shape matching, direction/location, enclosure, foundation, trabeated construction, posting, engineering, and proportional reasoning. Codes were classified into five broad categories: symmetric relations, patterning, shapes, direction/location, and architectural principles.
Correlational analyses indicate a significant relationship between age and overall SPAGAR activity (r = .34, <italic>p</italic> < 0.01). No significant differences existed between gender and overall SPAGAR activity. Moreover, there were no significant socioeconomic class differences in SPAGAR activity. Case study results suggest that involvement in SPAGAR activity is closely associated with physical constraints, social interaction, and cultural tools within the preschool setting.
Both psychological and educational implications emerge from the present study. First, more than any other mathematical activity, SPAGAR comprises nearly one-third of the children's free play. Second, results indicate that low-income children possess a wealth of knowledge in spatial and geometric concepts. Third, naturalistic observation is a powerful tool for tapping into young children's spontaneous spatial and geometric behavior. Finally, results demonstrate the need for early childhood mathematics educators to place more emphasis on spatial and geometric concepts and the architectural principles that underlie them.