Young children's understandings of length measurement: A developmental progression
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Recent reform movements in mathematics education have emphasized the need to improve mathematics education. Research on hypothetical learning trajectories (Simon, 1995) has the potential to successfully connect the process of teaching and learning through emphasizing instruction based on the developmental progressions children might follow in the learning of various mathematical concepts. Developmental progressions can guide teachers in choosing appropriate activities that help kids move along these progressions (Clements, Sarama, & DiBiase, 2002). The purpose of this study was to investigate how young children develop concepts and skills related to length measurement, with an emphasis on strategy use. The focus was on the description of the developmental progression the majority of young children follow as they advance in the domain of length measurement. The study used a convenience sample of 121 children, approximately 30 from each grade level of pre-kindergarten through second grade. All the children were individually interviewed, and the interviews were videotaped. Although the interviews followed a strict script (Appendix A) in the fashion of task-based interviews (Goldin, 1997, 2000), they were enhanced by Piaget's technique of clinical interviewing (Ginsburg, 1997). Based on the developmental progression from the learning trajectory developed as a foundation for the research-based development of the Building Blocks early childhood mathematics curriculum (Clements & Sarama, 2004b; Sarama & Clements, 2003), tasks were designed to measure every level of the progression. The data sources included the video footage of the interviews, and the notes taken by the interviewer during the interviews. Data were analyzed using Rasch measurement (Bond & Fox, 2001; Hawkins, 1987; Snyder & Sheehan, 1992; Wright & Mok, 2000) and qualitative methods. Based on quantitative and qualitative data this study proposes and details a modified developmental progression. It provides descriptions of the developmental levels, including the tasks and the "mental actions on objects" that define each level. The findings of the study can help provide teachers and other professionals with a model of developmental progressions for the domain of length measurement. Developmental progressions, besides connecting the process of teaching and learning, also provide information for developing research based curricula and standards (Clements, 2002; Clements, Copple, & Hyson, 2002; Clements, Sarama et al., 2002). The results of this study also contribute to what is known about how young children develop understandings of the concepts and strategies related to length measurement.