Length measurement in the early years: teaching and learning with learning trajectories

ABSTRACT

Measurement is a critical component of mathematics education, but research on the learning and teaching of measurement is limited. We previously introduced, refined, and validated a developmental progression – the cognitive core of a learning trajectory – for length measurement in the early years. A complete learning trajectory includes instructional activities and pedagogical strategies, correlated with each level of the developmental progression. This study evaluated a portion of our learning trajectory, focusing on the instructional component. We found that the instruction was successful in promoting a progression from one level to the next for 40% of the children, with others developing positive new behaviors (but not sufficient to progress to a new level). We identified specific characteristics of the interventions’ tasks and teacher–child interactions that engendered learning. The use of standard or multiple nonstandard units may play different roles at different points in the learning trajectory.

KEYWORDS:

• Early childhood education
• learning theory
• learning trajectories
• elementary math
• measurement

Acknowledgments

The findings and statements in this manuscript do not represent the views of the National Science Foundation. Our thanks go to Ellen Joseph, Douglas Van Dine, Ron Dolgin, Maria Vukovich, and Kate Newburgh, who helped implement or analyze this research.

Notes

1. See the complete learning trajectory in (Barrett et al., 2017; Clements & Sarama, 2014a; Sarama & Clements, 2009) and at LearningTrajectories.org. Research is unclear about the placement and role of an additional level, Indirect Length Comparer, so it is not considered here.

Additional information

Funding

The research reported in this manuscript was supported by the National Science Foundation under Grant No. DRL-1222944.

Notes on contributors

Julie Sarama

Julie Sarama, Kennedy Endowed Chair and Distinguished University Professor, has taught high school mathematics, computer science, middle school gifted mathematics and early childhood mathematics. She directs 6 projects funded by the National Science Foundation, Institute of Education Sciences, and others (30 total) and has authored over 80 refereed articles, 7 books, 60 chapters, and over 100 additional publications.

Douglas H. Clements

Douglas H. Clements is Distinguished University Professor and Kennedy Endowed Chair at the University of Denver, Colorado. Clements has published over 166 refereed research studies, 27 books, 100 chapters, and 300 additional works on the learning and teaching of early mathematics; computer applications; research-based curricula; and taking interventions to scale.

Jeffrey E. Barrett

Jeffrey E. Barrett is a Professor of Mathematics Education in the Department of Mathematics at Illinois State University. His research examines how students coordinate number and space as they learn mathematics, and how teachers may improve their practice by attending to developmental accounts of students’ reasoning.

Craig J. Cullen

Craig J. Cullen is a Professor of Mathematics Education in the Department of Mathematics at Illinois State University. His research focuses on children’s understanding of geometric measurement as well as the role of technology in the teaching and learning of mathematics.

Aaron Hudyma

Aaron Hudyma is a research assistant doctoral student at the University of Denver.

Yuly Vanegas

Yuly Vanegas Muñoz is a lecturer in the Serra Húnter program. She teaches Didactics of Mathematics at the University of Lleida. Currently, she is the coordinator of the group: Research in Early Childhood Mathematics Education of the Spanish Society for Research in Mathematics Education - SEIEM.