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Utah's Foremost Platform for Undergraduate Research Presentation
2018 Abstracts

Building the Foundation: Characteristics and Achievement Patterns of Three-Year-Olds’ Evolving Mathematical Knowledge

Alyssa Collins, Utah State University


The NAEYC recommends that early childhood mathematics education be research-based and developmentally appropriate. Currently, research indicates that early number sense predicts later mathematics achievement, hence, teachers feel pressure to ensure young students meet specific mathematics benchmarks. Mathematics learning trajectories provide a research-based background for expectations for where students should be in their mathematics learning development. In this vein, an in-depth look at actual students’ development in the context of their classrooms is warranted. The purpose of this multiple-case study was to document and describe the characteristics of 5 three-year-olds’ evolving mathematical knowledge over the course of a year in a play-based preschool classroom. The research questions that guided this study included: 1) In what ways do three-year-old preschoolers’ mathematical knowledge develop over a year?, 2) What are the characteristics of their evolving mathematical knowledge?, 3) What are their patterns of achievement?, and 4) What are their characteristics of engagement as their mathematical knowledge evolves? This research involved the collection of multiple assessments (i.e., the TEAM and IGDIs), observations, and teacher interviews for the purpose of triangulation. The data were analyzed in terms of assessment scores, learning trajectory codes, and other open coding methods. We are still analyzing the data, but the preliminary results indicate that one-to-one correspondence and cardinality are key skills that these three-years-olds acquired. One-to-one correspondence and cardinality represent turning points in these students’ mathematical knowledge. The preliminary results suggest that these students need additional opportunities to make shifts in other concepts on the mathematics learning trajectories. The implications for this research include the practical use of learning trajectories to observe students’ evolving mathematical knowledge. Other implications may be the importance of guided and consistent mathematics instruction in addition to spontaneous free-play situations. A multiple-case study provides an in-depth look at children’s development across learning trajectories in the context of their classroom. This study provides context-based evidence for how and why these preschoolers’ mathematics knowledge is evolving and can inform preschool instructional practices and assessments. Recommendations for guided practice, content integration, and multiple opportunities to use one-to-one correspondence, cardinality, subitizing, counting, and part-whole ideas will be provided.