Evaluating a Basic Assumption of Learning Trajectories: The Case of Early Patterning Learning

Arthur J Baroody, Nursel Yilmaz, Douglas H. Clements, Julie Sarama

Research output: Contribution to journalArticlepeer-review

Abstract

Although hypothetical learning trajectories (HLTs) are often viewed as a valuable instructional tool, little research has directly evaluated their value. A basic assumption of HLTs is that ordering instructional activities by developmental difficulty enhances learning. A randomized control trial (RCT) served to evaluate this assumption with a hypothetical learning trajectory (HLT) for early patterning. The RCT (n = 16) entailed comparing two patterning interventions that involved the same activities, but only one ordered them based on an HLT. Each intervention involved twelve 15- to 20- minute sessions. Quantitative data were collected from testing before and 2 weeks after the intervention sessions; qualitative data were collected during the instruction sessions. The former indicated that both interventions were significantly and substantively successful in promoting transfer in identifying the core unit of repeating patterns and extending such patterns. As predicted, a small effect size favored the HLT-Like intervention for core identification but not extending patterns. Training on core identification or extending patterns was significantly and substantially more successful with 4- than with 3-year-olds, especially those less than 3.75-years of age. Moreover, qualitative analyses revealed that translating patterns into letters was much easier than doing so into concrete formats and that the former can be introduced early in patterning instruction while the latter may need to be postponed. Reasons why instructional ordering did have a stronger impact and implications for further HLT research are discussed.
Original languageEnglish (US)
Pages (from-to)8-32
JournalJournal of Mathematics Education
Volume14
Issue number2
DOIs
StatePublished - Nov 2021

Keywords

  • Young children
  • Learning trajectories
  • Curriculum
  • Patterning

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