Kim and Opfer (2017) found that number-line estimates increased approximately logarithmically with number when an upper bound (e.g., 100 or 1000) was explicitly marked (bounded condition) and when no upper bound was marked (unbounded condition). Using procedural suggestions from Cohen and Ray (2020), we examined whether this logarithmicity might…

Analogical reasoning is a fundamental cognitive skill of drawing relationships between representations, often between prior knowledge and new representations, that allows for bootstrapping cognitive and language development (Gentner, 2003). Analogical reasoning proficiency develops substantially during childhood, though the mechanisms underlying…

Research findings: Using a sample of 568 students from 61 kindergarten classrooms whose primary caregivers completed a questionnaire describing their child's early childhood education and care (ECEC) by year from birth to pre-kindergarten, we identified seven pathways characterizing children's ECEC experiences using a latent class analysis. Once…

Learning, development, and response to instruction often involve changes in the strategies that learners use to solve problems. In this chapter, our focus is on mathematical problem solving in both children and adults. We offer a selective review of research on three classes of factors that may influence processes of strategy change in…

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, in press) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments…