At the onset of the coronavirus disease (COVID-19) global pandemic, our interdisciplinary team hypothesized that a mathematical misconception--whole number bias (WNB)--contributed to beliefs that COVID-19 was less fatal than the flu. We created a brief online educational intervention for adults, leveraging evidence-based cognitive science…

Relational reasoning is a hallmark of human higher cognition and creativity, yet it is notoriously difficult to encourage in abstract tasks, even in adults. Generally, young children initially focus more on objects, but with age become more focused on relations. While prerequisite knowledge and cognitive resource maturation partially explains this…

Children's cognitive control and knowledge at school entry predict growth rates in analogical reasoning skill over time; however, the mechanisms by which these factors interact and impact learning are unclear. We propose that inhibitory control is critical for developing both the relational representations necessary to reason and the ability to…

This research targets children's informal strategies and knowledge of fractions by examining their ability to create, interpret, and connect representations in doing and communicating mathematics when solving fractions tasks. Our research group followed a constant comparative method to analyze clinical interviews of children in grades 2-6 solving…

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…

In the present chapter, we review the evidence for several principles that are especially promising for improving mathematics instruction. Using the classification scheme proposed by Koedinger et al. (2013), we begin with principles that focus on improving memory and fluency: scaffolding, distributed practice, and feedback. We then move to worked…

The purpose of this study was to assess the added value of dynamic assessment (DA) beyond more conventional static measures for predicting individual differences in year-end 1st-grade calculation (CA) and word-problem (WP) performance, as a function of limited English proficiency (LEP) status. At the start of 1st grade, students (129 LEP; 163…

This study examined how toddlers gain insights from source video displays and use the insights to solve analogous problems. Two- to 2.5-year-olds viewed a source video illustrating a problem-solving strategy and then attempted to solve analogous problems. Older but not younger toddlers extracted the problem-solving strategy depicted in the video…

Developmental predictors of children's fraction concepts and procedures at the end of fourth grade were investigated in a 2-year longitudinal study. Participants were 357 children who started the study in third grade. Attentive behavior, language, nonverbal reasoning, number line estimation, calculation fluency, and reading fluency each…