Jenny Yun‐Chen Chan

Relational language is thought to influence mathematical skills. This study examines the association between relational language and number relation skills —knowledge of cardinal, ordinal, and spatial principles—among 104 U.S. kindergartners (5.9 years; 44% boys; 37% White, 25% Black, 14% Asian, 24% other) in the 2017–2018 academic year. Controlling for general verbal knowledge, executive function, and counting and number identification skills, relational language predicted later number relation skills, specifically number line estimation, β = .30. Relational language did not differentially predict number line estimation performance in children with low or high number relation skills, likely due to the restricted ranges of data within subgroups. Number relation skills, specifically number line estimation and number ordering, may be a pathway between relational language and mathematical skills.

Worked examples are effective learning tools for algebraic equation solving. However, they are typically presented in a static concise format, which only displays the major derivation steps in one static image. The current work explores how worked examples that vary in their extensiveness (i.e., detail) and degree of dynamic presentation (i.e., static vs. sequential line‐by‐line vs. dynamic format that demonstrates the problem‐solving process) impact learning. We conducted an online experiment in which 230 algebra students completed a pretest, studied worked examples in one of six presentation conditions, and completed a posttest. We found that overall, students improved from pretest to posttest after viewing the worked examples; we did not find significant differences on posttest performance between worked example presentations. These results have implications for the design of worked examples in online tutoring systems as well as for cognitive load theory and perceptual learning theory in the design of worked examples.