Based on our work teaching undergraduate Calculus courses, we offer insight into teaching the chain rule to reduce cognitive load for students. A particularly difficult topic for students to grasp, problems likely arise due to student struggles with the concept of function and, particularly, function composition relative to when they first…

In this personal essay, I explain how my use of visual modelling has the capacity to broaden constructionism in five important ways. (1) It introduces new techniques for students to describe and document, in a personal way, what they are actually doing in modelling. (2) It introduces the big ideas of mathematical modelling and computational…

Memory for numbers improves with age. One source of this improvement may be learning linear spatial-numeric associations, but previous evidence for this hypothesis likely confounded memory span with quality of numerical magnitude representations and failed to distinguish spatial-numeric mappings from other numeric abilities, such as counting or…

Children's spontaneous focus on numerosity (SFON) is described as an unprompted tendency that is stable across contexts. The attention to number task (AtN), an experimental forced-choice picture-matching task designed to evaluate select aspects of children's focus on numerosity, may reveal whether task materials can implicitly prompt children to…

Low-income preschoolers have lower average performance on measures of early numerical skills than middle-income children. The present study examined the effectiveness of numerical card games in improving children's numerical and executive functioning skills. Low-income preschoolers (N = 76) were randomly assigned to play a numerical magnitude…

Children in developing countries often lack sufficient support for early learning skills prior to beginning school. This research evaluates an educational media intervention using an animated cartoon program, "Akili and Me." The program was originally created in Tanzania to teach early learning skills. This program was adapted in content…

This volume focuses on the implications of digital technologies for educators and educational decision makers that are not widely represented in the literature. The chapters contained in the volume are based on the presentations at the 2020 edition of the CELDA conference and cover multiple developments in the field such as deploying learning…

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic…