Traditional knowledge-component models describe students' content knowledge (e.g., their ability to carry out problem-solving procedures or their ability to reason about a concept). In many STEM domains, instruction uses multiple visual representations such as graphs, figures, and diagrams. The use of visual representations implies a…

We investigated whether children at the ages of two and three years understand that a speaker's use of the definite article specifies a referent that is in common ground between speaker and listener. An experimenter and a child engaged in joint actions in which the experimenter chose one of three similar objects of the same category to perform an…

The representation of numbers is commonly viewed as an ordered continuum of magnitudes, referred to as the "mental number line." Previous work has repeatedly shown that number representations evoked by a given task can be easily altered, yielding an ongoing discussion about the basic properties of the mental number line and how malleable…

Participants read a series of news articles, each containing a target event followed by 2 causes. To study the ease with which readers update their mental representation as they proceed through the text, the certainty of the first cause was manipulated: It was presented as either a certain explanation of the subsequent target event or as a…

Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…

We present an inference algorithm for perturbation models based on Poisson regression. The algorithm is designed to handle unclassified input with multiple errors described by independent mal-rules. This knowledge representation provides an intelligent tutoring system with local and global information about a student, such as error classification…

This paper reports on a case-study design experiment in the domain of fraction as number-measure. We designed and implemented a set of exploratory tasks concerning comparison and ordering of fractions as well as operations with fractions. Two groups of 12-year-old students worked collaboratively using paper and pencil as well as a specially…

Building on 2 previous studies (B. R. Ekstrand, 1967; B. R. Ekstrand, M. J. Sullivan, D. F. Parker, & J. N. West, 1971), the authors present 2 experiments that were aimed at characterizing the role of retroactive interference in sleep-associated declarative memory consolidation. Using an A-B, A-C paradigm with lists of word pairs in Experiment 1,…