This study sought to explore whether access to definitions and general representations influences the construction of general direct arguments. Data was collected in college mathematics courses for prospective elementary school teachers. Participant arguments were analyzed along two variables: the generality of the representations and the…

Recommended learning goals for students in introductory statistics courses include the ability to recognize and explain the key role of randomness in designing studies and in drawing conclusions from those studies involving generalizations to a population or causal claims (GAISE College Report ASA Revision Committee, 2016). The purpose of this…

A well-documented curricular gap exists in L2 pedagogy between the introductory courses, focusing mainly on language, and advanced courses, focusing mainly on literary content. Intermediate learners, despite their proficiency, generally have difficulty in bridging this gap, as it requires a shift from decoding to interpreting and analyzing texts.…

Traditional mathematics education focuses on teaching rote procedures to solve problems, though these procedures are not usually motivated by goals. As a result, students have trouble flexibly using procedures and generalizing their knowledge to solve novel problems that differ from the problems they practice during instruction. In the following…

This study presented sets of 15 multiplication facts to each of 4 third-grade participants. The items were presented by an iPod each session three times at three different time delays. When mastery was achieved on a set (80% correct across 3 consecutive sessions), the participant moved on to a new set. Generalization probes were administered…