Imagine a large randomized controlled trial study of a mathematics educational intervention planned in two large urban districts. District 1 gets a new administrator and drops out. In the meantime, the state test changed, so one of the planned outcome measures is no longer usable. Teacher dropout is high. And, as the analysis is being completed,…

Most community college students in the U.S. must complete at least one developmental class, such as elementary algebra, before they can enroll in a college-level mathematics course. Increasingly common in such courses is the use of a web-based activity and testing system (WATS). This report presents initial results of a mixed-methods study of…

A variety of computerized interactive learning platforms exist. Most include instructional supports in the form of problem sets. Feedback to users ranges from a single word like "Correct!" to offers of hints and partially to fully worked examples. Behind-the-scenes design of such systems varies as well --from static dictionaries of…

This is an extended conference proceedings report [Long Paper] based on a shorter contributed report at the same conference. A variety of computerized learning platforms exist. In mathematics, most include sets of problems to complete. Feedback to users ranges from a single word like "Correct!" to offers of hints and partially- to…

College algebra fulfills general education requirements at many colleges in the United States. The study reported here investigated differences in mathematics achievement between undergraduates in college algebra classes using one of two homework methods: "WeBWorK," an open-source system for web-based homework, or traditional…

In the United States, undergraduates--regardless of their field of study--generally must complete a mathematics course to meet breadth-of-study requirements. This report is aimed at providing a research foundation for practical efforts to improve teaching and learning in such college mathematics service courses (e.g., college algebra, liberal arts…

This article reports on the logical reasoning efforts of five prospective elementary school teachers as they responded to interview prompts involving nonsense, natural, and mathematical representations of conditional statements. The interview participants evinced various levels of reliance on personal relevance, linguistic contextualization, and…

This study investigated the influence of regular structured writing about problem solving on college algebra students' locus of control, flexibility of articulation, and accuracy in responding to written problem tasks. The writing assignments, acronym PSOLVE, provided students a framework for expressing their thoughts about mathematical actions,…

In two previous studies we investigated the non-routine problem-solving abilities of students just finishing their first year of a traditionally taught calculus sequence. This paper reports on a similar study, using the same non-routine first-year differential calculus problems, with students who had completed one and one-half years of traditional…

This study examines the K-12 mathematical experiences of U.S. university students via an expressive writing assignment: a mathematical autobiography essay. The essays of 67 college students, out of over 300 enrolled in 16 sections of a college liberal arts mathematics course, were analyzed using constant-comparative methods. Two categories of…