Whereas some educational designers believe that students should learn new concepts through explorative problem solving within dedicated environments that constrain key parameters of their search and then support their progressive appropriation of empowering disciplinary forms, others are critical of the ultimate efficacy of this discovery-based…

Introduction: The achievement goals framework has been researched and used to explain and account for individuals' learning and academic achievements. Over the past three decades, progress has been made in the conceptualizations and research development of different possible theoretical models of achievement goals. Notably, in this study, we…

Describes a remedial college course in which discovery-based teaching and physical models are employed to teach students how to think. Discusses program content, program structure, program goals, results of the course, and the impact on student success in future science and math courses. (DKM)

The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…

Compares the decisions facing teachers in current reform proposals to decisions made by teachers participating in the Madison Project in the 1960s. Discusses teaching methods utilized, lesson planning, and teacher/student interactions. Reports Madison Project teacher's responses to interview transcripts of the tutoring project at Berkeley,…

This book represents a compilation of the views and ideas of the late Hans Freudenthal, representing his last major contribution to the field of mathematics education. Rather than a presentation of new views, Freudenthal selected and streamlined old ideas, many gathered from his lectures in China, and formed a review of questions and issues in…

Presents an analysis of the question in the title which involves a discussion of fractions, number theory, and probability through modeling, exploring, and other mathematical connections. (MKR)

Discusses "connectionism," an alternative learning model wherein meaning resides in the function of the whole state of a network, rather than being localizable in certain symbols or areas. Topics discussed include integration with other learning models; the culture of the mathematics classroom; and characteristics of alternative…

Presents a historical and content background of the metric system. Describes 1 of a series of integrated hands-on lessons for grades 4-7 to teach the measuring of volume with metrics. Provides a worksheet for the lesson and a concept map of the metric system. (MDH)

Teaching cases have been utilized in professional training and can offer dramatic accounts of problems teachers may confront in the classroom. This case study examines a fact-based story of a third-grade teacher's confrontation with the mother of an African-American child who disagrees with the innovative approach utilized in her child's…