This paper describes an approach for pre-service or in-service mathematics education that teaches sophisticated mathematics using only the tools of high school mathematics. The idea is to start with a standard problem from high school mathematics and let the solution to this problem serve as a platform for asking good mathematical questions and…

Utopianism, which is a distinctive vocabulary of hope, teaches us that society, including its physical sites of social and political practice, are both imagined and made and that we can accordingly believe they can be reimagined and remade. This paper exemplifies how exercises of the utopian imagination within teacher education curricula are able…

Explains four instructional approaches with varied learning processes and provides guidelines for the use of each. Describes receptive instruction, that is highly controlled; behavioral instruction that assumes learning occurs through a gradual building of skills; the situated guided discovery approach, including constructivism and social…

Describes a methodology for supporting exploratory learning that attempts to limit learning space, called exploration space, and adequately control the cognitive load learners would face in their exploration process. In Exploration Space Control (ESC) the extent of exploration space is controlled according to domain complexity, but also to…

Describes the ninth-grade curriculum of the Downingtown Educational Enrichment Program (DEEP) that includes student design and implementation of independent-study contracts. The program serves identified gifted students through a year-long scheduled elective course option that meets every other day and offers one-half credit. (CR)

Presents the 1999 winners of the Foxfire Exemplary Classrooms Awards. The winners were diverse in grade level, urban and rural settings, years of experience with the Foxfire core practices, and ideas about how to implement the Foxfire approach. Activities and experiences from each winning classroom are highlighted. Criteria for winning an award…

Open-ended learning environments (OELEs) provide contexts to support exploration, experimentation, and problem-solving. This paper creates a context for understanding the issues and challenges associated with the design and development of OELEs. Discussion first centers on characteristics of OELEs which differ from traditional learning…

Defines inquiry, a student-centered discovery process, and introduces Pathways to Knowledge(TM), an information process model that provides stages and strategies for anyone interested in gathering, using, and evaluating information. Describes the six stages of Pathways: Appreciation, Presearch; Search; Interpretation; Communication; and…

Presents evidence against the use of standardized curricula and testing and in favor of discovery-based instruction. Describes a successful experience with a relatively new form of discovery-based instruction, the scenario educational computer software. (AEF)

Describes implementation of the "process workshop" model for university chemistry classroom instruction. Defines process workshop as a classroom environment where students are actively engaged in learning a discipline and developing essential skills by working in self-managed teams on activities that involve guided discovery, critical thinking,…

Discussed is the classroom suitability of an open learning computer microworld centered around families of quadratic equations that provides a framework for exploring questions about parabolas to establish the link between the graphical and the algebraic representations of quadratic equations. (JJK)

The availability of user-friendly tools for designing learning environments resulted in an innovative shift of design focus. This shift has been noticed from a user-centred, although passive and reactive, design approach to a participatory, at responsibility and self-directedness directed, design approach. This latter innovative and promising…