International calls have been made for reasoning-and-proving to permeate school mathematics. It is important that efforts to heed this call are grounded in an understanding of the opportunities to reason-and-prove that already exist, especially in secondary-level geometry where reasoning-and-proving opportunities are prevalent but not thoroughly…

Describes a model for generative teaching of comprehension that focuses on students' knowledge base and preconceptions; motivation; attention; and generation of new models and explanations. Generative teaching procedures for facilitating comprehension in elementary school are reported. (Author/LB)

Describes 15 types of analogies, their facilitating function in mental processing, the kinds of knowledge for which they are most effectively employed, and their applicability across subject matter. Eight steps for constructing and presenting analogies and types of analogical relationships are included. Prevention of misconceptions is discussed.…

Words are only one way of symbolizing ideas. Numbers, pictures, graphs, maps, diagrams, photographs, and other means are also used to convey information. Researchers refer to notational systems such as graphs, diagrams, and maps as "inscriptions." Inscriptions are tools that help people to perceive and to talk about spatial worlds. Spatial…

A cognitive or internal representation refers to an organized system of information which reflects certain, but not all, of the information about reality being represented. This paper considers various opinions, controversies, and debates about what representation is, how it comes about, and what forms of representation can be distinguished. The…

An inquiry attempted to build an agenda for research that would result in a cognitive theory of instruction capable of informing educational practice and extending the limits of knowledge about how people learn and develop. What would such a theory look like, how close are we to having one, and what directions must be followed to further its…

A sequential-developmental approach to the assessment of individuals from the earliest sensorimotor period through the level of abstract reasoning is discussed. The assessment is hierarchically sequenced and is concerned with how and why individuals process information. The assessment procedures provide practical data on levels of development. (JN)

Well-known questioning strategies, built on question classification systems, are examined. Types of question classification systems are identified as: "hierarchical," which are sequential and cumulative; "non-hierarchical," which are based on elements which should not be rank ordered; systems which are "context-bound" to specifics; and…

Systematic cognitive development, through planned experiences in the context of course work, should be a component of teacher education programs, together with opportunities to apply that learning in practicum settings. Training in cognitive skills (analysis of error, comparison and contrast, categorization, identifying relationships among…