Considers young peoples' views of infinity prior to instruction in the methods mathematicians use in addressing the subject of infinity. Presents a partially historical account of studies examining young peoples' ideas of infinity. Four sections address potential pitfalls for research in this area and the work of Piaget, issues concerning the…

Demonstrates how research-based knowledge about students' incompatible answers to different representations of the same task could be used in mathematics instruction. Describes the 'It's the Same Task' research-based activity which encourages students to reflect upon their own thinking about infinite quantities and avoid contradictions by using…

Analyses several examples of tacit influences exerted by mental models on the interpretation of various mathematical concepts in the domain of actual infinity. Specifically addresses the unconscious effect of the figural-pictorial models of statements related to the infinite sets of geometrical points related to the concepts of function and…

Encouraging children to think about their learning through simple, easy-to-plan activities facilitates better understanding and retention of science concepts. (Author)

The role of equivalence class formation in delayed position recognition span performance was examined with three mentally retarded adults. Matching-to-sample training established equivalence classes. In subsequent span tests, subject-produced numeral names led to dramatic increases in span scores. The equivalences provided precursors of verbal…

Provides a rebuttal to critical comments on the author's earlier article concerning the concept of epistemological rationality. Main disagreements center on the view that the use of terms with evaluative connotations about cognitive functions have a potential for abuse and that one cannot make judgments about the relative efficacy of the…

Eliminative connectionism as a theory of how humans generalize universal relationships to unfamiliar instances cannot account for the way universals are extended to arbitrary items. The discussion shows that the class of eliminative connectionist models currently in vogue cannot extend universals outside the training space. (SLD)

Focuses on students' ideas of average in differing contexts from two perspectives, one of which reflects the structural complexity of concepts as they are expressed and the other which documents the prevalence of ideas associated with three common mathematical measures of average--mean, median, and mode. (Contains 35 references.) (ASK)

The learning organization concept is the lowest of a three-stage hierarchy of learning-wisdom-enlightenment. This sequence is related to the evolution of the human mind from prepersonal to personal to transpersonal. (SK)

Focuses on children creating representations on paper for situations that change over time. Articulates the distinction between homogeneous and heterogeneous spaces and reflects on children's tendency to create hybrids between them. (Author/MM)

Reviews vantage theory and makes a claim that it does not replace, but coexists with a semantics for color terms. Identifies basic facts about countability in English, and presents further evidence of the fact that the grammar of number and quantification in English is exploited to reveal different conceptualizations of what is spoken of. Claims…

Presents the semantic information theory, formulated by the philosopher Fred Dretske, as a contribution to the discussion of metatheories and their practical implications in library and information science. Highlights include mathematical communication theory; digitization, perception, cognition, and concept formation; information and knowledge;…

In a recent study of conceptual combination, Estes (2003) presented evidence for the priming of relational information in the absence of shared constituents between the prime and target (e.g., "pancake spatula" was interpreted more quickly following "bacon tongs" than following "city riots"). He argued that these data support the view that…

This paper considers mathematical abstraction as arising through a natural mechanism of the biological brain in which complicated phenomena are compressed into thinkable concepts. The neurons in the brain continually fire in parallel and the brain copes with the saturation of information by the simple expedient of suppressing irrelevant data and…

Sociocultural and cognitive perspectives hold to epistemically different views on knowledge acquisition and change. While sociocultural perspectives point to social experience as the principal source of knowledge, cognitive perspectives emphasize the importance of the individual mind and reasoning as the primary source of knowledge. Herein, I…