Surface and relational similarity were examined in two experiments involving isomorphic and nonisomorphic analogical transfer, using direct-mapping and cross-mapping conditions. In the first experiment, third and sixth graders exhibited mapping based on relational similarity more frequently than did kindergartners; in the second, most four- to…

A social semiotic approach to math is necessary because of the increasing significance of abstract tools in the workplace. A case study from the coal mining industry illustrates the need to recognize mathematics as a socially constructed system and to contextualize math instruction. (SK)

Describes a study in which 383 children in grades 1 through 5 were individually interviewed to find out at what point they construct unit iteration out of transitive reasoning. Indicates that most children construct unit iteration out of transitive reasoning by fourth grade. Suggests a better approach to the teaching of measurement that presents…

Traces the evolution of college students' assumptions about knowledge and how it is gained, and examines how their judgment can be enhanced through teaching. Summarizes seven stages of reflective judgment, including three stages of prereflective thinking, two stages of quasi-reflective thinking, and two stages of reflective thinking. Suggests ways…

Encourages teachers to listen more carefully to what students say. Discusses two modes of reasoning in an effort to understand more deeply what students hear and the styles of reasoning that they might use in mathematics. (Contains 12 references.) (ASK)

Three experiments examined the role of representations in adolescents' deductive reasoning. Findings indicated that, with age, conditional reasoning improved on tasks containing permission conditional relations; reasoning fallacies increased on tasks containing causal conditional relations. Valid conditional inferences were more common on problems…

Formulates a framework for characterizing elementary children's (n=20) statistical thinking based on a review of research and a cognitive development model, and refines it through a validation process. Proposes four thinking levels which represent a continuum from idiosyncratic to analytic reasoning. Results confirm the four levels of children's…

Considers the cognitive mechanisms available to individuals which enable them to operate successfully in different parts of the mathematics curriculum, such as children's arithmetic shows divergence in performance. Explains how students cope with the transition to advanced mathematical thinking in different ways, leading once more to a diverging…

Describes students' investigative work that resulted from playing the game Set in an attempt to show how such games can be used to develop mathematical reasoning. (ASK)

Reacts to the publications "Curriculum Guidance for the Foundation Stage" and "National Numeracy Strategy: Framework for Teaching Mathematics from Reception to Year 6" published by the Department for Education and Employment in Great Britain. Makes the case for the marrying of formal and informal, abstract and concrete…

This article argues that advanced mathematical thinking, usually conceived as thinking in advanced mathematics, might profitably be viewed as advanced thinking in mathematics (advanced mathematical-thinking). Hence, advanced mathematical-thinking can properly be viewed as potentially starting in elementary school. The definition of mathematical…

Four experiments examined children's ability to reason about the causal significance of the order in which 2 events occurred (the pressing of buttons on a mechanically operated box). In Study 1, 4-year-olds were unable to make the relevant inferences, whereas 5-year-olds were successful on one version of the task. In Study 2, 3-year-olds were…

Two experiments explored the effect of linguistic input on 18-month-olds' ability to form an abstract categorical representation of support. Infants were habituated to 4 support events (i.e., one object placed on another) and were tested with a novel support and a novel containment event. Infants formed an abstract category of support (i.e.,…

In this paper, we explore Peirce's work for insights into a theory of learning and cognition for education. Our focus for this exploration is Peirce's paper The "Fixation of Belief" (FOB), originally published in 1877 in "Popular Science Monthly". We begin by examining Peirce's assertion that the study of logic is essential for understanding…

The teaching and learning of statistics has impacted the curriculum in elementary, secondary, and post-secondary education. Because of this growing movement to expand and include statistics into all levels of education, there is also a considerable interest in how to teach statistics. For statistics concepts that tend to be very difficult or…