Two studies with 28 Boston College undergraduates tested the hypothesis that people who report a poor sense of direction (SOD) have an impaired ability to use spatial information in an abstract or symbolic way. The hypothesis was not supported. Poor SOD correlates to a mental egocentrism in self-to-environmental-object relations. (TJH)

Proposes a model of mathematics conceptual development consisting of two phases: abstraction and generalization. Illustrates model by references to the development of multiplication and angle concepts. (19 references) (MKR)

Asserts that poetry is a basic way for individuals to learn enough about their culture to become a welcome member of it. Offers the views on poetry of several poets. Discusses the benefits of using poetry, rather than logical mathematical thought, to teach students how they view reality. (PRA)

Visual learning enhances cognitive understanding of abstract concepts. Perception of such ideas as causality is enriched by visual examples. Perceiving should not be separated from thinking. (SK)

Three experiments involving 107 adults who performed mental rotation tasks explored how location information is incorporated into image representation. Results suggest that image is coded retinotopically in image representations and that there is no spatiotropic transform in the early stages of visual processing. (SLD)

Investigates procedural understanding of university students at the freshman level, prior to instruction, in the context of experimental work in physics. Proposes two types of reasoning used by students in the laboratory. Indicates a high degree of consistency of these modes of reasoning across experimental phases of data collection and…

Evaluated the contribution of rule, exemplar, fragment, and episodic knowledge in artificial grammar learning using memorization versus hypothesis testing training tasks in 5 experiments involving a total of 163 college students. There was no evidence that memorization led to abstraction of rules or encoding of whole exemplars. Results support an…

The ability of some individuals with mental retardation to identify prime numbers despite their lack of necessary arithmetical skills is discussed. The article suggests that a distinction between prime and nonprime numbers can be made by utilizing the tendency of visual perception to be symmetrically organized. (Author/DB)

Demonstrates that even very young children are capable of abstract thought and expressions of their own spirituality, and argues that spirituality can and should be a part of the educational curriculum. The author suggests that spirituality in education, if nurtured, enhances the educational experience and helps the child fully develop as a human…

Describes the mathematical processes that occur during problem solving, reasoning, and communication. Provides examples from mathematics education research with preschoolers. (ASK)

Presents an exploratory study with expert university students to determine how students could reseal the rupture and restore a sense of unity between the figural and conceptual components of conic sections. Suggests certain tools of semiotic mediation which could be introduced to enable students to achieve the conceptual oversight that is possibly…

This paper describes the process for employing two principal instruments for relating the categories identifying the central phenomenon in grounded theory analysis. The Conditional Relationship Guide contextualizes the central phenomenon and relates structure with process. The second tool, the Reflective Coding Matrix, captures the higher level of…

This article describes the rich thinking that can go into solving a difficult equation. The authors also give some sources for challenging mathematical problems.

In 4 experiments, the authors explored the role of visual layout in rule-based syntactic judgments. Participants judged the validity of a set of algebraic equations that tested their ability to apply the order of operations. In each experiment, a nonmathematical grouping pressure was manipulated to support or interfere with the mathematical…

Preinstruction SAT scores and normalized gains (G) on the force concept inventory (FCI) were examined for individual students in interactive engagement (IE) courses in introductory mechanics at one high school (N=335) and one university (N=292), and strong, positive correlations were found for both populations (r=0.57 and r=0.46, respectively).…