This paper gives a brief introduction to a discipline called the cognitive science of mathematics. The theoretical background of the arguments is based on embodied cognition and findings in cognitive linguistics. It discusses Mathematical Idea Analysis, a set of techniques for studying implicit structures in mathematics. Particular attention is…

An overarching learning theory is presented, based on assumptions that all learning includes (1) external learner-environment interaction and internal acquisition and elaboration and (2) cognitive, emotional, and social dimensions. The framework depicts four types of learning: cumulative, assimilative, accommodative, and transformative. (Contains…

Outlines a model of mathematical understanding as a whole, dynamic, nonlinear, recursive growing process, entailing "folding back" for the reconstruction of inner level knowing. Presents examples from seventh graders' work. Discusses teacher awareness of student level of understanding, and implications for development of mathematics…

Presents background information about Vygotskian theories. Describes Vygotsky's Zone of Proximal Development (ZPD). Discusses a model of attitude development that incorporates the ZPD, meta-awareness, the components of an attitude, and factors influencing attitude development. Suggests educational implications. (45 references) (MDH)

Proposes a model for the growth of mathematical understanding based on the consideration of understanding as a whole, dynamic, leveled but nonlinear process. Illustrates the model using the concept of fractions. How to map the growth of understanding is explained in detail. (Contains 26 references.) (MKR)

This paper summarizes the recent work of the Maryland Physics Education Research Group on analyzing student learning in introductory university physics. This work is carried out in a model of student thinking and learning based on principles from cognitive science. The model permits a better understanding of, and diagnosis for, the state of both…

A 32-item self-efficacy scale for computer programming was developed, primed to the C++ programming language. The scale was administered to 421 students at the beginning and end of an introductory course in C++ programming. There was growth in self-efficacy between two administrations of the scale 12 weeks apart, particularly for students who…

Describes a study that investigated whether scientific and nonscientific understandings in the same content area are linked. Finds that students' (n=107) explanations indicate that they were using an "if-then" type of reasoning which linked scientific and nonscientific conceptions. Contains 39 references. (Author/WRM)

The concept of consciousness played a central role in Vygotsky's research and theory. Unfortunately, with the advent of behaviorism, consciousness fell into disfavor. One of the major obstacles in studying consciousness is that there is no single acceptable definition of the term. Various researchers have dealt with five different aspects of…

This paper analyzes Bogdanov's theory of knowledge as found in philosophical dialogues and essays. The style of Bogdanov's writing and his ideas on philosophy, science, scientific constructs, truth, human knowledge, objectivity and ethics are discussed. These ideas are compared to the constructivist view of knowledge. (CW)

This paper suggests that the systems of representations that we use in mathematics have a cultural origin and concludes that the knowledge produced with the help of these systems of representation likewise has a cultural origin. This assertion forces a reformulation of the issue of objectivity in terms that differ from those inherited from…

Compared the effects of constructivist instruction and instruction based on texts and demonstration on third-graders' conceptualization of force. Found that constructivist instruction was more effective. Patterns of reasoning related to force were identified in levels of conceptualization. (JPB)

Introduces the ideas of "distal" knowledge of the nature of science and "proximal" knowledge of the nature of science. Suggests that viewing these two kinds of knowledge structures within modern information processing frameworks that delineate roles of epistemological and metacognitive knowledge in learning should guide future research. (Contains…

The Enneagram is a model of human consciousness. It describes each of the nine strategies that people adopt to understand the world and others. This guidebook is intended to be used with the video of the same name, which describes the nine perspectives on learning. The book provides a Type-related context to the comments made by the students on…

Issues concerning student intellectual development during college are considered in a symposium paper and in two reactions by faculty members. The symposium was sponsored by Bowling Green State University as part of the Academic Outcomes Project, which explores the effect of college on student growth and development. The reflective judgment model…