Investigates whether distinctions in cognitive structures between formal and concrete operational students effect their ability to produce an accurate cognitive structure, retain geometric content, and retain cognitive structures. Concludes that clear structures can be derived for the students. (Author/YP)

Student comments about having time in class to think and solve problems are presented. Stressed are teaching methods which allow students to familiarize themselves with the problem, think about solution processes, work through the solution process, and reflect while solving a problem. (CW)

The purpose of this study was to investigate the effect of an eclectic thinking processes model on the logical reasoning abilities of students in grades six through twelve. The experimental school consisted of 159 students whereas the control school had 111 students. The Group Assessment of Logical Thinking (GALT) was administered to the sample as…

The author defines and discusses the cognitive theory of constructivism as it relates to teaching mathematics. It is suggested that the philosophical and theoretical view of knowledge and learning embodied in constructivism offers hope that educational processes will be discovered enabling students to acquire deep understanding rather than…

Compared are the van Hiele levels of geometric thinking and the geometry curriculum recommended by the National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics. Activities which illustrate the various levels are provided by grade level with procedures. (CW)

Reported is a naturalistic study of the role of mathematical paradoxes in the preservice education of high school mathematics teachers. Findings indicate that the model of resolving paradoxes as applied in this study has relevance to such aspects of mathematics education as cognitive conflicts, motivation, misconceptions, and constructive…

Identified is research related to concept formation; the chronology of identity and equivalence conservations; the relationship of mental age to performance on number concept tasks; perceptual, attentional, linguistic, and social factors; and the potential use of cognitive developmental criteria as measures of ability for both normal and retarded…

Children's responses to an alternative model over three lessons were described and their learning assessed in a posttest. Their responses and performances were compared to that of a similar group of children learning through a conventional number line model. The two models were compared from practical and theoretical viewpoints. (Author/CW)

The contrast between the teaching of reading and mathematics is drawn. A new set of learning conditions for mathematics is presented based on a model of reading instruction. Immersion, demonstration, engagement, expectations, responsibility, use approximation, response, refinement, and outcomes are discussed. (CW)

This monograph represents 5 years of collaborative discussions among individuals interested in improving the teaching and learning of mathematics beginning in 1985 with the planning of a conference and culminating in the production of this collection of 13 papers to be presented at the conference. Chapters include: (1) an introduction…

Discussed are some situations students face that result in cognitive conflict, possible sources of these conflicts, and strategies which students use to resolve, remove, or circumvent them. A global account for observed systematic errors is offered based on a general problem-solving rule called the "Matching Rule." (KR)

After observing secondary school students having great difficulty learning geometry in their classes, Dutch educators Pierre van Hiele and Dina van Hiele-Geldof developed a theoretical model involving five levels of thought development in geometry. It is the purpose of this monograph to present English translations of some significant works of the…

Begins with the assumption that by practicing something one often learns something else. A discussion is presented on the historical and social development of knowledge, the cognitive development of students, the role of teachers, and the meaning of learning situations. (PK)

Discussed are inconsistencies and cognitive conflict with respect to current mathematical knowledge of students and how that knowledge might be modified is discussed. The inconsistencies that students generate for themselves and those produced by the teacher are described. (KR)

Discussed are the issues of inconsistencies and compartmentalization and the use of inconsistencies in the classroom. Included are discussions on paradoxes, the naive student, logical reasoning ability, and the development of the students' cognitive structures. (KR)