An understanding of geologic time is comprised of 2 facets. Events in Earth's history can be placed in relative and absolute temporal succession on a vast timescale. Rates of geologic processes vary widely, and some occur over time periods well outside human experience. Several factors likely contribute to an understanding of geologic time, one of…

Summarizes experiments indicating that a basic key to learning is the development of concepts of pattern recognition and the appropriateness of using a particular theorem. (Author/SK)

Preservice teachers observed the performance of primary children (age 8) doing a variety of concrete mathematical tasks. (SD)

This paper discusses the theories of conceptual change and how they explain the difficulties in mathematics learning, especially in enlarging the number concept. Two studies are presented, one of which examines the research questions: What is the role of prior knowledge in students' answers to questions about the density of rational and real…

College students, in three experiments, learned to recite a counting pattern in the base three number system. Although all subjects learned to a criterion of two errorless trials, learning with different rule systems resulted in different levels of understanding and performance on transfer tasks. (GDC)

The uses of verbal rules in solving arithmetic problems are presented. Thirty-six problems were used in individual testing of five students who were enrolled in a remedial mathematics course at a community college. Two or three weeks prior to the individual exams, the students had been tested in their class on the material. The study indicated…

A study of a class of numbers called 'Good numbers' can provide students with many opportunities for investigation, conjecture, and proof. Definitions and proofs are presented along with suggested questions. (MNS)

Research on college students' ability to estimate means and variances for sets of data showed that they were more able to estimate means, and that various characteristics of the data (e.g. magnitude of numbers) influenced the accuracy of estimates. (SD)

Preservice elementary teachers were given the task of showing a special case of the Pythagorean theorem by paper cutting. In the process they developed approximations to the square root of two. (SD)

Examples of diversions with cards that may be used to illustrate the concept of a cyclic group and structural properties of the integers modulo a prime are presented. (MNS)

This book attempts to introduce students to the creative aspects of mathematics through exploratory problems. The introduction presents the criteria for the selection of the problems in the book. Criteria indicate that problems should: be immediately attractive, require data to be generated or gathered, appeal to students from junior high school…

Provided are examples from many domains of mathematics that illustrate the Fubini Principle in its discrete version: the value of a summation over a rectangular array is independent of the order of summation. Included are: counting using partitions as in proof by pictures, combinatorial arguments, indirect counting as in the inclusion-exclusion…

This paper describes a workshop that aims to change adult students' attitudes toward early number work in order to give them a different perspective and help them make mathematics their own so that they will no longer be looking for the teacher's approval to tell them whether what they have done is correct. (ASK)

This book is about children's needs for intellectual rigor, as seen through the work and discourse of five undergraduate elementary education students who constructed a number system in base five and then reflected on their experience in the light of what they know about young children's mathematics. The deeper purpose of developing a number…

Eleven research reports in the area of models of learning mathematics are presented in this publication of the Mathematics Education Reports series. The papers represent a mixture of theories, viewpoints, and references to other areas. Content areas addressed range from preschool to college levels. All the papers are concerned with the learning of…