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)

A systematic search is given for products where reversing the digits does not change the answer. Related questions are suggested that can be solved by the same discovery approach. (MP)

An activity is presented that involves an unusual multiplicative operation on natural numbers. Described are interesting properties that students may discover when using the new operation. (JP)

The algorithms for finding cube roots is approached by slicing a cube. (SD)

An activity project is described which encourages students to question and experiment. Appendices provide examples of student results. (MNS)

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…

Presents a mathematics investigation in which students discover number patterns in physical structures and express their generalizations algebraically. (MKR)

A three-dimensional classification system of mathematical problems is given. A background philosophy is constructed through an analysis of different approaches to problem-solving research, leading to the statement of 5 theses and the objectives for the study. An exploratory study of mathematical problem-solving processes is conducted within this…

Some number investigations on the multiplication table are provided by a sequence of four activity sheets. Beginning with examples of triangular and square numbers, the activities lead to the generalization. (MNS)

Five activities involving an array of numbers called an even triangle are given. Properties of the triangle are listed and some generalizations are proven. (MP)

Presents three investigations that extend the problem of counting the number of squares on a grid in two dimensions to an analogous problem of counting the number of cubes in a three-dimensional cubic array. (MDH)

A set of three worksheets is provided, along with a guide for the teacher. Using manipulative materials, students investigate the difference between the consecutive sums of the numbers along the three sides of a triangle. (MNS)

The activity provides practice plotting points in the Cartesian plane, develops inductive skills in pattern recognition, develops verbal and translation skills, and acquaints students with some properties of linear relations. Three worksheets are included. (MNS)

These documents are three separate sets of student problems and teaching guides geared towards calculators. Series A is designed for pupils from ages 10 to 13; "B" is structured for 13 through 16, and "C" for 16 through 19. The materials are designed to provide activities for investigation and exploration of number properties and patterns that are…