This paper introduces an artistic model of planning and problem solving. The model is based on a case study of processes engaged in by a college art student during the course of producing a senior thesis in batik (a wax-resist fabric dyeing process). Based on the premise that knowledge of the creative process is essential to understanding the…

This monograph focuses on educational research on the processes and natures of problem-solving activities in mathematics. The first chapter presents an overview to both the field and the document itself. All of the studies reported reflect interrelated investigations carried out at the University of Madison-Wisconsin, as partial fulfillments of…

The exploration mode of content presentation is discussed. (MP)

Some uses of fruits and seeds to facilitate problem solving and cognitive processes in young children are suggested. (MR)

Twenty-three children in each of 2 first-grade classrooms were observed as they worked in pairs with the computer language Logo in a learning-by-discovery context. Describes children's behaviors related to planning, correction of errors, reflection, causality, and procedure-writing. (RJC)

Describes a laboratory course, modeled on the approach developed by Robert Karplus for physics laboratory courses, emphasizing discovery learning. (SK)

The mathematical nature of the product barcode that now appears on many supermarket goods is discussed. Particular attention is given to the nature and formula of a "check digit" used to verify that product numbers are correctly scanned. Several possible student activities related to this code and others are suggested. (MP)

A discussion of the reasons for the new design of international standard typing paper (AY) with dimensions of 210 mm by 297 mm leads to a discussion of the ratio of the sides and geometric concepts involving similar rectangles. (MP)

Some uses of a computer in a high school statistics class are presented. The increased student involvement in the lesson is seen as a result of the line demonstration of the mathematical concepts involved. A special application program written in BASIC is included. (MP)

An approach to teaching geometry is promoted that allows students to decide for themselves what they could prove from given information. Such an approach allows pupil involvement in the personal process of discovering mathematical ideas and formulating problems. It is noted these methods will not work for all. (MP)

These exercises are designed to expose students to the nature and effects of inflation and consumption rates. Pupils are expected to see how long it takes for costs to increase to certain levels, and how quickly various growth rates can deplete a finite resource. Worksheets suitable for duplication are provided. (MP)

A problem that is seen to allow room for student discovery and exploration is detailed. A discussion starts with an examination of the generation of a general equation for the sum of a set of consecutive integers, and leads to an exploration of more complex sums. (MP)

The unmarked protractor appears to have been ignored in considerations of construction tools other than the standard straightedge and compass. Some geometric problems are presented which are designed to be done using only the unmarked protractor. They are thought to provide challenges to better students. (MP)

A set of programs, designed to supplement a high school or college course in trigonometry, is described. Student exploration is stressed. (MP)

This article describes and tests a theory of scientific discovery learning based on the Scientific Discovery as Dual Search (SDDS) model. A study of 22 university chemistry students determined that conditions for performing a search operation in hypothesis space include sufficient knowledge of the search operation and reasons for choosing a…