This paper discusses the theoretical problem of matching and abstraction of concepts as the processes occur in human minds, and the structures used to represent these processes for use in automated, knowledge based systems. A basic premise of the paper is that hierarchies play a crucial role in structuring knowledge and in solving problems. Data…

When a simple game was presented as a challenge to a primary-school girl, she solved the problem, and went on to generalize her solution. (SD)

The author organizes some of the information known about the problem of dividing space by five planes in general position along with its extensions, and consolidates it to highlight some interesting patterns in both methods of solving analogous problems and their results. (MN)

Presents historical development on the construction of magic squares. Techniques presented for construction of even-numbered magic squares, and in particular the four-by-four magic square. (RP)

Three worksheets provide exercises involving triangular arrays of numbers. (SD)

Reviews studies of eye movements in reading and other information processing skills such as picture viewing, visual search, and problem solving. (BD)

Activity sheets posing problems in which students must examine and test various possibilities are presented. (SD)

Two theories of clinical problem solving are contrasted; studies of medical problem solving are described; evidence is presented to highlight the central role of experience in development of problem-solving competence; and implications for teaching and assessment of problem solving, especially in medical education, are suggested. (MBR)

Multibase arithmetic blocks are used to investigate the minimum number of blocks of each size to make a square of a given size in a given base. Generalizations are made to any size and any base through pattern recognition. The problem is extended to rectangles, cubes, and rectangular solids. (LS)

Describes an activity that utilizes four pattern blocks to help students understand and explain perimeter. Engages students in making and supporting conjectures about a scenario that involves trains composed of various shapes with different perimeters. (DDR)

Presented are 44 examples in which students are invited to guess what pattern of numbers is emerging and to decide whether the pattern will persist. Topics of examples include Pascal's triangle, integers, vertices, Fibonacci numbers, power series, partition functions, and Euler's theorem. The answers to all problems are included. (KR)

Motivated by the brain, neural networks are a right-brained approach to artificial intelligence that is used to recognize patterns based on previous training. In practice, one would not program an expert system to recognize a pattern and one would not train a neural network to make decisions from rules; but one could combine the best features of…

Artificial intelligence (AI) is the field of scientific inquiry concerned with designing machine systems that can simulate human mental processes. The field draws upon theoretical constructs from a wide variety of disciplines, including mathematics, psychology, linguistics, neurophysiology, computer science, and electronic engineering. Some of the…