Abstraction is a major concept in computer science and serves as a powerful tool in software development. Pattern-oriented instruction (POI) is a pedagogical approach that incorporates patterns in an introductory computer science course in order to structure the learning of algorithmic problem solving. This paper examines abstraction processes in…

The books in this series provide an essential ingredient in the transition from concrete mathematical experience to the symbolic reasoning used in algebra. They aim to guide the student in building and extending manipulative patterns, collecting numerical data, and analyzing the results. The main objective of the activities in this book is for the…

The relative importance of spatial-position as a memory aid in a block pattern reproduction task was investigated by analyzing the object-selection and object-placement strategies of 69 nursery school children. Subjects were given a task modeled on Piaget's assessment of Static Reproductive Images and Action that had been modified into a…

This study examined the development of young children's ability to solve linear patterning problems and investigated constructs of logical thinking which underlie the hierarachical order of the cognitive processes involved. A total of 252 children ranging in age from 4 through 7 years participated in the study. A range of ability and socioeconomic…

A familiar Christmas song described as a second-year algebra problem is presented in "The Twelve Days of Christmas". Five strategies for solving inequalities are discussed in "Solving Algebraic Inequalities". (JT)

Two experiments demonstrate that 10- and 13-year-olds can learn to detect interactive patterns in data. Results also indicate the advantages of creating formal models of solution strategies and using them as a basis for instructional procedures. (Author/DEP)

A method for solving certain types of problems is illustrated by problems related to Fibonacci's triangle. The method involves pattern recognition, generalizing, algebraic manipulation, and mathematical induction. (MP)

The author describes various professionals' need for the ability to diagnose problems in their areas of expertise. Three psychological models are examined: (1) scientific rationality, (2) the template model, and (3) the interactionist model. The author discusses the integration of information on diagnostic processes into the adult professional…

Cross-sectional and longitudinal data from students as they advance through the middle school years (grades 6-8) reveal insights into the development of students' pattern generalization abilities. As expected, students show a preference for lower-level tasks such as "reading the data," over more distant predictions and generation of abstractions.…

Three games played with regular bridge decks of cards are described. By playing the games students gain practice in use of basic operations on integers and in the development of strategies. (SD)

Cognitive theories of problem solving and suggestions made by cognitive psychologists regarding how to teach problem solving are reviewed. Theories and suggestions from creativity research are also considered. The results are summarized in terms of a description of how high levels of proficiency in problem solving are acquired and how problem…

A set of geometric pieces is used to solve problems involving geometry, combinations, division, and money. (JT)

A problem concerning the generation of an array of numbers is posed. The author examines the use of this problem in several secondary-school and college classes. (SD)

This activity is designed to help students recognize and extend rectangular patterns and to use patterning to formulate rules for "nth" cases. Three worksheets are included. (MNS)

Curiosities offer an interesting alternative to traditional methods of attacking problems. An illustrative situation is given, with graphical, computer, and analytical methods used to solve the problem. (MNS)