Although abstraction is widely understood to be one of the primary components of computational thinking, the roots of abstraction may be traced back to different fields. Hence, the meaning of abstraction in the context of computational thinking is often confounded, as researchers interpret abstraction through diverse lenses. To disentangle these…

A familiar procedure for generating magic squares is reviewed. A surprising pattern is noted. (MNS)

Described are results obtained by students investigating double-diagrams, including discoveries of properties and accompanying proofs. (MP)

Relationships between the linear dimensions, surface area, and volume of parallelepipeds are examined. (SD)

Four categories of abuses are discussed: calculations, games and puzzles; mystical button pushing; and checking answers. Useful activities are illustrated for the categories of calculations, patterns, exploration, applications, and new content. (MP)

Advocated is developing intuitive ideas of limits whenever the opportunity arises in elementary mathematics. Examples are given for geometry, fractions, sequences and series, areas, probability, graphing, and the golden section. (MNS)

Similar rectangles are the basis of a set of activities using newspaper. Topics arising include infinite series and Pythagorean theorem. (MP)

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

Transformations are defined and described through many examples. Teaching aids and activities for teaching about transformations are suggested. (JT)

Presents three investigations related to the game Bulgarian Solitaire. Investigations ask students to find and represent optimal solutions to the problem, to identify cyclical solution patterns for different numbers, and to respond to questions involving the number and nature of the cyclical solutions. An appendix provides answers to questions.…

Using the methods described, pattern representation of operations in modular systems can be developed. (SD)

Activities are described that reinforce knowledge of multiplication facts and also give students practice in making generalizations that improve problem-solving skills and provide a foundation for work with fractions. (MNS)

The problem-solving skills of logical thinking, critical thinking, visualization, and communication skills are linked with some activities for students. Sample activities with logic, strategies and patterns, breaking fixed notions, open-minded problems, spatial visualization, and communication are described. (MNS)

Activities and problems are interspersed with commentary in this book on the learning and teaching of mathematics. The emphasis is on helping students to enjoy mathematics through an awareness of structure and patterns. The chapter titles are as follows: (1) "My Three Sons--A Game"; (2) "The Tower Game"; (3) "Mathematical Games on a Different…