This book uncovers the important issues in language learning and teaching in the intelligent, digital era. "Social connectivity" is a contemporary style of learning and living. By engaging in the connectivity of physical and digital worlds, how essential parts of language learning and teaching can be achieved? How can the advanced…

Discusses the place of problem posing in mathematics education. Shares some approaches to implementing problem posing and critiquing in the classroom. (ASK)

Presents a classroom scenario in which a student concocts a unique solution to a standard circle exercise and the class attempts to verify if the solution works for all cases of the problem. (MKR)

Views the mathematics curriculum in terms of things that can be worked out by someone (necessary) and things about which everyone needs to be informed (arbitrary). This view clarifies the roles that teachers and students have within the complexities of teaching and learning. (Contains 11 references.) (ASK)

Suggests that issues surrounding the teaching of algorithms focus not on whether to teach them but rather on balancing and connecting the development of algorithmic thinking. Presents an approach to help students develop their algorithmic thinking. Contains 18 references. (ASK)

Many teachers and administrators have recognized that problem solving and reasoning represent two of the primary goals in the education of children. In order for teachers to achieve these goals, they must have appropriate materials available to them. This book includes materials to help teach and assess problem solving and reasoning. The first six…

This book addresses different types of thinking, including critical, creative, and analytical, and presents a variety of problem-solving strategies, along with specific ways they can be taught to students. The main emphases of the book are thinking and mathematics, problem solving, and the application of computational skills. The problem-solving…

Analyzes a discussion among students as they try to find the perimeter and area of an irregular shape on a geoboard. Considers implications for teaching and suggests reflecting on discourse, students' attributes, and mathematical tasks. (DF)

Argues that the way in which students solve a particular problem can be analyzed to gain insight into how students think about the mathematics involved. Discusses the use of knowledge gained from listening to student conversations about their strategies to orchestrate classroom discussions. (ASK)

Reports on a mathematical investigation of fractals and highlights the thinking involved, problem solving strategies used, generalizing skills required, the role of technology, and the role of mathematics. (ASK)

Presents the results of a study that aimed to incorporate a wide range of problem posing situations into students' problem solving in a classroom project with mathematically-able students in the first two years of secondary school. (Contains 15 references.) (ASK)

Develops a diagnostic framework that supports teaching and learning in situations that are suitable for students having difficulty in addressing basic problems. Uses data collected from 47 students in a senior mathematics course. Contains 63 references. (Author/ASK)

Presents an activity to involve students in mathematical communication and creative thinking. The activity is similar to the "pass it along" gossip game in which each person in a chain adds a piece of information. The class analyzes the resulting mathematics problem using George Polya's problem-solving techniques. (MKR)

Presents an activity, involving pentagons and using a figure manipulator such as The Geometer's Sketchpad, that requires students to reason geometrically without making unsubstantiated assumptions based on diagrams. (MKR)

Utilizes the notion of a students' proof schemes and outlines categories of proof schemes to evaluate the justifications given by students so that teachers can plan instruction to move them toward more sophisticated ways of reasoning. Contains 22 references. (ASK)