Five reasons are discussed for teaching estimation involving utility, problem solving, concept formation, calculations, and attitude. Specific types of estimation are analyzed and examples given. (MP)

A distinction is made between basic computational skills and skills related to applied mathematics and verbal problem solving. The advantages of using calculators for teaching the latter skills are discussed. (MP)

Examples from almanacs are used to provide real-life problems that involve estimating, computing, and thinking. (MP)

The author suggests that, through using the outlined question model and suggested classroom activities, elementary students will improve their abilities to analyze routine, one-step word problems and make a plan for the solution. It is further argued that the same algorithm can be applied to multistep problems by using specified questions. (PK)

Suggests that problem-solving extensions are appropriate experiences for differentiating learning experiences for students with high abilities. The extensions fall into four major categories: pattern and generalization, new concepts and vocabulary, creativity, and making value judgments. (PK)

This classic reprint was first published in 1955. Fehr discusses how to determine what is taught, and makes specific comments on the roles of planning, meaning, practice, learning, and problem solving. (MNS)

Indicates the shortcomings of paper-and-pencil tests. Reports the effect of an interview-and-teaching method for students who obtained correct answers by a mechanical process but lacked a conceptual foundation. Five references are listed. (YP)

Applies the Lesh Translation Model to develop conceptual understanding by showing relationships between five modes of representation proposed by Lesh to learn multiplication of fractions. Presents five teaching activities based on the translation model. (MDH)

Proposes helping students understand fractions by establishing connections between students' informal knowledge of fractions and the mathematical symbols used to represent fractions. Sample dialogues demonstrate how these connections can be made. (MDH)

Presents teaching methods to rectify the tendency of students and even teachers to divide the smaller number into the larger in problem situations requiring division, while recognizing the impossibility of the answer in the situation. (MDH)

Described are three activities and variations that can help students to understand the concept of place value. Allowing students to use concrete materials and helping them to bridge the gap between manipulatives and paper-and-pencil tasks are emphasized. (KR)

Presents four sets of activities to develop the concepts of data analysis and graphing. Students estimate sample populations using beans, examine graphs from newspapers and magazines, predict the most popular color of cars, and simulate quality control in a manufacturing process. (MDH)

Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)

Instructional strategies are presented that illustrate ways of developing students' understanding of nonnumerical notation that are compatible with a constructivist stance. The concepts of using letters to represent a range of values and those used to represent unknowns are discussed. (KR)

Discusses the two overgeneralizations "multiplications makes bigger" and "division makes smaller" in the context of solving word problems involving rational numbers less than one. Presents activities to help students make sense of multiplication and division in these situations. (MDH)