Describes how 7th grade students were transitioned from using informal, conceptual methods to solving proportion problems using a formal procedure. (YDS)

Illustrates a way in which students can estimate the ratio of an area of a circle using the radius square. Discusses why the same value of pi appears in both the formulas for the circumference and the area of the circle. (YDS)

Provides a model for teachers to engage children in understanding problems and communicating their solutions in order to lead them toward becoming mathematically powerful learners. (Author/NB)

Explores self-regulated learning (SRL) theory in light of the reform vision of mathematics education depicted with "Principles and Standards for School Mathematics," asserting that implementation of mathematics reform makes possible the development of self-regulated learners while also necessitating developing self-regulated learners.…

Techniques for teaching linear regression are provided. Discussed are leverage and the hat matrix in simple regression, residuals, the notion of leaving out each observation individually, and use of this to study influence on fitted values and to define residuals. Finally, corresponding diagnostics for multiple regression are discussed. (MNS)

Provides problems to illustrate the potential power of mathematical intuition when confident problem solvers take the time to "play" with a problem and follow their instincts. (MKR)

Discusses varieties of open-ended problems in mathematics, including problems that are unsolved in the field of mathematics, are open with respect to solution method, are open to interpretation of the problem or solutions, or that invite other problems as follow-up. (Author/MKR)

Gives a short biography of George Polya and a summary of his suggestions for teachers. (15 references) (MKR)

Describes four word-and-picture problems through which students can hone their math skills, all of which involve shopping for goods and calculating prices of items that they would buy. Notes that shopping creates real-life problem-solving situations. (MDM)

Describes a study that investigates the difficulties students have with word problems and aims to find out what can be done to help students achieve some success with word problems while working independently. Concludes that a problem-solving approach to teaching mathematics and word problems is beneficial. Contains 20 references. (ASK)

Represents a college professor's view of children doing math after seven consecutive years of working with approximately 150 children solving word problems. (ASK)

Describes a personal problem solving-inquiry journey, working on a problem suggested by an activity on probability observed in a junior primary classroom. Presents reflective thoughts about the mathematical and pedagogical lessons to be learned from this journey. (ASK)

Suggests using manipulatives with young children to create imaginary solutions to fantasy situations. Includes activities that use the problem-solving format: stating the problem, brainstorming solutions, experimenting, carrying out the solutions, and evaluating the solutions. (JOW)

Presents solutions for a problem concerning doubling a recipe from a previous article on number concepts in the October 1997 issue. (ASK)

Shares a series of problems designed to provide students with opportunities to develop an understanding of applications of the definite integral. Discourages Template solutions, solutions in which students mimic a rehearsed strategy without understanding as the variety of problems helps prevent the construction of a template. (Author/ASK)