Self-advocacy, self-management, self-regulation, and self-knowledge are complex terms, often considered forms of self-determination. Whatever term you may use, helping young adults with intellectual disability (ID) make authentic decisions about their own goals and behaviors often results in passive agreement. Even though advancing…

Presents a generalization to the classic prisoner problem, which is inherently interesting and has a solution within the reach of most high school mathematics students. Suggests the problem as a way to emphasize to students the final step in a problem-solver's tool kit, considering possible generalizations when a particular problem has been…

This note contains material to be presented to students in a first course in differential equations immediately after they have completed studying first-order differential equations and their applications. The purpose of presenting this material is four-fold: to review definitions studied previously; to provide a historical context which cites the…

A metacognition model that can help understand general problem-solving deficits in learning disabled students is presented. Two components of metacognition are highlighted: executive processes and attributional beliefs. An educational package combining these components with specific strategy training is illustrated as an approach to improving…

Describes students' generalization strategies and justifications as they engage in patterning activities. (YDS)

Discusses the process of generalization. Illustrates the process by generalizing the classic problem of how a farmer can get a fox, a goose, and a bag of corn across a river in a boat that is large enough only for him and one of the three items. (MDH)

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)

Investigates the question concerning the maximum number of lines of symmetry possessed by irregular polygons. Gives examples to illustrate and justify the generalization that the number of lines of symmetry equals the largest proper divisor of the number of sides. Suggests related classroom activities. (MDH)

Presents 5 activities for the K-1, 2-3, 4-5, 6-8 grade levels and for in the home in which students explore the concept of combinations. Each activity includes a lesson plan to investigate a combinatorics problem appropriate for that grade level. Provides reproducible worksheets. (MDH)

Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…

Presents an activity in which students develop their own theorem involving the relationship between the triangles determined by the squares constructed on the sides of any triangle. Provides a set of four reproducible worksheets, directions on their use, worksheet answers, and suggestions for follow-up activities. (MDH)

Domino games are used to illustrate problem-solving techniques in a college principles-of-mathematics course. Students develop tables and use Pascal's triangle to find the total number of pips and the sum of numbers on the pieces. (DC)

Presents a hands-on mathematics task that can be investigated experimentally to produce a sequence of numbers. Describes ways to extrapolate values of the table of numbers by formulating and verifying a conjecture related to the pattern in the numbers. (MDH)

Many of the most talented authors and artists of the past and present have shared their thoughts and their gifts with young children through picture books. Many picture books allow young children to explore important ideas and to stretch their minds far beyond rote memorization. Young children absorb knowledge at a very rapid pace. In an age of…

Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)