Presents a problem solving strategy developed by a second grade student that goes beyond modeling an intuitive or informal interpretation of an operation to solve division problems. Concludes that good teaching should build on pupil's existing preinstruction knowledge and recognize a pupil's attempts at creative solutions. (MDH)

Discusses research findings that relate to teaching fractions for conceptual understanding. Gives teacher/student dialogues that illustrate the thought processes of students as they form part-whole and improper fraction concepts. (MDH)

Described is a strategy that shows students how one mathematical concept can be connected to another. The emphasis is on both process and product and can lead to creating a learning environment where students do mathematics as mathematicians do. (KR)

Discusses the use of drawings to nurture problem-solving attitudes and independent learning. Drawings help develop thinking skills, clarify misconceptions, develop representational preferences, supply a context for relationships in K-8 mathematics, and illustrate mathematical connections. (MDH)

Describes the benchmark and decomposition-recomposition estimation strategies and presents five techniques to develop students' estimation ability. Suggests situations involving quantities of candy and popcorn in which the teacher can model those strategies for the students. (MDH)

Described is a strategy where students write stories to help in the process of solving problems. The strategy is a five-step process which includes prewriting, writing, conference, revising and editing, and publication. (KR)

Describes four methods to structure estimation activities that enable students to make connections between their understanding of numbers and extensions of those concepts to estimating. Presents activities that connect estimation with other curricular areas, other mathematical topics, and real-world applications. (MDH)

Describes the method to solve problems called T-E-M-T-T: trial, error, and modified trial through technology. The method integrates students' skills of estimation, mental computation, and appropriate choice of calculator use. Includes 2 activities for each of grades K-4 and 5-8 that illustrate the method. (MDH)

Presents two spreadsheets for middle school students applying Polya's heuristic to help develop number sense, reasoning abilities, and problem-solving skills. Spreadsheet 1, "the coin problem," allows students to vary coin quantities to total $8.32. Spreadsheet 2, "ratios," develops number relationships while finding 3 3-digit…

Presents three features of "Good" questions: requires students to do more than simply remember a strategy to answer; promotes student learning while answering the question; and have several acceptable answers. Considers how questions can be used to cater to the range of student abilities. (MDH)

Discusses how a single problem can be utilized to discuss mathematical skills and concepts at several different levels. Presents a problem involving fractions examined at the following four levels according to the abilities of the students: (1) finding solutions; (2) identifying methods for finding solutions; (3) exploring similar examples; and…

Provides excerpts from videotaped dialogue between two third grade students and their interactions with their teacher while solving a counting problem to describe student thinking and communication during the task. Discusses the teachers' role in the dialogue and implications for classroom practice. (MDH)

Presents the results of a survey of 165 seventh grade students asked to respond yes, no, or maybe to 21 metacognitive statements about their cognitive activity on a mathematical word problem. Suggests how to use the responses as a basis for developing classroom activities. (MDH)

Elaborates the final step of Polya's heuristic model, reflecting, to improve students' problem-solving performance. After checking answers for accuracy, the following steps are suggested: (1) test reasonableness and practicality; (2) write a summary paragraph; (3) find other solutions; (4) change the conditions; and (5) extend the problem. (MKR)