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…

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)

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)

Presents a three-phase process that connects writing and cooperative problem solving to each other and to mathematical skills and concepts. The three phases are: (1) writing to communicate mathematics; (2) cooperative learning; and (3) problem solving. Provides examples illustrating each phase. (MDH)

Presents a series of activities developed from the "Arithmetic Teacher's" regular feature entitled "Problem Solving: Tips for Teachers" to help students develop skills in each of the four steps of Polya's problem-solving process: (1) Understanding the Problem; (2) Making a Plan; (3) Carrying Out the Plan; and (4) Reflecting…

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…

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)

Describes the use and rationale of "Silent Teaching," a teaching technique in which the teacher remains silent as students generate and evaluate hypotheses while trying to understand an as-yet undiscovered concept. (MDH)

Describes the "number 2 arithmetic challenge," an activity in which students score points by creating examples using the number 2 that satisfy an unknown rule. Computers are utilized to verify and record examples. Conflicts with computer responses create situations to explore negative numbers, fractions, mixed numbers, the order of…

Recommendations for teaching problem solving stem from a discussion of the differences in the functioning of the left and right hemispheres of a person's brain. (JT)

Instruction in estimation is proposed as a natural context to develop and practice important thinking skills. These skills are described and estimation activities are proposed for each. (MNS)

One view of mathematical thinking is described, followed by detailing of the characteristics of a problem-solving program necessary to develop this kind of thinking. (MNS)

When the words "problem" and "answers" are used in connection with computational exercises, students think they are solving problems. Distinguishing between computational forms and problems is illustrated with a variety of topics. (MNS)