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)

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)

Explores possible outcomes of using the "Professional Teaching Standards" as a set of tools to construct productive conversations about teaching. Presents a discussion taking place in the author's third grade classroom illustrating discourse in the classroom, accompanied by the author's commentary on the lesson. (MDH)

Proposes the technique of group discussions in the learning of mathematics. Examines the teacher's role in creating an environment that encourages student participation; presents four techniques to initiate discussions in elementary school classes; and offers five attributes teachers need to develop in students for effective discussions. (MDH)

Describes an activity that demonstrates a teaching-learning model in which students ask yes or no questions to determine an unknown number on a number line. Provides a sequence of five steps to carry out the activity and suggestions for extending and expanding the activity for different grade levels. (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…

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)

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)