An account is given of the importance and role of trust in motivating teachers to understand students and develop instructional approaches. Three examples of student actions, teacher learning, and instructional change that resulted from understanding students' goals are presented, as well as guidelines for teacher reflection. (Contains 3 figures.)

Five characteristics necessary for a computer puzzle to be considered ideal are listed along with an example of such a puzzle. Several other puzzles lacking some of these characteristics are also listed and discussed. (MN)

This paper summarizes our analysis of the complexity of ratio problems at Grades 6 and 7, and reports a two-year experiment related to the teaching and learning of rational numbers and proportionality in these grades. Two classes were followed and observed. Part of the teaching material was common to both classes, mainly the objectives and the…

Questions regarding the type of teacher input and its effect on immediate and delayed performance in student problem-solving are examined. Specific guidelines for the classroom teacher are then suggested. (Author/MA)