The effects of two instructional strategies for sequencing examples and nonexamples of the concept "parallelogram" were compared for sixth graders. A rational sequence was favored over a random sequence at the formal level of concept attainment; no interaction effect was found between the strategy and students' mathematical ability. (MNS)

Assignment projects for high-achieving ninth graders were developed, and a comparative evaluation study indicated that they were effective. It bacame clear that teachers needed more practical support, so a diagnostic study was undertaken, leading to the establishment of a link between a categorization of student difficulties and a hierarchy of…

Over half of the 101 preservice elementary teachers studied accepted inductive arguments as valid mathematical proofs, while over 60 percent accepted correct deductive arguments. Over one-third simultaneously accepted inductive and deductive arguments. More examples of the limitations of empirical evidence and of the power of mathematical proof…

The effects of teaching strategy, relevant knowledge, and strategy length on high school students' mathematical learning ability were studied. Performance was found to increase as levels of relevant knowledge increased. Characterization strategies were found to be more effective than exemplification strategies for students with high relevant…

Three important elements needed for constructing expert mathematics lessons are described: rich agendas, consistent but flexible lesson structures, and clear, understandable explanations. Each is discussed in terms of its hypothetical characteristics and then tested by comparing two novice and four expert elementary mathematics teachers. (MNS)

Examined were the effects of student cognitive entry behavior, prescribed mastery level, and information about criterion on mathematics achievement. Studied were 36 third graders assigned to four levels of being informed. Findings differed for children at low and high entry levels. (MNS)

This aptitude-treatment interaction study explored the relationship between cognitive restructuring ability and treatments varying in the amounts of teacher guidance on tasks with fractions. An interaction was found between cognitive restructuring ability and levels of teacher guidance for items having continuous perceptual distracters. (MNS)

Ten teachers successfully taught first- and second-grade children to count up while keeping track with finger patterns. Learning to subtract by counting up greatly improved children's performance on take-away, compare, and equalize word problems, and enabled them to accelerate by as much as three years their learning of subtraction topics. (MNS)

Results in 487 reports were integrated by meta-analysis to study characteristics of problem solvers, conditions for harder and easier problems, effects of different instructional methods on problem-solving performance, and effects of classroom-related conditions on problem-solving performance. Problem solving related positively to measures of…