Described is The Catalyst Conference convened by the Research Advisory Committee of the National Council of Teachers of Mathematics (NCTM) to stimulate research on the effects of the NCTM "Standards for Curriculum and Evaluation" as a guide for change in mathematics education. Six focus areas were identified. (MDH)

A dialogue between Socrates and a researcher who claims to know what constitutes effective teaching is used to critique the implicit assumptions held by researchers. Teacher effectiveness research is criticized, and potential bridges for communication suggested. (MNS)

Confrey's article is criticized on the basis of unbalanced content coverage, distortions in the treatment of the content that is covered, and the lack of readiness to come to grips with the realities of classroom teaching. (MNS)

Several lines of needed research on teaching are discussed, including process-outcome research, structuring the content for clarity, teaching cognitive skills and problem-solving strategies, recitation and boardwork, seatwork and homework, conceptual change teaching, classroom organization and grouping, cooperative learning methods, sex equity,…

Argues that, though ethnography is a powerful methodology, it has rarely been used by educational researchers. Describes the research tradition of ethnography, compares ethnography with more common educational research practices, and discusses advantages of improved commuication for both mathematics education and educational anthrpology. (PK)

Concrete problems were significantly less difficult than abstract problems at both junior and senior high school levels, as previously observed at elementary school level. Factual problems were significantly less difficult than hypothetical problems at junior and senior high school levels, in contrast to elementary school results. (MNS)

Results of 120 studies were combined by meta-analysis to determine effects on mathematics test performance of factors other than knowledge of content. Conditions that enhanced performance included testwiseness training, praise, word problem pictures, and frequent testing. Conditions depressing or not affecting performance were also noted. (MNS)

Investigated were the effects of spatial training on calculus achievement, spatial visualization ability, and the use of visualization in solving problems on solids of revolution. Sex differences were found favoring women in calculus achievement and men in spatial visualization ability. (MNS)

For an entire school year, 24 seventh-grade classes were taught problem-solving strategies; in 14 of these classes the instruction was supplemented by calculators. Mixed findings resulted for both problem solving and calculator use. (MNS)

Eleven retarded children with mental ages (MA) less than 4.5 years were examined to evaluate whether there is a critical MA for learning basic counting principles and how an understanding of counting develops. Results are discussed in terms of individual needs. (MNS)

Sixteen Brazilian third graders aged 8-13 were given problems involving multidigit computation. School-taught algorithms were likely to be used in school-taught problems, with little carry-over to real problem situations, but resulted in more incorrect answers. (MNS)

Three models are compared in terms of detail, scope, attention to individual differences, and how they deal with qualitative change and semantic processing. Two are information-processing models of arithmetical word problem-solving performance, and the third is a model of children's counting types and thinking strategies. (MNS)

Senior-year mathematics test scores are highly dependent on the number of mathematics courses taken at the level of Algebra I or above. Sophomore students with similar levels of mathematics achievement may be expected to improve similarly regardless of race or sex by taking additional mathematics courses. (MNS)

Four methods of solutions and 12 calculative strategies were found from introspective reports of 15 skilled and 15 unskilled students in grades 11 and 12 doing mental multiplication. Unskilled students used strategies more suited to written than mental computation, while skilled students used strategies based on number properties. (MNS)

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)