A structured system of visual features is seen to parallel the propositional hierarchy of operations usually associated with the parsing of algebraic expressions. Women more than men were found to depend on these visual cues. Possible causes and consequences are discussed. Subjects were secondary and college students. (Author/DC)

Approximately half of a group of 12-year-old students were taught fraction and ratio topics by a concrete process-oriented method. The others were taught in the regular way. The concrete, process-oriented approach resulted in significantly improved achievement in, and attitude toward, fractions and ratios. (Author/DC)

Seventh-grade students were tested to uncover arithmetic errors. Answers and intermediate steps were analyzed and models to represent students' behavior were developed. Certain errors were common across students. Others were tied to the format of the test item. Some superficial understandings of mathematical concepts were exposed. (Author/DC)

Secondary geometry students were tested for van Hiele level of thinking, geometry knowledge and achievement, and proof-writing achievement. Proof-writing achievement correlated significantly with van Hiele level entering geometry knowledge and geometry achievement. The predictive validity of the van Hiele model was supported. (Author/DC)

Research of expert-novice differences is reviewed seeking to show experts possess a large body of domain specific knowledge. It was postulated that experts possess schemas enabling them to classify problems, call up the appropriate automated rules, then apply these to obtain the solution. (DC)

Explores the relationship between high school students' beliefs about mathematics and their mathematical performance. Reports: (1) the students' attributions of success or failure; (2) perceptions of mathematics; (3) comparative views of school mathematics, English and social studies; (4) motivation; and (5) personal performance. A questionnaire…

Examines aspects of the images and definitions that college students and junior high school teachers have for the concept of function. Provides a seven-item questionnaire. Describes and categorizes the various images and definitions of the concept. (YP)

Describes the understanding, nature, and meaning of mathematical culture and the implications of mathematical culture for mathematics education. (YP)

Summarizes several intervention efforts and programs dealing with the underrepresentation and lower achievement levels of minorities and women in mathematics. Suggests five directions for new approaches and an expanded research base. (YP)

Lists references of 16 research summaries, 152 articles, and 220 dissertations alphabetically by author within each category. Provides the grade or age level for each reference. A brief abstract is presented for most of the references. Journals searched and author index by content are included. (YP)

Investigates the development of concepts and processes associated with computational estimation. Twelve students at each of grades three, five, seven, and nine were interviewed. The older children understood better than the younger children what was asked but were uncomfortable with estimation processes and outcomes. (Author/YP)

Classifies children's solution strategies by degree of abstraction and by use of physical objects. Children in grades one, two, and three were given two multiplication and four division word problems that differed in semantic structure. (Author/YP)

Analyzes error patterns of kindergartners' mental addition task. Eight weeks of computational practice affected the errors of unpracticed combinations on a retest. Seven of 10 children mastered previously unknown combinations involving zero by learning a relationship rather than the practice and memorization of individual facts. (Author/YP)

Analyzes the Second International Mathematics Study data on the use of instructional aids by 103 Ontario grade eight mathematics teachers using dual-scaling analysis. The effect of instructional aids did not remain after the influence of topic coverage was removed. (Author/YP)

Describes the development and validation of a short form of the My Class Inventory (MCI) assessing classroom psychosocial environment. Reports a case study involving the use of the short form of MCI in attempts to improve a sixth-grade mathematics class. Provides all 25 items of the short version of MCI. (YP)