Summarizes a reanalysis of the data from an investigation of a test designed to measure a learning sequence in geometry based on the work of van Hiele (1986). Discusses the test based on the Rasch model. (YP)

Provides an alternative analysis of the reliability associated with the van Hiele Geometry Test based on the assumption that the norm-referenced reliability coefficients provided by the developers were inappropriate. Discusses the agreement coefficient and the kappa coefficient. (YP)

Responds to Crowley's and Wilson's articles on the reliability of the van Hiele Geometry Test. Discusses the issue of the difficulty of trying to maximize content validity while minimizing measurement error. (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)

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)

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 patterns of sex differences for responses to problems across the countries involved in the Second International Mathematics Study. Reports no substantial gender effects on any of the content areas using the median polishing method. (YP)

Documented are major categories of errors that appear as children learn decimal fractions. Then the conceptual sources of these errors are established. Different curriculum sequences influence the probability that these classes of errors will appear. They can be used as diagnostic tools to detect children's understanding of mathematics topics.…

Data from the Second International Mathematics Study indicated that the retention rates of countries accounted for some achievement differences. However, achievement differences for the more able students across countries were not related to the rate at which countries retained students. Instead, variables such as opportunity to learn were needed.…

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…

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)

Students at concrete or formal operational reasoning levels made similarity judgments on geometric concepts and mathematical expressions on ratio, proportion, and similarity. Clear prototypical maps could be derived for both groups. Formal operational students structured subject matter content significantly more like subject matter experts than…

Studied were the misconceptions that preservice elementary teachers have about multiplication and division. Results indicated that they are influenced by the same primitive models as students; the most common errors made by both groups are quite similar. (MNS)