Self-instructional booklets containing the advance organizer, cognitive set, and post organizer varying according to experimental treatment were randomly assigned within nine Algebra 2 classes. Results showed a significant interaction between advance and post organizers: either one used separately facilitated learning and retention, but when used…

This chapter examines the scope of the mathematical content educators expect students to understand after they have participated in mathematics courses. It is organized under four headings: (1) Traditional School Mathematics, to clarify what the shift is away from; (2) Mathematics as Human Activity, to portray the direction the shift is toward;…

Presented is the task analysis for "Developing Mathematical Processes, Arithmetic, Book 1: Comparing and Equalizing Objects and Sets." This task analysis consists of identifying the behavioral objectives necessary for comparing and equalizing objects and sets and arranging them in a logical sequence for instruction. The 52 items in this task…

Responds to the question of how to know whether reforms have an influence on student learning. Discusses the shift in epistemology about the learning of mathematics, systemic notions about schooling, appropriate evidence related to the notion of schooling practices, and assessing mathematics literacy. (Contains 12 references.) (ASK)

This chapter covers assessment issues in classrooms and offers a possible assessment program. The purpose is three-fold: (1) to examine ways of documenting students' understanding using a domain-based approach to assessment; (2) to present examples of assessment items related to this approach; and (3) to discuss difficulties that have arisen as…

Tests were given after instruction in probability and four weeks later to 25 sixth graders. Correlation between achievement scores for each student was .78. Retention ratios for individuals, total tests, each objective, and each item indicated high initial performance may contribute to high retention. (Author/DT)

To help the reader understand the scope and diversity of the Wisconsin R & D Center's research effort in mathematics, four perspectives are presented: (1) the Center's approach to research, development, and practice; (2) the origins of the current research effort; (3) a description of current research; and (4) a projection for future research. (JP)

The purpose of this study was to determine whether a process model could be constructed using steps identified from flow charts which accounted for somewhat more variance in predicting the difficulty of two-digit multiplication problems than did a process model developed by Cromer. Cromer's data and variables were used as a starting point. Ten new…

The purpose of this study was to determine whether a process model could be constructed using steps identified from flow charts which accounted for somewhat more variance in predicting the difficulty of two-digit multiplication problems than did a process model developed by Cromer. Cromer's data and variables were used as a starting point. Ten new…

This publication contains sixteen abstracts of papers presented at the Research Reporting Sessions of the National Council of Teachers of Mathematics (NCTM) Annual Meeting. The investigations reported by Anthony, Creswell, Higgins, and Weise focus on curriculum and classroom innovations in the school mathematics program. Investigations by Gibbons,…

Thirty concepts from the areas of sets, division, and expressing relationships were studied with twelve tasks dealing with naming or selecting attributes or concepts involved. A factor analysis indicated that all concepts were measures of a single functional relationship and that all tasks measure a single underlying trait. (LS)

Findings from five related studies carried out in Tasmania, Australia in 1979-80 are summarized. The first study attempted to determine the memory capacity of a cross-sectional population of children aged 4-7, while the second study was designed to portray differences on a variety of mathematically related developmental tasks for the same…