This study focused on (1) the relation or transition between the measurement and partitive settings for division, and (2) the study of these two interpretations in general case where the remainder is not necessarily zero. Ninety-four second-grade pupils from four classrooms (two in each of two schools) were presented, through individual…

To ascertain if children's use of manipulatives and/or the teacher's presentation of the problem in parts (chunking) affect children's ability to model and/or solve addition and/or subtraction problems, 146 first-grade subjects were administered the Houston Addition and Subtraction Problem-Solving Test which provided accuracy and modeling scores…

This study compared the error patterns of third- and fourth-grade children on addition, subtraction, and multiplication exercises in horizontal and vertical formats. The research design used parallel eight-item tests for each operation; the only difference between items on parallel forms was the formal (horizontal or vertical) of the computational…

The author investigates elementary school students' performance when solving selected open distributive sentences in relation to three factors (Open Sentence Type, Context, Number Size) and identifies and classifies solution methods attempted by students and students' errors in performance. Eighty fifth-grade students participated in the…

This study examined the effects of number of illustrative examples and number of practice problems given on seventh graders' achievement in a unit on probability. Four treatment groups were used, one for each combination of two levels of number of examples and two levels of number of practice problems. Prior to treatment students were pretested on…

This booklet is the final report on a project designed to determine the extent to which students in grades 2, 3, and 4 who were having particular difficulty in learning number concepts were not yet conserving number. A test of number conservation was given to all children assigned to the remedial group; 10 of the 23 were found to be nonconservers.…

Eleven research reports in the area of models of learning mathematics are presented in this publication of the Mathematics Education Reports series. The papers represent a mixture of theories, viewpoints, and references to other areas. Content areas addressed range from preschool to college levels. All the papers are concerned with the learning of…

The objective of the study was to determine the effect which a unit dealing with recursive definitions would have on students' achievement in applying the principle of mathematical induction (PMI). Twenty-four secondary school students were randomly assigned to control and experimental groups. Students in the control group studied programmed units…

A continuation of the field test of Developing Mathematical Processes (DMP) was conducted in eight schools. Four were multiunit schools located in settings ranging from small town to large city; the remaining schools were conventionally organized and located in large urban areas. The purpose of the field test was (1) to determine the effectiveness…

Abstracts of 36 research reports are provided. The reports were prepared by investigators for presentation at the 55th annual meeting of the National Council of Teachers of Mathematics. A broad range of topics related to mathematics education is covered. Nine reports deal with problem solving, eight are concerned with instructional methods, five…

This document was developed to provide some perspectives on the use of case studies and other clinical approaches in mathematics education. A large portion of the paper contrasts several research strategies, discussing in detail some of the procedures and results of three distinctive types of clinical studies. The perspectives and the premises of…