This study investigated the relative effectiveness of three methods of using manipulative materials for instructing third-grade students on addition and subtraction of two-digit numbers. Subjects (N=124) were selected from a larger pool from two schools on the basis of scores on a prerequisite skills measure and the pretest. They were randomly…

Reported are the results of a study made to determine the effects of independent study with experimental matematical materials upon selected achievement measure, and the grade level at which these materials can be used most effectively. Experimental treatments were randomly assigned to three classes within two elementary schools at each of the…

Interaction between pupils' cognitive styles and instructional method in effecting achievement was studied. The instructional variables were sequencing and use of manipulative materials. Ninety sixth-grade students were ranked on Sigel's Cognitive Style Test. The upper and lower 36 were defined as high and low analytic pupils, respectively. Nine…

The purpose of this study was to determine if college students could benefit from the use of visual and manipulative aids while studying a mathematical topic. A sample of 33 freshmen were pretested for mathematical ability, divided into ability levels by means of ACT composite scores, and randomly assigned to one of three treatment groups for a…

The purpose of the study was to examine the effect of instruction using Dienes' perceptual variability principles on primitive generalization and mathematical generalization. The following was studied: the effect of achievement-to-criterion on one, two, or three non-symbolic embodiments of an objective using a selected class of variables on the…

The purpose of the study was to examine the effect of instruction using Dienes' perceptual variability principle on the development of ability to operate with symbols in a meaningful way. The following was studied: whether an increase in the number of enactive and/or iconic embodiments of a concept utilized in an instructional episode will produce…

This study involved the development, pilot testing, and evaluation of units for a college mathematics course for general education. The units emphasized a concrete approach to instruction and the manipulation of objects, images, and symbols. Three classes, all taught by the researcher, were involved in the study: a control group, a pilot test…

This study concerns concrete manipulatives for use in mathematics education, specifically in the realm of negative numbers and the operations on them. The author presents a review of relevant theory, practice, and research and develops guidelines regarding characteristics of manipulative materials. He concludes that present practice in teaching…

The purpose of this study was to determine whether the use of electric calculators offered an effective remedy for the lack of success and the corresponding negative attitude of the low achiever in mathematics. Two hundred and one low achievers were randomly scheduled into one of five control sections or into one of five experimental sections.…

The purpose of this study was to investigate the effectiveness of guided discovery and concrete materials on mathematics learning. From the seventh grade of one school, 40 students were selected who were at least one standard deviation above or below the mean on two mathematics achievement tests. Five high ability and five low ability were then…

The purpose of this study was to obtain insights into the learning of concepts in metric and non-metric geometry by fifth and sixth grade students. A total of 102 students were divided into two groups characterized by the amount and type of concrete activities used. A pretest and two posttests were given. Results showed that older students and…

The purpose of the study was to determine the effects of type of grouping (multibase (M) or base ten (T) ) and the time that base representations are introduced (initially (EB) or after counting, reading and writing numerals (LB) ) on achievement in numeration in grade one. Four intact classes of 110 students participated, and a 2 x 2 factorial…

A curriculum for a ninth grade class is described with apparatus and experiments which involve active manipulation, through which the learner develops concepts and skills. Questions are designed to help the student express himself verbally. The affective development is fostered by game playing, by discussion and by children working in pairs or in…

Investigated was the readiness of fifth, seventh, and eighth graders trained to empirically gather data by manipulating objects and materials with their hands, and to transfer this skill to a problem situation outside the classroom. After one semester's training in the science process under investigation, the increase in the use of the strategy of…

This study was conducted to determine the relative effectiveness of the use of three different combinations of enactive, ikonic and symbolic representation in teaching multiplication to third-grade students. Ninety students in three classrooms were instructed in accordance with the assigned treatment for nine weeks. Groups were equated using the…