Enrichment activities for fourth-grade mathematics are presented. Some of the activities reinforce principles taught in the regular program; others introduce new concepts to challenge students. The activities are divided into the following categories: number pictures; multiplying or dividing by 10, 100, or 1000; tic-tac-toe word problems; map…

Enrichment activities for fifth-grade mathematics are presented. They are intended to be a continuation of the program started in the fourth grade. Some of the activities reinforce principles taught in the regular program; others introduce new concepts to challenge students. The activities are divided into the following categories: number…

Related research suggests that children may show some simple understanding of event covariations by the early elementary school years. The present experiments use a rule analysis methodology to investigate covariation judgments of children in this age range. In Experiment 1, children in second, third and fourth grade judged covariations on 12…

Describes a four-phase method of helping students who are mathematically unsophisticated and have difficulty relating their common sense, English-language understanding of a system to an abstract, mathematical description. The approach uses interactive simulation models. (Author/IRT)

In workshops for inservice teachers, volunteers learn concepts through the activities they will later use in their classrooms. In follow-up sessions the success of activities with young children is discussed. The activity described here involves attribute blocks. (SD)

This material is a supplement to existing mathematics programs for young learners. The activities presented are based on assumptions about the young problem solver which are difficult to address in standard mathematics texts. In these pages it is assumed that each learner brings to the problem-solving effort a very personal experience base and a…

In most mathematics problem solving work, students' motivation comes from trying to please their teachers or to earn a good grade. The questions students must tackle are almost never generated by their own interest. Seven open-ended college algebra-level problems are presented in which the solution of one question suggests other related questions.…

This book was written to help teachers to plan and implement an effective multiplication-division basic fact program. When it is determined that children have gained an adequate concept for an operation, the next long-range goal is fact memorization. Children need to respond quickly and correctly to number facts and retain this learning over time.…

Independent neighborhood schools in inner-city areas serve primarily minority students. They are in a position to assist American educators in understanding the best methods of teaching minorities who usually do not reach their full academic potential in public schools. Teachers in independent schools use culture and sometimes religion as a basis…

Rhetoric and mathematics have much in common that can help explain the composing process. Common elements of rhetoric and mathematics important to the teaching of writing are (1) relationships between syntax and semantics, (2) practices of representation, and (3) focus on problem solving. Recent emphasis on "repair processes" in mathematics is…

This exploratory study describes fourth-grade students' opinions and knowledge about fractions. A coherent and elaborate fraction knowledge base results when students establish connections between their conceptual knowledge and procedural knowledge of fractions. One possible juncture between concepts and procedures might involve establishing…

This document contains detailed directions for constructing a device that mechanically produces the three-dimensional shape resulting from the rotation of any algebraic line or curve around either axis on the coordinate plant. The device was developed in response to student difficulty in visualizing, and thus grasping the mathematical principles…

Students enjoy learning by doing and by manipulating objects. This paper describes classroom activities using rods with various lengths and different colors. The activities included are: (1) preparation of rods; (2) elementary addition and subtraction; (3) fractions; (4) concept of greater than, less than, and equals; (5) simple division and…

This survey reflects new developments in the mathematics curriculum as emphasized in the curriculum frameworks and state-adopted textbooks. The first section describes the procedure for the development of the survey and the rationale for the topics and types of questions included on the mathematics portion of the test. The second section describes…

The purpose of this study is to contribute to an understanding of how errors could be employed in mathematics instruction so that the students use them constructively in support of their learning of mathematics. A teaching experiment was designed to create an ideal context in which the pedagogical approach to errors as springboards could be…