Presents activities that have been used successfully in leading students from concrete experiences through pictorial and symbolic representations of important numeration concepts and patterns, including place value, multiples, and rounding. Each activity includes concept or skill fostered, list of materials needed, recommended grade level, and…

The need to provide understandable problems and ways to help children understand problems are explored. An interview with a sixth grader depicts his incorrect strategies and leads to suggestions for teaching problem solving using a range of mathematical models for each operation. (MNS)

Fourth-grade students' understanding of the order and equivalence of rational numbers was investigated in 132 interviews during an 18-week teaching experiment. Six children were instructed individually and as a group at two sites, with instruction relying heavily on manipulative aids. Strategies used to compare fractions were identified. (MNS)

Patterns and directions are given for making bulletin boards that teach language arts and mathematics skills through hands-on student involvement. The boards help teach multiplication tables, word contractions, letter sounds, homonyms, compound words, alphabetization, and other skills. (PP)

Three lessons are outlined which employ "scholar dollars," pretend bills and coins of different denominations that students can make and use to help solve subtraction, division, and decimal problems. The technique clarifies difficult mathematical concepts by making them less abstract. (PP)

Meaningful educational activities and cognitive tools might improve students' active involvements in the teaching-learning process and encourage their reflections on the concepts and relations to be investigated. It is claimed that usage of manipulatives not only increase students' conceptual understanding and problem solving skills but also…

This research offers empirical evidence of the importance of supplying diverse symbolic representations in order to support concept development in mathematics. Graphical representation can be a helpful symbolic tool for concept development in the conceptual field of additive structures. Nevertheless, this symbolic tool has specific difficulties…

Algebra is one of the top priorities of mathematics instruction for the elementary and middle grades. This book is designed to help 6-8 teachers meet the challenge of making algebra an integral part of their mathematics instruction and realize both what to teach and how to teach central algebraic concepts. Classroom-tested lessons help teachers…

Algebra is one of the top priorities of mathematics instruction for the elementary and middle grades. This book is designed to help 3-5 teachers meet the challenge of making algebra an integral part of their mathematics instruction and realize both what to teach and how to teach central algebraic concepts. Classroom-tested lessons help teachers…

The concept of function is central in mathematics and grows in importance as one progresses in depth and breadth of understanding mathematics. Results from national assessment progress reports indicate that the majority of students do not comprehend the concepts of function and graphing. Technology has the potential to improve the understanding of…

This book is a compatible instructional component to any algebra textbook and was developed by University of Hawaii under the Dwight D. Eisenhower Mathematics and Science Education Improvement Act. The tasks align with the content and instructional approach used in daily classes that emphasize standards-based teaching and learning. The tasks…

This is a story about screen interactivity and its magical early influences. It includes a brief history of the evolution of the computer, with examples from contemporary applications in art and museum education. I believe it is important to know about the early days of drawing on the screen to get a sense of the continuum of ideas that has led us…

A review of several studies on the role of concrete and symbolic models in facilitating the learning of mathematical ideas, and a discussion of their implications for instruction are presented. (DT)

Suggestions for organizing and implementing a math-lab approach are given. Devices useful with the topic of place value and manipulations with the geoboard are discussed extensively. Many other materials are listed and referenced. (LS)