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…

This geometric instructional unit concentrates on student use of three-dimensional manipulative aids. Rigorous definitions are avoided as students use categorical reasoning based on their own experiences. Through their own discovery of relationships, it is hoped students will become interested in geometry, aware of geometric forms in the world,…

The stimuli in two artificial letter learning experiments varied in print size and dimensionality. Preschool children made the least errors when the stimuli were three dimensional, large print, and the children were directed to manipulate the letters. Replication with kindergarten children failed to show any differences among the treatments.…

Some suggestions are given of how various decimal concepts can be introduced using Multibase Arithmetic Blocks, base ten. (MN)

Track cards are manipulative materials used to promote verbalization, spatial perception, eye-hand coordination, simple problem solving, and fun in doing mathematics. (JT)

Thirty-nine elementary education majors used manipulative aids to work laboratory exercises while thirty-nine control subjects completed the same exercises without the use of manipulative materials. No significant differences were found between groups in demonstrating numerical and structural properties of the four basic arithmetic operations…

Strategies are suggested to assist students with reading comprehension difficulties. Strategies include: (1) developing appropriate background through discussion of story concepts, brainstorming, conceptual webbing, and kinesthetic or tactile experiences; (2) asking students to predict what will happen; (3) reciprocal questioning between students…

Narrates an account of teaching mathematical concepts to junior high school students using manipulative materials and small and large group games. The following concepts are explained through game descriptions using numeration or Dienes blocks: regrouping decimals, and place value. (DST)

A summer program for in-service elementary teachers is described. Five topics were the focus: diagnosis and analysis of achievement, designing instructional sequences, concrete manipulative materials, puzzles and games, and problem solving. (MNS)

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)

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…