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In mathematics, a manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name. The use of manipulatives provides a way for children to learn concepts in a developmentally appropriate, hands-on and an experiencing way. The use of manipulatives in mathematics classrooms throughout the world grew considerably in popularity throughout the second half of the 20th century. Mathematical manipulatives are frequently used in the first step of teaching mathematical concepts, that of concrete representation. The second and third step are representational and abstract, respectively. Mathematical manipulatives can be purchased or constructed by the teacher. Examples of commercial manipulatives include tangrams; Cuisenaire rods; numicon〔(Numicon )〕 patterns; color tiles;base ten blocks (also known as Dienes or multibase blocks);〔http://www.zoltandienes.com/〕 interlocking cubes; pattern blocks; colored chips;〔http://www.learner.org/courses/learningmath/number/session4/part_c/index.html〕 links; fraction strips,〔http://www.taw.org.uk/demo/mathematics/shapes/fractionStrip.htm〕 blocks, or stacks; Shape Math;〔http://shapemath.com/〕 Polydron; Zometool; rekenreks and geoboards. Examples of teacher-made manipulatives used in teaching place value are beans and bean sticks or bundles of ten popsicle sticks and single popsicle sticks. Virtual manipulatives for mathematics are computer models of these objects. Notable collections of virtual manipulatives include (The National Library of Virtual Manipulatives ) and the Ubersketch. Multiple experiences with manipulatives provide children with the conceptual foundation to understand mathematics at a conceptual level and are recommended by the NCTM. Some of the manipulatives are now used in other subjects in addition to mathematics. For example, Cuisenaire rods are now used in language arts and grammar, and pattern blocks are used in fine arts. ==In teaching and learning== Mathematical manipulatives play a key role in young children’s mathematics understanding and development. These concrete objects facilitate children’s understanding of important math concepts, then later help them link these ideas to representations and abstract ideas. Here we will look at pattern blocks, interlocking cubes, and tiles and the various concepts taught through using them. This is by no means an exhaustive list (there are so many possibilities!), rather, these descriptions will provide just a few ideas for how these manipulatives can be used. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Manipulative (mathematics)」の詳細全文を読む スポンサード リンク
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