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• #### Index 371-386

 BOX 7-2 Mathematics Activities with Different Size Groups The Building Blocks Program dedicates several weeks to shape composition. One theme is puzzles. In a whole-group setting, the teacher asks the children what puzzles they like to solve at home and at school. She discusses various types of puzzles and what puzzles are, showing some examples, telling the children she will put them all out in the mathematics centers. She then introduces a new kind of puzzle: outline puzzles that can be completed with geometric shapes (e.g., pattern blocks or tangram pieces). She solves a simple puzzle with the children, using their ideas as to solutions. Later, with small groups of four children, the teacher introduces several of the outline puzzles. She carefully observes children’s solutions to these, evaluating where each child is in the learning trajectory for shape composition. Based on these observations, she provides individuals with puzzles at different levels of the learning trajectory (or mathematics teaching-learning paths), individualizing the challenge for each child. Meanwhile, the teacher’s assistant observes and discusses children’s work with the puzzles in the mathematics center, as well as supervising those in other centers, allowing the teacher to concentrate on the small-group work. One special center involves a series of computer activities, the Piece Puzzler series, in which children also solve puzzles by manipulating pattern blocks or tangram pieces to complete similar outline puzzles. They use icons of the geometric motions to slide, turn, and flip the shapes into place. Individualized help and feedback are offered to them immediately. For example, if they put on too large a shape, covering the puzzle and also other areas, the computer activity makes the shape transparent and shows them that it covers too much (something difficult to show with physical manipulatives). Also, the computer activity automatically adjusts the levels of the puzzle to match the children’s development along the learning trajectory.

ment. Among the typically observed play experiences in an early childhood classroom are constructive play, such as block building; play with table toys (manipulatives, puzzles, Lego blocks); pretend play; mathematical play; and games, including ones in which mathematics is a secondary focus, as well as ones in which mathematics is the primary focus. (Of course children also engage in outdoor play, rough-and-tumble play, and other forms of play that have benefits as well.)

###### Block Building

Play, especially block play, provides valuable opportunities for children to explore and engage in mathematical activity on their own (Ginsburg, 2006; Hirsch, 1996). Young children enjoy playing with blocks, and there is evidence that they naturally engage in mathematical play with them (Seo

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