Magazine article Teaching Children Mathematics

Solving Geometric Problems by Using Unit Blocks

Magazine article Teaching Children Mathematics

Solving Geometric Problems by Using Unit Blocks

Article excerpt

Sarah, a normally cheerful child, began to cry as she attempted to put together a new puzzle. "This puzzle doesn't work!" she wailed. "There are too many pieces. They won't all fit back in!" Four-year-old Sarah, who did not conserve number, did not realize that the quantity of pieces stays the same regardless of changes in their position or arrangement. To her, the puzzle had somehow "grown" more pieces!

Like all children, Sarah will have many such experiences before she enters school. She will spend a great deal of time stacking blocks, rolling balls, and fitting together puzzle shapes. These actions and explorations serve as the foundation for developing geometric thinking and should be nurtured and extended in children's early classroom experiences.

Working with Unit Blocks

For young children, geometry is often a skill of the eyes and hands as well as of the mind, and geometric experiences should focus on the manipulation of familiar objects, such as the unit blocks found in many kindergarten and primary-grade classrooms. Designed and developed in 1915 by Caroline Pratt (Pratt 1948), these wooden blocks are interrelated in size; the sizes are based on a mathematical proportion of 1:2:4. Most of the blocks have the same width and thickness, which makes them useful in displaying equivalent relationships [ILLUSTRATION FOR FIGURE 1 OMITTED]. Children can replace larger blocks by combining blocks, thus furthering their conceptualization of various mathematical and geometric relationships. Unit blocks are so flexible and adaptable that children can use them without teacher guidance or control. "The beauty of block play is that it brings the built environment to life and puts it under the control of the child, who can make it what s/he wants it to be. There are no constraining rules" (Walker 1995).

Unit blocks are a mainstay of many kindergarten and primary-grade classrooms, and they are often viewed as a medium for eye-hand coordination and social-skill development. Working with unit blocks also nurtures geometric thinking in powerful ways. As children build, they internalize the geometry of size and shape and the measurement of height, length, area, volume, and angle. They also make generalizations about balance, gravity, and space.

Recognizing the learning potential inherent in unit blocks and valuing the role that they can play in developing geometric thinking, two kindergarten teachers and a first-grade teacher worked to develop cognitively appropriate ways to extend block-building experiences, to ask leading questions, and to pose new problems for children to solve with blocks. The fruits of their efforts, and suggestions for other primary teachers, are described in this article.

Exploring Shape and Investigating Structures

First and foremost, the teachers believed that when using unit blocks in a classroom setting, it was important to give young learners adequate time to develop and construct conceptual understanding. These teachers also wanted children to have opportunities to collaborate and to share their ideas and discoveries with others. With these goals in mind, the kindergarten teachers, who had adjacent classrooms, decided to place their block areas close together on a shared wall so that both classes could cooperate on large structures. Despite these efforts, the children in the classes continued to build separate structures for several weeks, although they occasionally observed one another's work. One day the teachers overheard two children arguing.

"It's no fair! Your class has more blocks than we do!"

"It's not true!" said Kevin. "We have the same!"

"No, you have more!" insisted Raj. "I can see you do!"

"Na-ah, you have just the same as us," countered Kevin.

Jenny, the class peacemaker, asked Raj, "Well, how do you know we have more?"

"'Cause you can tell by looking!" answered Sean, a child in the other class. …

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