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Summary

The Principles

The Project

Puzzles and Geometry

Number

Mathematical Competencies

 

 

 

 

 

 

 

 

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Summary

Building Blocks is one of a small number of projects (nationwide) that the National Science Foundation (NSF) has funded to create mathematics curriculum materials for young children. The Building Blocks project created exemplary mathematics materials designed to enable all young children to meet the new preK-grade 2 standards developed by the National Council of Teachers of Mathematics (principal investigator Doug Clements was on the writing team for NCTM's Principles and Standards for School Mathematics). These materials are a complete mathematics curriculum at Pre-K, and supplement and enrich existing curricula at K-2 (with extensions to grade 6). They use print, manipulatives, and computers extensively.

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The Principles

The National Council of Teachers of Mathematics' Standards and the Building Blocks project emphasize a vision of mathematics for young children that

  • (a) builds upon young children's experiences with mathematics,
  • (b) establishes a solid foundation for the further study of mathematics,
  • (c) incorporates assessment as an integral part of learning events,
  • (d) develops a strong conceptual framework that provides anchoring for skill acquisition,
  • (e) involves children in "doing mathematics,"
  • (f) emphasizes the development of children's mathematical thinking and reasoning abilities,
  • (g) includes a broad range of content, and
  • (h) makes appropriate and ongoing use of technology, including calculators and computers.

These educational principles also are consistent with the National Association for the Education of Young Children's recommendations for developmentally appropriate education. The need for appropriate, challenging, and effective preschool and Kindergarten mathematics programs is especially salient for low-income children at risk for later school failure.

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The Project

Our project, whose complete title is, "Building Blocks-Foundations for Mathematical Thinking, Pre-Kindergarten to Grade 2: Research-based Materials Development," illustrates these principles. Our basic approach is finding the mathematics in, and developing mathematics from, children's activity. We wish to help children extend and mathematize their everyday activities, from building blocks to art to songs to puzzles (this is the first meaning behind the Building Blocks name). Thus, Building Blocks activities are based on children's experiences and interests, with an emphasis on supporting the development of mathematical activity. Mathematization emphasizes representing activity - creating models of activity with mathematical objects, such as numbers and shapes, and mathematical actions, such as counting or transforming shapes. Our materials embody these actions-on-objects in a way that mirrors the theory- and research-based mathematical activity, or mental actions-children's cognitive building blocks (e.g., creating, copying, uniting, and disembedding both units and composite units-the second meaning of the name). To accomplish this, we created computer environments to supplement a wide range of off-computer activities. Research has convinced us that computers can both be developmentally appropriate and mathematically powerful for young children (Clements & Swaminathan, 1995).

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Puzzles and Geometry

A simple illustration of providing experiences with mathematical actions-on objects builds on young children's experiences with, and love of, puzzles. Children fill in puzzle outlines using an extended set of pattern blocks (a popular manipulative in which shapes have standard side lengths and angle measures). Different combinations are encouraged. On the computer, they may make a combination of 2 green triangles by gluing, then duplicate this unit to fill the outline. That is psychologically different from covering it with 20 separate triangles.

 

For a challenge, they find a way to use the fewest blocks to fill an outline. (Note that you can also choose to glue two triangle and create a blue rhombus.) In another activity, children are challenged to build a picture with physical blocks and copy it onto the computer, requiring the use of specific tools for the geometric motions of slide, flip and turn.

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Number

In another set of activities, children learn one-to-one correspondence, counting, and equality. For example, children “get just enough” treats or scissors for the children at their table and in other real-world situations throughout the day. A computer activity challenges them to help a character get ready for a party, beginning with setting the table. At a higher level of the same activity, an on-screen character requests a certain number of items to add to the table. If a dish is missing, a character at the table may say, “I don’t have a dish!” This type of natural feedback helps young children learn.

See the Project Writings for more examples and descriptions.

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Mathematical Competencies

In these ways, the materials develop basic mathematical building blocks-ways of knowing the world mathematically (and the third meaning of the name)-organized into two areas:

  • (a) spatial and geometric competencies and concepts and
  • (b) numeric and quantitative concepts, based on the considerable research in that domain.
  • Three mathematical subthemes,
  • (a) patterns and functions,
  • (b) data, and
  • (c) discrete mathematics (classifying, sorting, and sequencing) are woven through both main areas.

Most important will be the synthesis of these domains, each to the benefit of the other.

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