
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 preKgrade 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 PreK, and supplement and
enrich existing curricula at K2 (with extensions to grade 6).
They use print, manipulatives, and computers extensively.


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 lowincome children at risk for later
school failure.


The
Project
Our
project, whose complete title is, "Building BlocksFoundations
for Mathematical Thinking, PreKindergarten to Grade 2: Researchbased
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 actionsonobjects in a way that mirrors the theory and
researchbased mathematical activity, or mental actionschildren's
cognitive building blocks (e.g., creating, copying, uniting, and
disembedding both units and composite unitsthe second meaning
of the name). To accomplish this, we created computer environments
to supplement a wide range of offcomputer activities. Research
has convinced us that computers can both be developmentally appropriate
and mathematically powerful for young children (Clements & Swaminathan,
1995).


Puzzles and Geometry
A
simple illustration of providing experiences with mathematical
actionson 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.


Number
In another set of activities, children learn onetoone correspondence,
counting, and equality. For example, children “get just
enough” treats or scissors for the children at their table
and in other realworld 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 onscreen 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.


Mathematical
Competencies
In
these ways, the materials develop basic mathematical building
blocksways 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.

