Developing Spatial Abilities in the Early Grades
Liedtke, Werner W., Teaching Children Mathematics
Most, if not all, geometry learned in the early years should be conceptual in nature, state Hiebert and Lindquist in Mathematics for the Young Child (1990). The authors point out that students need the opportunity to develop spatial sense, and they share the observation that " [t]oday, children are often able only to name selected examples of geometric figures. In place of this superficial learning, children in conceptual development classes identify and produce exemplars and nonexemplars of geometric concepts, compare and contrast geometric figures, examine relationships among sets of figures, and explore properties of given figures" (pp. 28-29).
After a brief response to the question, What is spatial sense? this article is devoted to sample activities and tasks that are conducive to developing spatial sense and to reaching the goals of the "conceptual development classes" identified by Hiebert and Lindquist. These activities and tasks were selected because they can be used by teachers to supplement a list of ideas included in two excellent references on the topic, the February 1990 focus issue of the Arithmetic Teacher and the chapter in Mathematics for the Young Child titled "Geometric Concepts and Spatial Sense" (Brunt and Seidenstein 1990). Although the tasks will be described by referring to a specific group or a specific combination of geometric blocks, they can easily be adapted for different types or combinations of blocks as well as for different types of materials. Another positive aspect of these activities is the fact that they can present an excellent opportunity for young students to "talk mathematics."
The February 1990 focus issue of the Arithmetic Teacher is devated to spatial sense. In this issue, Wheatley (1990) suggests that spatial sense be thought of in terms of imagery. Spatial sense is defined as "an intuitive feel for one's surroundings and the objects in them" by the Curriculum and Evaluation Standards for School Mathematics (NCTM 1939, 49). That document concludes that to develop this "intuitive feel," students must have experiences that focus on relationships; on the direction, orientation, and perspective of objects in space; on the relative shapes and sizes of figures and objects; and on how a change in shape relates to a change in size.
"Central to the Curriculum and Evaluation Standards is the development of mathematical power for all students" (NCTM 1991, 1). One important component of mathematical power is "connecting." An examination of the sample activities that are described in this article should make it apparent that various aspects of connecting can best be accommodated by a teaching sequence that begins with an examination of three-dimensional objects or blocks.
Since the ability to "communicate mathematically"--through talking and writing--involves correct use of terminology and conventions, care must be taken to model accurate terminology. Appropriate modeling is important for all topics of mathematics learning, but especially for geometry, since many young children tend to confuse terms and may label things or parts of things incorrectly. For example, names of special two-dimensional shapes are assigned to three-dimensional objects--a cube may be called a square; a reference to triangle is likely to refer to the inside of a triangle; and the terms figure and shape are often used incorrectly.
A set of at least two of many different types of blocks as well as similar blocks can be used for a wide variety of activities. Blocks that are unpainted or are all of the same color are advantageous, since they are more likely to result in having students focus on desirable or relevant characteristics. The buckets of wooden geometric solids that are available from catalogs or stores for teachers or a box of Geo-blocks (Elementary Science Study, Webster Division, McGraw-Hill Book Co.) are well suited for the tasks included in this article. …