Mathematics and Young Children
During the early childhood years, children develop cognitive understandings that are foundational to learning the mathematical content described in the NCTM standards. One such understanding is the ability to classify. Putting objects or ideas with similar characteristics into groups demonstrates classification competence.
Although this cognitive ability seems simple for us as adults, children require considerable practice and time to understand classification. For example, a 3-year-old child given a set of colored blocks and asked to “put blocks together that are the same” may playfully organize and reorganize the blocks, not really using any logical thinking in creating his groupings.
Classification skills are fundamental to many mathematical concepts. For example, writing the numeral 43 requires an understanding of the “tens place” and “ones place” as different groupings. In addition, the study of algebraic functions places a heavy emphasis on the ability to classify, for example, “Consider n to be the set of all integers greater than zero.”
Teachers and caregivers can provide many opportunities for practicing an understanding of classification. Mary Baratta-Lorton (1976), in her classic book Mathematics Their Way, provides many good ideas for simple materials that can be used for sorting and classifying tasks:
- People in the classroom
- Buttons for grouping
- Old bottle caps
- Natural materials for sorting such as acorns, leaves, rocks, and shells
- Nuts and bolts
- Teacher-directed activities using geoboards (square board with 25 regularly spaced pegs over which rubber bands can be stretched)
Ordering objects from smallest to largest is referred to as seriation. This sequencing can be based on height, weight, shades of color, or any other characteristic. This is another important cognitive task for young children to master. It is essential to an understanding of the number system.
Many opportunities to practice seriation are necessary for children to truly make sense of it. Although parts of this cognitive understanding are seen in many children at age 3 or 4, the full development of this concept is often reached as late as age 8 or 9. Piaget spent considerable time studying the growth of this developmental task (Flavell, 1963).
Many excellent commercial materials are available to give children practice with seriation. One well-known example is Montessori’s cylinder block. Each rectangular block has several wooden cylinders that fit into holes ordered from smallest to largest in the block. Children practice their sequencing skills by finding the right cylinder for each hole. Another set of materials that can be used for seriation activities are Cuisenaire Rods. These multicolored rods begin with a small cube as the basic unit and grow step by step to the longest rod, which is 10 units in length.
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