LEARNING MATHEMATICS
RESEARCH FINDING:
Children in early grades learn mathematics more effectively when
they use physical objects in their lessons.
COMMENT:
Numerous studies of mathematics achievement at different grade
and ability levels show that children benefit when real objects
are used as aids in learning mathematics. Teachers call these
objects "manipulatives."
Objects that students can look at and hold are particularly
important in the early stages of learning a math concept because
they help the student understand by visualizing. Students can
tie later work to these concrete activities.
The type or design of the objects used is not particularly impor-
tant; they can be blocks, marbles, poker chips, cardboard cutouts
--almost anything. Students do as well with inexpensive or
homemade materials as with costly, commercial versions.
The cognitive development of children and their ability to under-
stand ordinarily move from the concrete to the abstract. Learn-
ing from real objects takes advantage of this fact and provides a
firm foundation for the later development of skills and concepts.
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tion into the Role of Concrete and Semi-Concrete Materials in the
Teaching of Elementary School Mathematics." Ph.D. Dissertation,
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Fennema, E. (1972). "The Relative Effectiveness of a Symbolic
and a Concrete Model in Learning a Selected Mathematical Princi-
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4, pp. 233-238.
Jamison, D., Suppes, P., and Wells, S. (1974). "The Effective-
ness of Alternative Instructional Media: A Survey." Review of
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Piaget, J. (l952). The Child's Conception of Numbers. London:
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Suydam, M., and Higgins, J. (1977). "Activity-based Learning in
Elementary School Mathematics: Recommendations from Research."
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Environmental Education. ERIC Document No. ED l44840.