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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and a Concrete Model in Learning a Selected Mathematical  Princi-
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Jamison,  D.,  Suppes, P., and Wells, S. (1974).  "The Effective-
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