AMERICAN MONTESSORI SOCIETY POSITION STATEMENT MATHEMATICS EDUCATION

The Purpose of Mathematics Education

Mathematics arose as a way of solving problems associated with daily life -- involving space, size and quantity. The history of the development of mathematics is a history of problem solving. Inventions such as the place-value system, the numeral zero, fractions, negative numbers, and standardized units of measurement all arose from attempts to solve problems encountered in everyday life.

Over the centuries, as mathematics, science, and technology improved the lives of each generation, new problems begged to be solved. Over and over, they are solved by people who could think clearly and use concepts they had learned in new and imaginative ways.

Indeed, the ability to understand concepts clearly, then use those concepts to develop solutions to problems not encountered before, can be considered the purpose of all education, not only that of mathematics.

The Mathematics Education of American Children

It is up to each generation to ensure that its children will develop the thinking skills necessary to continue the advancement of civilization. However, a large number of studies are indicating problems with the mathematics education of American children. Test scores have fallen, and comparisons of American children with those of other countries show American children scoring at or near the bottom in mathematics. Furthermore, even within the United States, we have not seen a significant increase in children's mathematical performance over the past several years, despite our awareness of the problem.

Many groups have already formulated goals to solve this problem. In early 1990, President Bush and the U.S. governors endorsed goals to, among other things, have American students first in the world in mathematics achievement by the year 2000. The National Council of Teachers of Mathematics recently identified five critical goals necessary to improve that achievement: learning to value mathematics, becoming confident in one's own ability, becoming a mathematical problem solver, learning to communicate mathematically, and learning to reason mathematically.

What Do All Our Children Need?

Our nation must work toward ensuring that all American children come to school with sufficient rest and nutrition, and from families where education is valued and reinforced. Children's education will be most successful when schools and families work in cooperative partnerships.

We must work toward ensuring that the schools which these children attend are staffed with caring, intelligent teachers who communicate a love of learning, as well as the support staff necessary to help these teachers achieve success with all their children.

Finally, we must work toward ensuring that every school receives adequate financial support to do its job, as well as strong support from local businesses and government.

(1) Reprinted with permission from Curriculum and Evaluation Standards for School Mathematics, copyright March, 1989, by the National Council of Teachers of Mathematics.

Recommendations for America's Mathematics Education

Although mathematics was invented as a tool to solve problems, with generalizations and rules formulated after a great deal of experience, our children are not learning it that way.

The American Montessori Society advocates a vigorous, unified national effort to ensure that every American child receives a mathematics education characterized by the following features:

Preschool and Kindergarten Years:

* A strong emphasis on the development of large and small muscle coordination, spatial and size discrimination, and critical pre-math foundations, as well as aesthetically designed manipulative materials for learning beginning mathematical concepts.

Elementary Years:

* Structuring the education process around mathematical problem solving, and leading from that to the discovery, understanding, and memorization of concepts. * Repeating use of manipulative materials to teach and solidify those mathematical concepts, until students have sufficiently internalized them to work abstractly. * Structuring the educational day so children have large, uninterrupted blocks of time to use these materials and assimilate concepts. * Ongoing use of first-hand experiences, both in and out of the classroom, to apply and retain these concepts and skills, especially those which depend on forming collaborative relationships with other students. * Encouraging open discussion, collaboration and cooperation within the classroom.

Later Years:

* The continued use of concrete materials until the concepts they embody are solidly formed. * An even greater reliance on first-hand experiences, in and out of school, to use in applying learned skills. * A classroom atmosphere that encourages open discussion, collaboration and cooperation.

References

* John Chattin-McNichols. The Montessori Controversy. New York: Delmar Publishers, 1991. * Montessori in Contemporary American Culture. American Montessori Association. Heineman Educational Books, 1991.

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The American Montessori Society (AMS) is a non-profit educational society founded in 1960, whose purpose is to help children develop their potential through the educational principles of Dr. Maria Montessori. This includes the following: developing Montessori programs, accrediting schools, granting credentials, encouraging research, organizing seminars and symposia, and promoting all other areas which relate to the dissemination of Montessori philosophy.