Research Basis of EM - page 3

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Meaning and Skill

One of the perennial arguments in education is between those who want students to develop skill in carrying out procedures and those who want students to understand why those procedures work. Like most such either-or dichotomies, however, this is a false choice. In reality, children with weak conceptual understandings are hindered in their skill development, and children with weak skills are handicapped as they work towards higher levels of conceptual understanding (Carpenter, 1986).

Educators have long recognized that concepts and skills develop best when proper attention is given to both. In 1902, for example, Dewey stressed both that learning must be meaningful for the students and that learning must lead students into established disciplines of study. Years later, Brownell pointed out the necessity for a balance between skills and meaning: “In objecting to the emphasis on drill prevalent not so long ago, we may have failed to point out that practice for proficiency in skills has its place too” (1956). More recent researchers have also pointed out the unfortunate outcomes when a proper balance between meaning and skill is not maintained (Skemp, 1978; Baroody & Ginsburg, 1986; Resnick, 1987b).

Staff Development

During the New Math era, scant attention was paid to the staff development needs of elementary school teachers¹. Part of the Back-to-Basics movement of the 1970s was actually an emphasis on “teacher-proof” materials. Thus, when UCSMP was founded in 1983, the project’s Elementary Teacher Development Component was breaking new ground. One key finding from work carried out in the 1980s by Paul Sally and Sheila Sconiers at UCSMP was that staff development needed to focus on building teachers’ understanding of mathematics. Other work at the University of Chicago showed that while teachers used a variety of teaching formats in areas such as language arts and social studies, including student projects and small-group work, in mathematics instruction by those same teachers was dominated by individuals filling in answers on page after page of arithmetic problems (Stodolsky, 1988).

• Children begin school with a great deal of knowledge and intuition on which to build; by making use of this knowledge, far more can be accomplished in the primary grades than has traditionally been supposed.
• The curriculum should begin with children’s experience and should work to connect that experience with the discipline of mathematics; the materials should encourage the children’s own construction of knowledge.
• Curriculum development should proceed grade by grade starting at Kindergarten so that each grade can build on proven outcomes of the previous grade.
• The curriculum should be more than just arithmetic; geometry, data analysis, measurement, probability, algebra, and problem solving can be taught in elementary school; the curriculum should include rich problems, mathematical modeling, and cross-curricular connections.
• The curriculum should be balanced: concepts, skills, facts, and tools are all necessary.
• Excellent instruction is important.
• Reforms must take account of the working lives of teachers; teachers should be active collaborators in designing the curriculum.
• The pace should be brisk.
• Topics should be arranged in a helix; practice should be distributed rather than massed.
• The curriculum should make use of manipulatives, including calculators.
• The curriculum should include practical routines to help build the arithmetic skills and quick responses that are essential in a problem-rich environment.

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