A focus on the “people and systems issues,’' he said, is a “fundamental aspect of this document.’'
“This [approach] stands in contrast to the multi-tracked system in this country,’' said Christian R. Hirsch, a professor of mathematics and math education at Western Michigan University who edited the guide. “Currently, there is virtually no commonality between the sequences.’'
The document, “A Core Curriculum: Making Mathematics Count for Everyone,’' which was released last week, is one in a series of reports making up an “addenda series’’ of papers designed to amplify themes contained in the N.C.T.M.'s “Curriculum and Evaluation Standards for School Mathematics.’'
The core curriculum, which was released concurrently with the N.C.T.M.'s annual meeting in Nashville, is designed to help schools put into practice the standards’ philosophy that all students should be offered challenging math education.
“In contrast to current practices of prematurely tracking students into either college-preparatory sequences or ‘general mathematics’ sequences on the basis of narrow perceptions of performance or curricular goals, the ‘Standards’ recommends at least three years of mathematical study for every student...,’' a preface to the new document states.
Different Models
The document offers educators a method for transforming existing programs into a common-core program as well as different models for providing a common core of learning.
A “crossover model,’' which retains some of the elements of existing curricula, is designed to provide districts with a method for moving toward a common core, while maintaining familiar teaching structures.
The “enrichment’’ and “differentiated’’ models describe different types of common cores that might be adapted to certain school settings.
The enrichment model offers options for advanced study for students enrolled in a four-year course of study who move at a faster pace through the core curriculum.
The differentiated model, on the other hand, whould offer students a single three-year sequence of courses in which the same topics are addressed at different levels of abstraction. This model also offers a fourth year of study for students intending to go on to college.
While the document stresses a fundamental shift away from existing instructional methods, its authors believe its conclusions are realistic. Mr. Hirsch said that the document’s principal author, Steven P. Meiring, the math specialist for the Ohio Department of Education, brought to the project a strong sense of what can realistically be accomplished given the existing diversity of schools.
‘Real World’ Applications
The new document also stresses the need for the high-school mathematics curriculum to move away from the decades-old “Newtonian’’ approach, under which students study a specific sequence of courses largely in preparation for enrolling in calculus.
In the core curriculum, students would have an opportunity to enroll in a math curriculum that reflects a world in which math has increasingly become a tool of the social sciences and a variety of other disciplines.
But, the document notes, “as the application of mathematics to real-world problems has grown increasingly complex, the tools associated with the traditional curriculum have become limiting.’'
To accommodate such changes, the document stresses the importance of technology as a tool that allows every student to examine the connections between math in an academic setting and its real-world applications.
“Computer and calculator graphics not only bring these connections to the forefront of the curriculum, but also allow students to investigate connections in a dynamic way,’' the document states. “Moreover, the visualization approach offered by the technologies promises to afford more students greater access to mathematics.’'
The document also urges math educators to rethink what topics should be included in the curriculum.
“We will need to think deeply about mathematics content, its use, and its potential significance to students as well as about our approaches to teaching,’' it concludes.
Mr. Hirsch also said that an important feature of the document is a chapter designed to guide schools through the difficult process of implementing change in communities that are resistant to reform.
A focus on the “people and systems issues,’' he said, is a “fundamental aspect of this document.’'
The changes in approach must be reflected in math textbooks, the document cautions. Last month, Mr. Hirsch released portions of the document to textbook publishers and curriculum developers in Chicago at a joint meeting of the N.C.T.M. and the American Association of Publishers. (See Education Week, March 25, 1992.)
