by Donna F. Berlin
Support for moving beyond the separate-subject approach toward a holistic mathematical curriculum has a long tradition. As early as 1899, the Chicago Section of the American Mathematical Society endorsed the "correlation of work" for the subjects of arithmetic, geometry, and algebra. Variously called composite, correlated, general, or unified courses, the movement toward integrated mathematics gained momentum with the design of junior high schools in the 1920s. The appropriateness of integrated mathematics for adolescent learners was further advanced with the middle school movement of the 1970s and 1980s. An integrated view of mathematics is consistent with two key components of the middle school philosophy: interdisciplinary teaching and coherent learning.
In the United States, the National Council of Teachers of Mathematics (NCTM) has closely aligned the term connections with integrated mathematics. NCTM's Principles and Standards for School Mathematics (Reston, Va.: NCTM, 2000) recommends the following:
Instructional programs from prekindergarten through grade 12 should enable students to—
- recognize and use connections among mathematical ideas;
- understand how mathematical ideas interconnect and build on one another, producing a coherent whole; and
- recognize and apply mathematics in context outside of mathematics courses.
To obtain an accurate international perspective of integrated mathematics at the middle school level, a series of questions was posed to mathematics educators throughout the world. They were asked to share relevant sections of their national curriculum, textbooks, and lessons and activities. The following three-part vision emerged:
Integrated mathematics programs should—
- emphasize the interrelatedness of mathematical topics—for example, number, operations, algebra, geometry, measurement, data analysis, and probability—and provide a view of mathematics as a coherent, holistic field of study;
- connect mathematics with other subjects in the curriculum so that students engage in mathematics in context, extend and apply their knowledge, and experience coherent learning; and
- connect mathematics with students' interests, experiences, and real life to emphasize the pervasiveness of mathematical knowledge and the power of mathematical modeling.
The pedagogical approaches of problem-based, project-based, or thematic inquiry and investigation were most often represented in the integrated mathematics lessons and activities. Similarly, in the United States, these approaches are embodied in the National Science Foundation–sponsored comprehensive, Standards-based middle school curriculum programs: Connected Mathematics, Mathematics in Context, MathScape: Seeing and Thinking Mathematically, MATHThematics, and Middle-School Mathematics through Applications Project.
Internationally, most national curricula—for example, those of Canada, the Czech Republic, Israel, Italy, the Netherlands, Sweden, and the United Kingdom—endorse the vision of integrated mathematics, whereas other areas, for example, Palestine, plan to include this perspective in the near future. The national curriculum of Japan is moving toward a compulsory period for integrated study by 2002, consistent with the second part of the vision of integrated mathematics.
Although most national curricula are compulsory, I asked colleagues to reflect on the relationship between the intended curriculum and actual classroom practice. The overwhelming response was that the relationship depends on the teacher. Teachers' content knowledge, pedagogical knowledge, beliefs about the nature of mathematics, and availability of resources are essential elements in implementing integrated mathematics.
Clearly there is worldwide interest in, and attention to, integrated mathematics. Perhaps the International Association for the Evaluation of Educational Achievement should include "integrated mathematics" in its next cross-national analysis of mathematics and science curriculum guides, textbooks, and classroom practice.
|Donna F. Berlin, professor in mathematics, science, and technology education at Ohio State University, served as codirector of the 1991 Wingspread Conference on Integrated Science and Mathematics Teaching and Learning, is research coordinator for integration at the National Center for Science Teaching and Learning, and is the mathematics education associate for the Eisenhower National Clearinghouse for Mathematics and Science Education. Her professional interests include elementary and middle school mathematics education, the integration of mathematics and science education, and classroom-based research.