Equivalence: A Unifying Concept

Abstract

Artificial boundaries that separate the study of major areas of mathematics often result in fragmented learning. Recent recommendations that favor integrated curriculum may prove helpful in alleviating this problem. NCTM's Commission on Stan dards for School Mathematics recommends that students learn view mathematics as integrated whole rather than as iso lated set of (National Council of Teachers of Mathematics 1989, 84). The Col lege Entrance Examination Board (CEEB 1985, 39) supports an integrated curricu lum in which topics in each of the major areas are studied each year and the relation ships among topics are stressed. Key mathematical ideas pervade all of mathematics. They occur frequently in dif ferent areas of the program and during dif ferent years of study. These ideas play important role in demonstrating interrela tionships between apparently different mathematical topics. Equivalence exemplifies one of the un derlying themes of mathematics. Because the concept recurs throughout the school mathematics program and is not bound to any particular subject or topic, it serves to unify the various subjects and topics. Equiv alence can relate various segments of the mathematics program and help students de velop appreciation of the unity of math