International Handbook of Mathematics Education Part 1
ALAN J. BISHOP Monash University, Clayton, Victoria, Australia RATIONALE Mathematics Education is becoming a well-documented field with many books, journals and international conferences focusing on a variety of aspects relating to theory, research and pr
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Introduction to Section 1 JEREMY KILPATRICK University o/Georgia, Athens, USA
In most countries of the world, the 20th century has witnessed a rather strong stability in the structure of the school and university mathematics curriculum even as waves of reform have swept across the surface. Computational arithmetic, together with basic concepts of measurement and informal geometry, remains at the core of the primary school curriculum. Algebra appears in the middle grades, becoming more elaborated and formal as students move into secondary school and leading, through a study of rational, exponential, and trigonometric functions, to the calculus and higher mathematics. The so-called canonical curriculum (Howson & Wilson 1986) in school mathematics emerged in Western Europe after the Industrial Revolution. By early in the 20th century it had been adopted almost everywhere. Exceptions to the general lack of change in the mathematics curriculum since then have occurred over the past half century as traditional geometry has given way almost everywhere to a greater emphasis on transformations and vectors and as probability and statistics (or, increasingly, 'data handling') have made their way into many syllabi, beginning in the middle school grades. But any comparison of textbooks used at the tum of the century and today will show that the overall structure and emphasis have not changed greatly. Despite its structural stability, however, the mathematics curriculum, at both the school and university levels, has made two strong shifts in emphasis: one during the 1950s and 1960s and one over the last decade or so. The era of the 'new mathematics' brought to many countries greater efforts to attract students to the study of mathematics by emphasising its abstract structures. The hope and expectation were that students would understand and appreciate mathematics more if they could see the simplicity and elegance of its laws and that students with a thorough grounding in mathematical structures would be equipped to learn in later life the mathematics they would need but that could not be anticipated. Over the last few years, the curriculum has shifted, at least at the level of syllabi and textbooks, away from an emphasis on abstract structures toward efforts to include more realistic applications, with an emphasis on the ways in which mathematics is used in daily and professionallife. The curriculum can be seen as an amalgam of goals, content, instruction, assessment and materials. All these parts can be seen in the chapters in this section, although instruction is treated more fully in the subsequent section. The goals of mathematics instruction govern how the curriculum is organised by teachers and others and how it is experienced by students. In recent 7 A.J. Bishop et al. (eds.), International Handbook ofMathematics Education, 7 - 9 © 1996 Kluwer Academic Publishers,
years, mathematics educators have turned increased attention to formulating explicit instructional aims and objectives as 'mathematics for all' has become a
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