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Mathematics Education Curriculum, History of

The history of mathematics education curriculum is, in many ways, a history of formal education in the Western world. Embedded in the contemporary school mathematics curricula are a full spectra of philosophies, a variety of contested rationales, and a set of incommensurate beliefs about learning and teachingall of which attest to its long history and its central position in formal education.

The Emergence of Mathematics

The conflicted character of mathematics education curriculum is anchored to the variegated history of the discipline itself, starting with the very word mathematics. Derived from Latin, Greek, Gothic, and Germanic terms having to do with thinking, having one's mind aroused, and wakefulness, mathematics originally had to do with a more general notion of learning.

The strands of thought included under the umbrella of mathematics have changed considerably over the last few millennia. Originally conceived as a rather broad category, mathematics once included (among other domains) geometry, astronomy, and optics. Indeed, the mainstays of modern school and university mathematics curriculaalgebra and calculusare relative latecomers to the group.

To complicate matters, until relatively recently, certain aspects of the current category of mathematics were distributed in very different ways within formal educational institutions. For example, medieval universities tended to organize their curricula around Plato's trivium (grammar, logic, and rhetoric) and quadrivium (arithmetic, geometry, music, and astronomy), an organization which in itself was a significant refinement of more varied mixes in the education systems that were typical of ancient Egypt, Rome, and Greece. A major transformation in this structure was prompted by the mathematical research of René Descartes (15961650 CE) who is generally credited with defining modern mathematics. His two major contributions were, first, to emphasize the role of logic in mathematical argumentation and second, to introduce the x-, y-coordinate system as a means to pull together geometry, algebra, and analysis into a coherent domain (rather than three distinct strands of thought). These moves continue to be reflected in the structures and contents of modern curricula.

Key Moments in the History of Mathematics Education Curriculum

Setting aside the gross differences between ancient and contemporary conceptions of mathematics, it is fair to state that elementary mathematics (in particular, topics in basic arithmetic and plane geometry) were part of the education systems of most ancient civilizations, including ancient Vedic, Egyptian, Greek, and Roman societies. (Of course, in most cases, formal education was restricted to males of sufficiently high status.)

The most potent of these ancient influences on modern mathematics curricula is ancient Greece. On this matter, perhaps the three most notable in a long lineage of Greek thinkers are Pythagoras, Plato, and Euclid. Pythagoras (575490 BCE) freely mixed mysticism, philosophy, and mathematics (in modern terms) as he and his followers developed a significant opus of mathematical knowledge and institutionalized its teaching. Plato (428328 BCE), much influenced by Pythagoras, was the first to divide the trivium and quadrivium, and this structure was carried into the classical education of medieval Europe. Euclid (323283 BCE) is noted both for his substantial contributions to geometry and for formalizing the logical proof. Indeed, the Euclidean deductive proof still stands as the hallmark of mathematical argumentation.

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