Algebra is a branch of mathematics that studies relationships, structures, and quantities. Elementary algebra is a category of algebra that is concerned with solving arithmetic, operands, and arithmetic equations. Historians associate the origin of algebra to the early priests in Babylon four thousand years back. Algebra is known to have passed through three distinct stages in its development which are the rhetorical stage, the syncopated stage, and the symbolic stage. Moreover, algebra development was attributed to the simultaneous development of four other conceptual phases. The other developments are the geometric development that comprised most of the algebra concepts being geometrical. The second one was the static equation–solving stage. This represented the objective of numbers that satisfied certain relations. The dynamic phase concentrated on motion, while the abstract phase focused on mathematical structures (Boyer, 1991).
The development of algebra did not occur as disjointed stages but was noted to have some overlap. The first stage in the development of Algebra was the rhetorical stage. During this development, the algebra expressions were expressed in continuous prose without the use of equations. The next stage in the development of algebra was the syncopated algebra stage. This phase involved the use of abbreviations for those quantities and operations that were frequently recurring. The scholar who was credited with the development of syncopated algebra was Diophantus in 240 AD. Syncopated algebra did not immediately become the standard method until much later in the sixteenth century. The final phase in the development of algebraic mathematics was the symbolic stage. This stage was marked by the development of the current algebra symbols that we use nowadays. The algebra symbols that are used today were developed in a continuous process by Francois Viete in collaboration with Rene Descartes in 1540 – 1650. The use of symbols in algebra enhanced the learning of algebra mathematics greatly. It was greatly adopted in the mid-seventeenth century. The development of these symbols helped in the advancement of algebra arithmetic as the symbols become the object of manipulations, instead of being used as shorthand for describing computations procedures. Nowadays, the rhetoric learning process is taught to students to help them be able to synthesize the algebra concepts more appropriately. It usually helps the algebraic knowledge being expressed more suitably to enhance its understanding (Boyer, 1991).
The use of letters together with algebra symbols in algebra operations and relations helped to condense and reify algebra knowledge in a friendlier manner that made algebra learning easier to understand. This greatly enhanced the application of algebra knowledge in entirely new layers of mathematics. Sfard’s theory posits that for an appropriate understanding of algebraic mathematics, the historical development of algebra must be reproduced. He describes three characteristics phases that are necessary for developing the knowledge of algebra mathematics and mathematics skills in general. The first stage is the interiorization process which involves the manipulation of numbers which are then explained in prose to enhance the understanding. The second stage is referred to as the condensation stage and involves refining the expressions in a more manageable form, as done in the syncopated algebra stage. The final stage is the reification, where computation operations are changed into more permanent like entities to assume a structural orientation.
The introduction of symbols in algebra mathematics marked a significant stage in algebra development. It helped in the introduction of symbols to the unknowns, algebraic powers, and operations that enabled the development of analytical geometry. It then necessitated the transformation of geometrical problems into algebraic solutions. The study of algebra changed from learning polynomial equations to learning abstract mathematics systems that involved complex numbers. This is common in group algebra and quaternions that resulted in being the main unifying concepts in the 19th century. The arithmetic of complex numbers evolved into quaternions and the complex numbers being represented in the form a+bi while the quaternions are represented as a+bi+cj+dk form (Derbyshire, 2006).
List of References
Boyer, C. (1991).A History of Mathematics. New York: Prentice Hall.
Derbyshire, J. (2006).Unknown Quantity: A Real and Imaginary History of Algebra, New York: Prentice Hall.