Stages in the History of Algebra with Implications for Teaching Export

@article{citeulike:2819336, abstract = {Abstract\ \ In this article, we take a rapid journey through the history of algebra, noting the important developments and reflecting on the importance of this history in the teaching of algebra in secondary school or university. Frequently, algebra is considered to have three stages in its historical development: the rhetorical stage, the syncopated stage, and the symbolic stage. But besides these three stages of expressing algebraic ideas, there are four more conceptual stages which have happened along side of these changes in expressions. These stages are the geometric stage, where most of the concepts of algebra are geometric ones; the static equation-solving stage, where the goal is to find numbers satisfying certain relationships; the dynamic function stage, where motion seems to be an underlying idea, and finally, the abstract stage, where mathematical structure plays the central role. The stages of algebra are, of course not entirely disjoint from one another; there is always some overlap. We discuss here high points of the development of these stages and reflect on the use of these historical stages in the teaching of algebra.}, author = {Katz, Victor and Barton, Bill}, citeulike-article-id = {2819336}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/s10649-006-9023-7}, day = {19}, doi = {10.1007/s10649-006-9023-7}, journal = {Educational Studies in Mathematics}, keywords = {algebra, education, history, mathematics, teaching}, month = {October}, number = {2}, pages = {185--201}, posted-at = {2008-05-21 11:40:53}, priority = {2}, title = {Stages in the History of Algebra with Implications for Teaching}, url = {http://dx.doi.org/10.1007/s10649-006-9023-7}, volume = {66}, year = {2007} }

TY - JOUR ID - citeulike:2819336 L3 - citeulike-article-id:2819336 N2 - Abstract  In this article, we take a rapid journey through the history of algebra, noting the important developments and reflecting on the importance of this history in the teaching of algebra in secondary school or university. Frequently, algebra is considered to have three stages in its historical development: the rhetorical stage, the syncopated stage, and the symbolic stage. But besides these three stages of expressing algebraic ideas, there are four more conceptual stages which have happened along side of these changes in expressions. These stages are the geometric stage, where most of the concepts of algebra are geometric ones; the static equation-solving stage, where the goal is to find numbers satisfying certain relationships; the dynamic function stage, where motion seems to be an underlying idea, and finally, the abstract stage, where mathematical structure plays the central role. The stages of algebra are, of course not entirely disjoint from one another; there is always some overlap. We discuss here high points of the development of these stages and reflect on the use of these historical stages in the teaching of algebra. IS - 2 JF - Educational Studies in Mathematics EP - 201 TI - Stages in the History of Algebra with Implications for Teaching VL - 66 SP - 185 KW - algebra KW - education KW - history KW - mathematics KW - teaching AU - Katz, Victor AU - Barton, Bill PY - 2007/10/19/ UR - http://dx.doi.org/10.1007/s10649-006-9023-7 ER -