Taming the unknown: history of algebra from antiquity to the early twentieth century (original) (raw)
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The chapter begins by identifying, and placing in their historical contexts, the main issues in a longstanding debate over the purposes of school algebra. The following six purposes for school algebra, recognized by various writers over the past three centuries, are then identified: (a) algebra as a body of knowledge essential to higher mathematical and scientific studies, (b) algebra as generalized arithmetic, (c) algebra as a prerequisite for entry to higher studies, (d) algebra as offering a language and set of procedures for modeling reallife problems, (e) algebra as an aid to describing structural properties in elementary mathematics, and (f) algebra as a study of variables. The question is then raised, and discussed, whether school algebra represents a unidimensional trait.
Historical Perspectives on the Purposes of School Algebra
Mathematics Education Research Group of Australasia, 2017
In this paper, we identify, from historical vantage points, the following six purposes of school algebra: (a) algebra as a body of knowledge essential to higher mathematical and scientific studies, (b) algebra as generalised arithmetic, (c) algebra as a prerequisite for entry to higher studies, (d) algebra as offering a language and set of procedures for modelling real-life problems, (e) algebra as an aid to describing structural properties in elementary mathematics, and (f) algebra as a study of variables. We conclude with brief commentary on the question whether school algebra is a unidimensional field of study.
The Role of Algebra in School Mathematics
ICME-13 monographs, 2018
Algebra can be viewed as a language of mathematics; playing a major role for students' opportunities to pursue many different types of education in a modern society. It may therefore seem obvious that algebra should play a major role in school mathematics. However, analyses based on data from several international large-scale studies have shown that there are great differences between countries when it comes to algebra; in some countries algebra plays a major role, while this is not the case in other countries. These differences have been shown consistent over time and at different levels in school. This paper points out and discusses how these differences may interfere with individual students' rights and opportunities to pursue the education they want, and how this may interfere with the societies' need to recruit people to a number of professions.
Algebra and its teaching: An historical survey
The Journal of Mathematical Behavior, 1997
The subject of algebra has a history reaching back at least 4000 years. Ever since the Egyptians and Babylonians discovered how to solve equations, teachers have been searching for ways to present the material to their students, so that it can be effectively used. Despite the claims of recent years that algebra teaching needs to be “relevant”, it appears that historically, at least, algebra has nearly always been taught through the solving of artificial problems. Furthermore, it has generally been taught through its relationship to geometry. This article surveys the history of algebra with particular emphasis on the texts which have been used in the teaching of the subject. It also considers many instances where the use of historical ideas has been and could be useful in teaching algebra.
Teaching and Learning Middle School Algebra: Valuable Lessons from the History of Mathematics
And the Rest is Just Algebra, 2016
Algebra is often thought of as a 'gatekeeper' in school mathematics, being crucial to further study in mathematics as well as to future educational and employment opportunities. However, a large number of studies have highlighted the difficulties and cognitive obstacles that students face when they learn algebra. In response to growing concerns about students' fragile understandings and preparation in algebra, recent research and reform efforts in mathematics education have made algebra curriculum and teaching a focus of attention. Very little research, however, has paid attention to extracting ideas from the history of algebra for developing classroom teaching strategies. In this chapter, we examine some important issues in the history of algebraic ideas involving variables and exponents that can transfer well to the mathematics classroom of today.
Stages in the History of Algebra with Implications for Teaching
Educational Studies in Mathematics, 2007
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.
Notes for a History of the Teaching of Algebra
Handbook on the History of Mathematics Education, 2013
Abundant literature is available on the history of algebra. However, the history of the teaching of algebra is largely unwritten, and as such, this chapter essentially constitutes some notes that are intended to be useful for future research on this subject. As well as the scarcity of the works published on the topic, there is the added difficulty of drawing the line between the teaching of algebra and the teaching of arithmetic-two branches of knowledge whose borders have varied over time (today one can consider the arithmetic with the four operations and their algorithms and properties taught in schools as nothing more than a small chapter of algebra). As such, we will be very brief in talking about the more distant epochs, from which we have some mathematics documents but little information on how they were used in teaching. We aim to be more explicit as we travel forwards into the different epochs until modern times. We finish, naturally, with some reflections on the present-day and future situation regarding the teaching of algebra.
Numeracy, 2016
Andrew Hacker. The Math Myth, and Other STEM Delusions (New York, NY: The New Press). 256 pp. ISBN 978-1-62097-068-3 (also available as an e-book). The political scientist Andrew Hacker argues that calls for increasing proficiency in algebra and other higher mathematics are misguided, in that most occupations do not require higher math, even as math requirements account for the largest share of students failing to complete high school and college. He advocates numeracy instruction for improving students' ability to calculate and interpret numbers they will encounter in their lives.
CUADERNOS DE INVESTIGACIÓN Y FORMACIÓN EN EDUCACIÓN MATEMÁTICA, 2024
Various approaches to teaching and learning of Algebra within Mathematics Education come from classical studies in the History of Mathematics. Consequently, in this second discipline, a narrative literature review of contemporary sources, between 2000 and 2018, in prominent data bases and journals was carried out to identify new elements that could contribute to the strengthening of these approaches. We focused this review on the contributions of recent renowned mathematics historians that have had immersed in new findings related to the development of Algebra. In this paper, we present at least six considerations that can be problematized from the perspective of Mathematics Education, which generate new routes of investigation that could contribute significantly to a more robust and profound understanding of algebraic activity in general, and positively impact on the understanding of development of algebraic activity in mathematical education.