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Integrating History of Mathematics into the Classroom: Was Aristotle Wrong?

Throughout history humanity has collected an endless record of useful methods of calculation, techniques for solving problems, tools for surveying and measurement, logical problems and proofs. Yet rarely do we observe in the classroom the use of the remarkable method of false positions invented by Egyptians, or Euclid’s algorithm for finding greatest common factor without division. Such examples of great achievements in mathematics seem worthwhile to encourage appreciation of mathematics, as well as to demonstrate how History of Mathematics (HOM) provides conditions for gaining a rich experience and understanding of the development of mathematical concepts and their connections and interrelation. Nationwide professional councils (e.g., National Council of Teachers of Mathematics (NCTM), National Research Council (NRC) and National Council for Accreditation of Teacher Education (NCATE)) acknowledge the importance of the HOM in the school curriculum. The NCTM/NCATE Program Content Standards (2003) require all prospective mathematics teachers to “Demonstrate knowledge of the historical development” of number and number system, of Euclidean and non-Euclidean geometries, algebra, calculus, discrete mathematics, statistics and probability, measurement and measurement systems, and knowledge about contributions from diverse cultures” (NCTM/NCATE, 2003).

Furthermore, NCTM (NCTM, n.d.) co-supports a professional development scholarship emphasizing the history of mathematics and its importance and significance for learning mathematics.

Few research studies and scholarly writings (e.g., Swetz, 1994, Swetz et al 1995, Siu, 2004; Weng Kin, 2008) enthusiastically argue that the history of mathematics supplies endless opportunities to trace the roots and development of humanity, development of civilizations, and is likely to make an effect on students’ perception of the power of mathematics.

We concur with Wilder’s (1968) belief that mathematics is a “cultural phenomenon” (p.xi), and that meaningful learning of school mathematics must be facilitated by studying the cultural significance of mathematics, the role of the evolution of mathematical concepts and scientific discoveries. At the same time, we are concerned that teaching mathematics in total isolation from its history impoverishes the learning of mathematics, and deprives students from the exposure to such cultural phenomenon developed over the centuries.

Empirical studies focused on teachers’ perceptions of HOM (e.g., Philippou & Christou, 1998; Schram, Wilcox, Lapan & Lanier, 1988; Siu, 2004; Smestad, 2009; Stander, 1989) found that introducing teachers to the HOM activated their interests in the significance of mathematics and its history for learning the discipline. In parallel, the studies clearly indicated in spite of the peak in personal interest in HOM, these teachers did not express intentions of giving consideration to the inclusion of the HOM into their curriculum. All the above led us to launch a study which examined high school teachers’ perceptions of the nature of mathematics. In particular, we were interested in causes of apparent lack of the HOM integration into classrooms.

We operated under several assumptions. First of all, tracing the intellectual development of humankind by learning about the evolution of at least some mathematics concepts, students would have an opportunity to link the remarkable individuals, who tirelessly contributed to the development of the structure and language of mathematics to the concepts the students learn in school. If students perceive mathematics as a set of discrete topics with no historical background or discussion of historical significance, it is likely they will fail to see the connectedness and relevance of topics within mathematics and among related sciences. Krathwohl, Bloom, and Masia (1973) argued that when students are exposed to varied experiences related to the cultural and historical aspects of evolution of mathematics, they are likely to develop an appreciation of mathematics and its role in the development of our society.

We believe that a historical background provides a perspective that lays a foundation for learning. The HOM may be viewed as a window into the theory of the subject and is likely to provide a non-threatening opportunity for entry learning of mathematics. In particular, it may be beneficial to the student whose learning of mathematics is a struggle. Knowing that in the earliest stages of invention, many of the mathematical concepts were extremely difficult to refine, understand and accept for even the most gifted mathematicians. As an example, it is well known fact that Diaphantus rejected negative numbers and called them absurd. While as early as the seventh century different civilizations in the Middle East used negative numbers to represent debts and positive numbers to represent assets, later on in the seventeenth century in Europe, Descartes rejected negative roots of equations and called them ‘false’ numbers, Pascal regarded the result of subtraction of a whole number from zero as nonsense, and Arnauld argued against negative numbers because in his view they created dissonance in the theory of proportions.

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(Author: Regina M. Panasuk, Leslie Bolinger Horton

Published by Sciedu Press)

[schema type=”review” rev_name=”Excellent” author=”Evan Ballmer” pubdate=”2013-08-07″ user_review=”5″ min_review=”1″ max_review=”5″ ]