Theory of polygonal numbers with Cuisenaire rods manipulatives: Understanding Theon of Smyrna’s arithmetic in a history of mathematics classroom

2018 ◽  
Vol 34 (1) ◽  
pp. 12-22
Author(s):  
Günhan Caglayan
1987 ◽  
Vol 35 (4) ◽  
pp. 13-16 ◽  
Author(s):  
Abraham Arcavi

The arguments advocating the use of the history of mathematics in mathematics education have become widespread in recent years. Theoretical and practical guidelines for using history have also appeared, some of them accompanied by the description of actual experiences (see, e.g., the review by Booker [1985]).


Author(s):  
Suphi Önder Bütüner ◽  
Adnan Baki

In this action study, instructional environments were enriched with activities related to the history of mathematics in order to deepen students’ beliefs about mathematics and reveal for them fun, interesting, and useful activities. The study enrolled twenty-four 8th-grade students. Data were collected by using multiple data collection tools. The data regarding the students’ beliefs about mathematics were collected via written opinion forms and semi-structured interviews. Prior to the study, the students perceived mathematics as a branch of science that is closed to development and did not know why or how it flourished. After the study, they stated that mathematics is open to development and is used to solve everyday problems. The study revealed a decrease in students’ absolutist beliefs about mathematics, and students found math fun and interesting as a result of engaging in activities that promote active problem-solving. In the future, other action studies involving the history of mathematics may be used to teach different topics at different grade levels.


Author(s):  
Carryn Bellomo ◽  
Cassidy Wertheimer

As a high school algebra teacher continuing as a student in a Master’s of Mathematics Program, the author decided with the help of an advisor to see what effect incorporating history had on an Algebra II Honors course.  The following paper includes a brief review of research, analysis of ways to incorporate history of mathematics into the classroom, examples of methods used in the classroom, and the effect this had on student and teacher learning and attitudes.


2015 ◽  
Vol 9 (1) ◽  
pp. 59-87 ◽  
Author(s):  
Martin Calamari

In recent years, the ideas of the mathematician Bernhard Riemann (1826–66) have come to the fore as one of Deleuze's principal sources of inspiration in regard to his engagements with mathematics, and the history of mathematics. Nevertheless, some relevant aspects and implications of Deleuze's philosophical reception and appropriation of Riemann's thought remain unexplored. In the first part of the paper I will begin by reconsidering the first explicit mention of Riemann in Deleuze's work, namely, in the second chapter of Bergsonism (1966). In this context, as I intend to show first, Deleuze's synthesis of some key features of the Riemannian theory of multiplicities (manifolds) is entirely dependent, both textually and conceptually, on his reading of another prominent figure in the history of mathematics: Hermann Weyl (1885–1955). This aspect has been largely underestimated, if not entirely neglected. However, as I attempt to bring out in the second part of the paper, reframing the understanding of Deleuze's philosophical engagement with Riemann's mathematics through the Riemann–Weyl conjunction can allow us to disclose some unexplored aspects of Deleuze's further elaboration of his theory of multiplicities (rhizomatic multiplicities, smooth spaces) and profound confrontation with contemporary science (fibre bundle topology and gauge field theory). This finally permits delineation of a correlation between Deleuze's plane of immanence and the contemporary physico-mathematical space of fundamental interactions.


Author(s):  
Jed Z. Buchwald ◽  
Mordechai Feingold

Isaac Newton’s Chronology of Ancient Kingdoms Amended, published in 1728, one year after the great man’s death, unleashed a storm of controversy. And for good reason. The book presents a drastically revised timeline for ancient civilizations, contracting Greek history by five hundred years and Egypt’s by a millennium. This book tells the story of how one of the most celebrated figures in the history of mathematics, optics, and mechanics came to apply his unique ways of thinking to problems of history, theology, and mythology, and of how his radical ideas produced an uproar that reverberated in Europe’s learned circles throughout the eighteenth century and beyond. The book reveals the manner in which Newton strove for nearly half a century to rectify universal history by reading ancient texts through the lens of astronomy, and to create a tight theoretical system for interpreting the evolution of civilization on the basis of population dynamics. It was during Newton’s earliest years at Cambridge that he developed the core of his singular method for generating and working with trustworthy knowledge, which he applied to his study of the past with the same rigor he brought to his work in physics and mathematics. Drawing extensively on Newton’s unpublished papers and a host of other primary sources, the book reconciles Isaac Newton the rational scientist with Newton the natural philosopher, alchemist, theologian, and chronologist of ancient history.


Sign in / Sign up

Export Citation Format

Share Document