Calculators in the Classroom: A Proposal for Curricular Change

1980 ◽  
Vol 28 (4) ◽  
pp. 37-39
Author(s):  
Grayson H. Wheatley
Keyword(s):  
Eighteenth Century ◽  
Mathematics Curriculum ◽  
History Of Mathematics ◽  
Social Utility ◽  
Curricular Change ◽  
Careful Study ◽  
Division Algorithm ◽  
Elementary School Mathematics ◽  
History Of ◽  
Modern Mathematics

A careful study of the history of mathematics education will reveal that in this country computation has always been the focus of the elementary school mathematics curriculum. In the eighteenth century children were taught ciphering, rote computation with no attempt to develop an understanding of the process. During the nineteenth century there were a few persons like Warren Coburn calling for attention to meaning, but the curriculum remained computational. During the 1930s there was a movement toward social utility and developing meaning in mathematics. Then in the period from 1958 to 1971 there was an emphasis on teaching the structure of mathematics. Viewed from the perspective of today, there was one unfortunate aspect of the so called “modern mathematics” movement—much attention was given to rationalizing algorithms. The division algorithm, for example, was taught in great detail using a subtracting approach so that students would understand why the algorithm worked.

scholarly journals A short remark on Gödel incompleteness theorem and its self-referential paradox from Neutrosophic Logic perspective

2019 ◽  
pp. 21-26
Author(s):  
V. Christianto ◽  
◽  
◽  
F. Smarandache
Keyword(s):  
20Th Century ◽  
History Of Mathematics ◽  
The Self ◽  
Incompleteness Theorem ◽  
Aristotelian Logic ◽  
Binary Logic ◽  
Neutrosophic Logic ◽  
History Of ◽  
Incompleteness Theorems ◽  
Modern Mathematics

It is known from history of mathematics, that Gödel submitted his two incompleteness theorems, which can be considered as one of hallmarks of modern mathematics in 20th century. Here we argue that Gödel incompleteness theorem and its self-referential paradox have not only put Hilbert’s axiomatic program into question, but he also opened up the problem deep inside the then popular Aristotelian Logic. Although there were some attempts to go beyond Aristotelian binary logic, including by Lukasiewicz’s three-valued logic, here we argue that the problem of self-referential paradox can be seen as reconcilable and solvable from Neutrosophic Logic perspective. Motivation of this paper: These authors are motivated to re-describe the self-referential paradox inherent in Godel incompleteness theorem. Contribution: This paper will show how Neutrosophic Logic offers a unique perspective and solution to Godel incompleteness theorem.

Introduction: The History of Modern Mathematics – Writing and Rewriting

2004 ◽  
Vol 17 (1-2) ◽  
pp. 1-21 ◽  
Author(s):  
Leo Corry
Keyword(s):  
Nineteenth Century ◽  
History Of Mathematics ◽  
Present Issue ◽  
Tel Aviv ◽  
History Of ◽  
New Ideas ◽  
Ancient Mathematics ◽  
Modern Mathematics ◽  
September Issue

The present issue of Science in Context comprises a collection of articles dealing with various, specific aspects of the history of mathematics during the last third of the nineteenth century and the first half of the twentieth. Like the September issue of 2003 of this journal (Vol. 16, no. 3), which was devoted to the history of ancient mathematics, this collection originated in the aftermath of a meeting held in Tel-Aviv and Jerusalem in May 2001, under the title: “History of Mathematics in the Last 25 Years: New Departures, New Questions, New Ideas.” Taken together, these two topical issues are meant as a token of appreciation for the work of Sabetai Unguru and his achievements in the history of mathematics.

scholarly journals Towards African humanicity: Re-mythogolising Ubuntu through reflections on the ethnomathematics of African cultures

2020 ◽  
Vol 8 (2) ◽  
Author(s):  
Iman Chahine
Keyword(s):  
Mathematics Curriculum ◽  
History Of Mathematics ◽  
African Students ◽  
African Experience ◽  
The People ◽  
Indigenous Knowledge Systems ◽  
Collective Beliefs ◽  
Kinship Relations ◽  
History Of ◽  
Students Success

Throughout the history of mathematics, Eurocentric approaches in developing and disseminating mathematical knowledge have been largely dominant. Building on the riches of African cultures, this paper introduces ethnomathematics as a discipline bridging mathematical ideas with cultural contexts thereby honoring diversity and fostering respect for cultural heritages. Ethnomathematics promotes a conceptualisation of culture to include the authentic humanity of the people sharing collective beliefs, traditions, and practices. I propose the term African humanicity to refer to the authentic African experience that reflects genuine African cultural identity. I further argue that immersion in the ethnomathematical practices of African cultures provides insight into critical factors shaping African students’ success in mathematics. Drawing upon the vast literature on the ingenuity of African cultures, I present ethnomathematical ideas that permeate numerous African indigenous knowledge systems that could be introduced in the mathematics curriculum. These systems include folk games and puzzles, kinship relations, and divination systems.

Euler, Leonhard (1707–1783)

2018 ◽  
Author(s):  
Jeremy Gray
Keyword(s):  
Eighteenth Century ◽  
Quadratic Forms ◽  
Body Problem ◽  
History Of Mathematics ◽  
Body Motion ◽  
Integral Calculus ◽  
History Of ◽  
The Subject ◽  
High Level ◽  
Three Body

Leonhard Euler’s importance for the history of mathematics is undoubted. Not only was he the most prolific mathematician ever – his collected works so far run to 76 volumes and further editions of his correspondence are planned – he dominated the eighteenth century. He combined an extraordinary memory, a capacity for a huge range of interests, an exceptional technical facility, and an ability to work to a high level of abstraction with a natural clarity of expression. His importance extends beyond his many profound innovations in many fields, of which three can be mentioned here: - mechanics, which he built up from the motion of point masses through the theory of rigid body motion to aero- and hydrodynamics, with applications to ship design, gunnery, optics, and celestial mechanics, where he did important work on the motion of the Moon and the three body problem; - the calculus, where he successfully introduced the concept of a function as fundamental; and - number theory, including the theory of quadratic forms and the zeta function. It was also the force of his example that established the culture of publishing in mathematics, and replaced the markedly more secretive habits of Newton and Leibniz. His widespread correspondence stimulated others, his work at the head of the Academy of St Petersburg helped develop mathematics in Russia, and his textbooks on the differential and integral calculus and on algebra made the subject accessible to generations of students.

Mathematics, Epistemology, Ethics: Robert Musil, the Man Without Qualities

2018 ◽  
pp. 93-125
Author(s):  
Nina Engelhardt
Keyword(s):  
History Of Mathematics ◽  
Analytic Philosophy ◽  
Profound Change ◽  
Robert Musil ◽  
Double Function ◽  
History Of ◽  
Critical Questioning ◽  
Modern Mathematics ◽  
Literary Aesthetic

Chapter 3 argues that mathematics in Musil’s The Man without Qualities not only exemplifies the side of rationality but also encompasses mystical elements and transitional states between these opposites, tracing the identification of a non-rational element in mathematics to the debate between the logicist/formalist and the intuitionist schools. The chapter thus re-examines notions of the rational and non-rational and attempts at their synthesis from the perspective of the history of mathematics. It also demonstrates that, for Musil, mathematics answers to two major instances of modern crisis: the failing of reason and the loss of trust. Paradoxically combining critical questioning of its foundations and confidence in its usefulness, modern mathematics connects the approaches of analytic philosophy and outcome-focused pragmatism. The chapter thus argues that mathematics becomes a model not only of exactitude but also of vagueness and that in this paradoxical double-function it serves to inspire the critical trust needed to adjust epistemology, ethics and aesthetics in a time of profound change. Not least, in its own form The Man without Qualities translates the model of mathematics into literary aesthetic by reflecting simultaneous examination of its conditions and trust in the credit of fiction.

Stewart's Theorem, with Applications

1928 ◽  
Vol 21 (8) ◽  
pp. 465-478
Author(s):  
Richard Morris
Keyword(s):  
Eighteenth Century ◽  
Great Britain ◽  
History Of Mathematics ◽  
Text Book ◽  
History Of ◽  
Made In ◽  
Greek Geometry

The writer will introduce this paper by quoting a sentence from Cajori's History of Mathematics. “While in France the school of G. Monge was creating Modern Geometry, efforts were made in England by Robert Simson (1687-176) and Matthew Stewart (1717-1785) to revive Greek Geometry. The latter was a pupil of Simson and was one of the two prominent mathematicians in Great Britain during the eighteenth century.” Dr. David Eugene Smith speaks of Euclid as the most influential text-book on mathematics ever written. We are grateful to these two men, Simson and Stewart, for their labors in the Renaissance of Geometry.

Reviews and Evaluations

1968 ◽  
Vol 61 (2) ◽  
pp. 190-194
Author(s):  
Harold Tinnappel
Keyword(s):  
History Of Mathematics ◽  
Limited Success ◽  
Mathematical Thought ◽  
History Of ◽  
New Ideas ◽  
Working Out ◽  
Modern Mathematics

A translation of the first venture into the history of mathematics by a professor of Greek at Lausanne University, this book seeks with only very limited success “to explain the birth of modern mathematics by describing the progress of mathematical thought at the time of Plato” and to convince the reader that “twenty-five years of thought and discussion in Plato's Academy sufficed to delimit the field of mathematics in all its breadth [and] saw the working-out of new ideas on which the whole edifice of modern mathematics rests.”

Projects: Historical Modules Project

2000 ◽  
Vol 93 (8) ◽  
pp. 728
Keyword(s):  
High School ◽  
High School Teachers ◽  
National Science Foundation ◽  
Mathematics Curriculum ◽  
History Of Mathematics ◽  
Secondary Mathematics ◽  
Teaching Mathematics ◽  
School Teachers ◽  
National Science ◽  
History Of

The Historical Modules Project, a part of the Institute in the History of Mathematics and Its Use in Teaching (IHMT), is sponsored by the Mathematical Association of America (MAA) and supported by the National Science Foundation. In the project, eighteen high school teachers and six college teachers with experience in the history of mathematics have been working in six teams to develop modules for various topics in the secondary mathematics curriculum. These modules are intended to show teachers how to use the history of mathematics in teaching mathematics.

Sign in / Sign up

Export Citation Format

Share Document