CHI TIẾT NGHIÊN CỨU …

Tiêu đề

The role of mathematics in liberal arts education

Tác giả

Grabiner J.V.

Năm xuất bản

2014

Source title

International Handbook of Research in History, Philosophy and Science Teaching

Số trích dẫn

0

DOI

10.1007/978-94-007-7654-8_25

Liên kết

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85040598399&doi=10.1007%2f978-94-007-7654-8_25&partnerID=40&md5=dc68f015b6f2aa76a8faa44e041fb77d

Tóm tắt

The history of the continuous inclusion of mathematics in liberal education in the West, from ancient times through the modern period, is sketched in the first two sections of this chapter. Next, the heart of this essay (Sects. 3, 4, 5, 6, and 7) delineates the central role mathematics has played throughout the history of Western civilization: not just a tool for science and technology, mathematics continually illuminates, interacts with, and sometimes challenges fields like art, music, literature, and philosophy - subjects now universally considered to be liberal arts. Section 8 adds an international perspective to the contemporary liberal arts story by describing some instructive mathematical achievements from many cultures and societies. Finally, Sect. 9 addresses how contemporary mathematics teaching can use the history of mathematics viewed as a liberal art to enhance the appreciation and understanding of mathematics for all students. © Springer Science+Business Media Dordrecht 2014.

Từ khóa

Tài liệu tham khảo

Abbott E., Flatland: A Romance of Many Dimensions, (1884); Abbott E., Flatland, (1884); Biographies of Mathematicians, (2012); Tri-State Student Achievement Study, (2003); Arianrhod R., Seduced by Logic: Émilie Du Châtelet, Mary Somerville and the Newtonian Revolution, (2012); Aristotle, De Anima, pp. 535-603, (1941); Metaphysics, pp. 689-926, (1941); Aristotle, The Basic Works of Aristotle, (1941); Ascher M., Ethnomathematics: A Multicultural View of Mathematical Ideas, (1998); Ascher M., Mathematics Elsewhere: An Exploration of Ideas across Cultures, (2002); Ashcraft M.H., Math Anxiety: Personal, Educational, and Cognitive Consequence, Current Directions in Psychological Science, 11, 5, pp. 181-185, (2002); Babbage C., On the Economy of Machinery, (1832); Ball D.L., Hill H.C., Bass H., Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade and how can we decide?, American Educator, pp. 14-46, (2005); Barrett W., Irrational Man: A Study in Existential Philosophy, (1958); Barzun J., Teacher in America, (1945); Baudrillard J., Reversion of History, CTheory.net, (1994); Becker C.L., The Declaration of Independence: A Study in the History of Political Ideas, (1922); Berggren J.L., Episodes in the Mathematics of Medieval Islam, (1986); Berggren J.L., Mathematics in Medieval Islam, pp. 515-675, (2007); Boaler J., Staples M., Creating Mathematical Futures through an Equitable Teaching Approach: The Case of Railside School, Teacher’s College Record, 110, 3, pp. 608-645, (2008); Bonola R., Non-Euclidean Geometry: A Critical and Historical Study of Its Development. With a Supplement containing “The Theory of Parallels” by Nicholas Lobachevski and “The Science of Absolute Space” by John Bolyai, (1955); Boole G., An Investigation of The Laws of Thought, (1854); Boyer C.B., History of Analytic Geometry, (1956); Brewer J.W., Smith M.K., Emmy Noether: A Tribute to Her Life and Work, (1989); Burger E., Starbird M., The Heart of Mathematics: An Invitation to Effective Thinking, (2012); A Classification of Institutions of Higher Education, (1994); Cauchy A.-L., Cours d’analyse de l’Ecole Royale Polytechnique, (1821); Cauchy A.-L., Oeuvres, series 2, 3, (2009); Cauchy A.-L., Cauchy’s Cours d’analyse: An Annotated Translation, (2009); Cesareo F.C., Quest for Identity: The Ideals of Jesuit Education in the Sixteenth Century, pp. 17-33, (1993); Chapple C., Introduction, pp. 7-12, (1993); Chapple C., The Jesuit Tradition In Education and Missions, (1993); Chemla K., Using documents from ancient China to teach mathematical proof, pp. 423-429, (2012); Cicero M.T., De oratore, In Two Volumes, 1-2, (1942); Cicero M.T., De re publica; de legibus, (1928); Clifford W.K., The Postulates of the Science of Space, 1, pp. 552-567, (1956); Closs M., The Mathematical Notation of the Ancient Maya, Native American Mathematics, pp. 291-369, (1986); Cohen I.B., The Newtonian Revolution, (1980); Cohen I.B., Science and the Founding Fathers, (1995); For All Practical Purposes: Mathematical Literacy in Today’s World, (2013); Comte A., Cours de philosophie positive, 1, (1830); Condorcet M., Sketch for a Historical Picture of the Progress of the Human Mind, Condorcet: Selected Writings, (1793); Convergence; Cruz J.A.H.M., Education, Encyclopedia of the Renaissance, 2, pp. 242-254, (1999); Dahan-Dalmedico A., Sophie Germain, Scientific American, 265, pp. 117-122, (1991); D'Ambrosio U., Ethnomathematics and Its Place in the History and Pedagogy of Mathematics, For the Learning of Mathematics, 5, 1, pp. 44-48, (1985); Dauben J., Chinese Mathematics, pp. 187-385, (2007); Deakin M., Hypatia of Alexandria: Mathematician and Martyr, (2007); Descartes R., Discourse on Method, (1637); Descartes R., La géométrie, (1637); Dickens C., Hard Times, (1854); Elements; Ferrall V.E., Liberal Arts at the Brink, (2011); Fauvel J., Gray J., The History of Mathematics: A Reader, (1987); Fauvel J., Flood R., Wilson R., Music and Mathematics: From Pythagoras to Fractals, (2003); Field J.V., The Invention of Infinity: Mathematics and Art in the Renaissance, (1997); Field J.V., Musical cosmology: Kepler and His Readers, pp. 28-44, (2003); Frantz M., Crannell A., Viewpoints: Mathematical Perspective and Fractal Geometry in Art, (2011); Friedman M., Kant and the Exact Sciences, (1992); Gaukroger S., Descartes: An Intellectual Biography, (1995); Gerdes P., Geometry from Africa: Mathematical and Educational Perspectives, (1999); Gillings R.J., Mathematics in the Time of the Pharaohs, (1972); Gillispie C.C., The Edge of Objectivity, (1960); Grabiner J.V., The Centrality of Mathematics in the History of Western Thought, Mathematics Magazine, 61, (1988); Grabiner J.V., A Historian Looks Back: The Calculus as Algebra and Selected Writings, (2010); Grabiner J.V., How to Teach Your Own Liberal Arts Course, Journal of Humanistic Mathematics, 1, 1, pp. 101-118, (2011); Grant H., Mathematics and the Liberal Arts I, College Mathematics Journal, 30, 2, pp. 96-105, (1999); Grant H., Mathematics and the Liberal Arts II, College Mathematics Journal, 30, 3, pp. 197-203, (1999); Gray J., Ideas of Space: Euclidean, Non-Euclidean and Relativistic, (1989); Grendler P.F., Schooling in Renaissance Italy: Literacy and Learning, 1300-1600, (1989); Grendler P.F., The Universities of the Italian Renaissance, (2002); Grinstein L.S., Campbell P.J., Women of Mathematics: A Biobibliographic Sourcebook, (1987); Hadid Z., (2008); Hagengruber R., Emilie du Châtelet between Leibniz and Newton, (2012); Hanna G., de Villiers M., Proof and Proving in Mathematics Education, (2012); Hardy G.H., A Mathematician’s Apology, (1940); Haskins C.H., The Renaissance of the Twelfth Century, (1927); Heath T.L., The Thirteen Books of Euclid’s Elements, (1925); Heath T.L., Mathematics in Aristotle, (1949); Helmholtz H., On the sensations of tones, (1863); Helmholtz H., On the origin and significance of geometrical axioms, (1870); Von Helmholtz H., Popular Scientific Lectures, pp. 223-249; Henderson L., The Fourth Dimension and Non-Euclidean Geometry in Modern Art, (1983); Hill H.C., Rowan B., Ball D.L., Effects of teachers’ mathematical knowledge for teaching on student achievement, American Educational Research Journal, 42, pp. 371-406, (2005); Hobbes T., Leviathan, or the Matter, Form, and Power of a Commonwealth, Ecclesiastical and Civil, (1651); Burtt E., The English Philosophers from Bacon to Mill; Hoeflich M.H., Law and Geometry: Legal Science from Leibniz to Langdell, American Journal of Legal History, 30, pp. 95-121, (1986); Hoyrup J., In Measure, Number, and Weight: Studies in Mathematics and Culture, (1994); Horng W.S., Euclid versus Liu Hui: A Pedagogical Reflection, pp. 37-47, (2000); Huffman C., Archytas, The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), (2011); Hutcheson F., On computing the morality of actions, Inquiry into the Original of Our Ideas of Beauty and Virtue in Two Treatises, (1728); Hyman A., Charles Babbage: Pioneer of the Computer, (1982); Imhausen A., Egyptian Mathematics, pp. 7-56, (2007); Jacobs H.R., Mathematics: A Human Endeavor, (2012); Jaeger W., Paideia: The Ideals of Greek Culture, 3, (1944); Jeans J., Mathematics of Music, 4, pp. 2278-2309, (1956); Joseph G.G., The Crest of the Peacock: Non-European Roots of Mathematics, (2011); Kalman L., Legal Realism at Yale, 1927-1960, (1986); Kant I., Prolegomena to Any Future Metaphysics, (1783); Kant I., Critique of Pure Reason, (1781); Karp T.C., Music, pp. 169-195, (1983); Katz V.J., Using History to Teach Mathematics: An International Perspective, (2000); Katz V.J., The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, (2007); Katz V.J., A History of Mathematics: An Introduction, (2009); Kemp M., The Science of Art: Optical Themes in Western Art from Brunelleschi to Seurat, (1990); Kimball B., Orators and Philosophers: A History of the Idea of Liberal Education, (1995); Klein J., Greek Mathematical Thought and the Origins of Algebra, (1968); Kline M., Mathematics in Western Culture, (1953); Knorr W.R., The Evolution of the Euclidean Elements, (1975); Koblitz A.H., A Convergence of Lives: Sofia Kovalevskaia, Scientist, Writer, Revolutionary, (1983); LaPiana W.P., Logic and Experience: The Origin of Modern American Legal Education, (1994); Laplace P.-S., A Philosophical Essay on Probabilities, (1819); Leibniz G.W., Preface to the General Science and Towards a Universal Characteristic, Leibniz: Selections, pp. 12-25, (1677); Leibniz G.W., A new method for maxima and minima … and a remarkable type of calculus for them, pp. 271-280, (1684); Leslie D., Argument by contradiction in Pre-Buddhist Chinese Reasoning, (1964); Levinson S., Frames of Reference and Molyneux’s Question: Crosslinguistic Evidence, Language and Space, pp. 109-170, (1996); Levinson S., Language and Mind: Let’s Get the Issues Straight, Language in Mind: Advances in the Study of Language and Thought, pp. 25-46, (2003); Lovejoy A., The Great Chain of Being, (1936); Ma L., Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States, (1999); Women of Mathematics Poster, (2008); Maclaurin C., De viribus mentium bonipetis. MS 3099.15.6, The Colin Campbell Collection, (1714); Mahoney M., The Mathematical Career of Pierre de Fermat, 1601-1655, (1973); Malthus T.R., An Essay on the Principle of Population, as it Affects the Future Improvement of Society: With Remarks on the Speculations of Mr. Godwin, M. Condorcet, and other writers, (1798); Marr A., Between Raphael and Galileo: Mutio Oddi and the Mathematical Culture of Late Renaissance Italy, (2011); Marrou H.I., A History of Education in Antiquity, (1956); Martzloff J.-C., A History of Chinese Mathematics, (1997); Masi M., Arithmetic, pp. 147-168, (1983); Mazzotti M., The World of Maria Gaetana Agnesi: Mathematician of God, (2007); McInerny R., Beyond the Liberal Arts, pp. 248-272, (1983); McKirahan R.D., Principles and Proofs: Aristotle’s Theory of Demonstrative Science, (1992); Merz J.T., A History of European Thought in the Nineteenth Century, 1, (1904); Merzbach U., Boyer C.B., A History of Mathematics, (2011); Morrison K.F., Incentives for Studying the Liberal Arts, pp. 32-57, (1983); Neeley K.A., Mary Somerville: Science, Illumination, and the Female Mind, (2001); Newman J.R., The World of Mathematics, (1956); Newton I., Sir Isaac Newton’s Mathematical Principles of Natural Philosophy and His System of the World, (1687); Nussbaum M., Not for Profit: Why Democracy Needs the Humanities, (2010); Olson R., Science and Scientism in Nineteenth-Century Europe, (2008); Ortegay Gasset J., The Historical Significance of the Theory of Einstein, pp. 147-157, (1961); Orwell G., Nineteen Eighty-Four: A Novel, (1949); Packel E., The Mathematics of Games and Gambling, (1981); Pascal B., Pensées, (1669); Peirce B., Linear associative algebra with notes and addenda by C. S. Peirce, American Journal of Mathematics, 4, pp. 97-229, (1881); Plato, The Collected Dialogues of Plato, Including the Letters, (1961); Plato, Republic, pp. 575-844, (1961); Plofker K., Mathematics in India, pp. 385-514, (2007); Plofker K., Mathematics in India, (2009); Poincare H., Science and Hypothesis, (1905); Popkin R.H., The History of Scepticism from Erasmus to Spinoza, (1979); Porter T., The Rise of Statistical Thinking, 1820-1900, (1986); Proclus, A Commentary on the First Book of Euclid’s Elements, (1970); Quetelet A., Instructions populaires sur le calcul des probabilités, (1828); Rabinovitch N.L., Probability and Statistical Inference in Ancient and Medieval Jewish Literature, (1973); Reid C., Julia [Robinson]: A Life in Mathematics, (1996); Richards J.L., Mathematical Visions: The Pursuit of Geometry in Victorian England, (1988); Richards R., The Romantic Conception of Life: Science and Philosophy in the Age of Goethe, (2002); Robson E., Mesopotamian Mathematics, pp. 57-186, (2007); Robson E., Mathematics in Ancient Iraq: A Social History, (2008); Robson E., Stedall J., The Oxford Handbook of the History of Mathematics, (2009); Rose P.L., The Italian Renaissance of Mathematics: Studies on Humanists and Mathematicians from Petrarch to Galileo, (1975); Rudolph F., The American College and University, (1962); Seligman J., The High Citadel: The Influence of Harvard Law School, (1978); Sinaiko H.L., Energizing the Classroom: The Structure of Teaching, Reclaiming the Canon: Essays on Philosophy, Poetry, and History, pp. 241-252, (1998); Schiebinger L., The Mind Has No Sex: Women in the Origins of Modern Science, (1989); Singh P., The so-called Fibonacci numbers in ancient and medieval India, Historia Mathematica, 12, pp. 229-244, (1985); Siu M.K., Proof in the Western and Eastern Traditions: Implications for Mathematics Education, pp. 431-440, (2012); Smith A., The Wealth of Nations, (1776); Spinoza B., Ethics Demonstrated in Geometrical Order, (1675); Stahl W.H., Martianus Capella and the Seven Liberal Arts, (1977); Steen L.A., The Science of Patterns, Science, 240, pp. 611-616, (1988); Struik D.J., A Source Book in Mathematics, (1969); Taton R., siècle, (1964); Tarr J.E., Reys R.E., Reys B.J., Chavez O., Shih J., Osterlind S.J., The impact of middle-grades mathematics curricula and the classroom learning environment on student achievement, Journal for Research in Mathematics Education, 39, 3, pp. 247-280, (2008); Tobias S., Overcoming Math Anxiety, (1993); Tweddle I., An early manuscript of MacLaurin’s: Mathematical modelling of the forces of good; some remarks on fluids, (2008); Van Brummelen G., The Mathematics of the Heavens and the Earth: The Early History of Trigonometry, (2009); Voltaire F.M.A., Philosophical Dictionary, The Works of Voltaire: A Contemporary Version, 6, (1901); Voltaire F.M.A., Morality, (1901); Voltaire F.M.A., Sect, (1901); Wagner D.L., The Seven Liberal Arts and Classical Scholarship, pp. 1-31, (1983); Wagner D.L., The Seven Liberal Arts in the Middle Ages, (1983); Wagner M., The Geometries of Visible Space, (2006); Wardhaugh B., Mathematics, music, and experiment in late seventeenth-century England, pp. 639-661, (2009); Washburn D.K., Crowe D.W., Symmetries of Culture: Theory and Practice of Plane Pattern Analysis, (1998); Weil A., Sur l’étude algébrique de certains types de lois de mariage, Les structures élémentaires de la parenté, pp. 278-287, (1949); Weil A., On the Algebraic Study of Certain Types of Marriage Laws, The Elementary Structures of Kinship, pp. 221-229, (1969); Weizenbaum J., Computer Power and Human Reason: From Judgment to Calculation, (1976); Westman R.S., The Melanchthon Circle, Rheticus, and the Wittenberg Interpretation of the Copernican Theory, Isis, 66, 2, pp. 165-193, (1975); Williams L.P., Relativity Theory: Its Origins and Impact on Modern Thought, (1968); Wilson S., California Dreaming: Reforming Mathematics Education, (2003); Wollenberg S., Music and Mathematics: An Overview, pp. 1-9, (2003); Zamyatin E., We, (1952); Zaslavsky C., Fear of Math: How to Get over It and Get on with Your Life, (1994); Zaslavsky C., Africa Counts: Number and Pattern in African Culture, (1999); Zinsser J., La Dame d’Esprit: A Biography of the Marquise du Châtelet, (2006)

Nơi xuất bản

Springer Netherlands

Hình thức xuất bản

Book chapter

Open Access

Nguồn

Scopus