DOCSLIB.ORG

History of Chinese Linear Algebra

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
History of Chinese Linear Algebra History of Chinese Linear Algebra Written by Charles Luettgen Citadel Linear Algebra 530 Professor Mei Chen, Instructor Abbreviated history of Chinese Linear Algebra with references to Modern Western Linear Algebra Techniques of Gaussian Elimination and Solution by Determinants History of Chinese Linear Algebra • Chinese Character Development and Problems with Translating Them • General History of Chinese Mathematics and Linear Algebra • Chinese Multple Equation Solving compared to Gaussian Elimination • Chinese Determinants compared to Cramers’ Rule • Why you didn’t know this History of Chinese Linear Algebra • Writing developed 6600-6200 BC • >100,000 Chinese Characters (not alphabets) • Need for Standardization – Qin Dynasty (circa 220 BC) • Modern Simplification – Multiple Scripts added over time – 19 Century (some before but most after the reforms of the Peoples Republic of China) History of Chinese Linear Algebra History of Chinese Linear Algebra • Multiple Uses and Variants of Numbers • Development of the Zero, Negative Numbers, Powers and Fractions • Need to Solve multiple Equations for Taxes, Astronomy, Engineering and Surveying History of Chinese Linear Algebra Typical Counting Rods Numerals and counting board History of Chinese Linear Algebra History of Chinese Linear Algebra History of Chinese Linear Algebra • Chinese Multple Equation Solving compared to Gaussian Elimination C B A 0 0 3 0 4 0 4 0 0 11 17 38 (Transposed) A 3 0 0 38 B 0 4 0 24 C 4 0 0 11 History of Chinese Linear Algebra • Chinese Determinants compared to Cramers’ Rule – Chinese Method Used Guesses to Formulate Matrix Coefficients in Example Format – Chinese Method intended for Practical Daily Application • Cramer’s Rule uses General Proof Theorem to State Rule for all Examples – Cramer’s Rule for Mathematicians History of Chinese Linear Algebra • Chinese approach: • The 20 problems give a rule of double false position. Essentially linear equations are solved by making two guesses at the solution, then computing the correct answer from the two errors. For example to solve • ax + b = c • we try x = i, and instead of c we get c + d. Then we try x = j, and instead of c we obtain c + e. Then the correct solution is • x = (jd - ie)/(d - e). • The first problem essentially contains the "guesses" in its formulation:- • Certain items are purchased jointly. If each person pays 8 coins, the surplus is 3 coins, and if each person gives 7 coins, the deficiency is 4 coins. Find the number of people and the total cost of the items. [Answer: There are 7 people and the total cost of the items is 53 coins.] History of Chinese Linear Algebra • General case • Consider a system of n linear equations for n unknowns, represented in matrix multiplication form as follows: • where the n by n matrix has a nonzero determinant, and the vector is the column vector of the variables. • Then the theorem states that in this case the system has a unique solution, whose individual values for the unknowns are given by: • where is the matrix formed by replacing the ith column of by the column vector . • The rule holds for systems of equations with coefficients and unknowns in any field, not just in the real numbers. It has recently been shown that Cramer's rule can be implemented in O(n3) time,[6] which is comparable to more common methods of solving systems of linear equations, such as Gaussian elimination. History of Chinese Linear Algebra • Why You Didn’t Know This? – Complicated Character/ Number System – Great Wall of China/ Isolationism (up to 1500 AD) – Deterioration of Written Materials (2000 yrs old) – Burning of Books/ Erasure of Previous Regime – Lack of Math Skills amongst Translators – Vatican Conspiracy to Plagiarize Chinese Texts without Acknowledgement of Chinese Authors Starting as Early as 1607 AD to 20th century References • The Chinese Roots of Linear Algebra, (book review)Roger Hart, John Hopkins University Press, 2010, http://books.google.com/books?id=zLPm3xE2qWgC&dq=chinese+linear+algebra&source=gbs_navlinks_s • Chinese Roots of Linear Algebra, Roger Hart, 2009, http://uts.cc.utexas.edu/~rhart/algebra/main.html • • History of Math, Historical Modules for the Mathematics Classroom; Solving Systems of Linear Equations: Ancient Methods, , Creative Commons Attribution-ShareAlike 3.0 License, 4 Aug 2009, http://hom.wikidot.com/cramer-s-method-and-cramer- s-paradox • Chinese Mathematics, Wikipedia®, last modified on 6 November 2012,(two linked pages) http://www.crystalinks.com/chinamath.html ,http://en.wikipedia.org/wiki/Chinese_mathematics • Counting rods, Wikipedia®, last modified on 9 November 2012, http://en.wikipedia.org/wiki/Counting_rods • Rod calculus, Wikipedia®, last modified on 20 November 2012, http://en.wikipedia.org/wiki/Rod_calculus#System_of_linear_equations • Chinese Characters, Wikipedia®, last modified on 20 November 2012, http://en.wikipedia.org/wiki/Chinese_characters • Chinese Characters (Google Images), https://www.google.com/search?q=chinese+characters&hl=en&client=firefox- a&hs=uER&tbo=u&rls=org.mozilla:en- US:official&tbm=isch&source=univ&sa=X&ei=KVSrUJqaPIPC9QTKroGwCw&ved=0CEMQsAQ&biw=1440&bih=796&sei=a2Or UNLWM43e8AS5-4C4DA • Chinese Numbers (Google Images) https://www.google.com/search?q=chinese+numbers&hl=en&client=firefox- a&hs=NvT&tbo=u&rls=org.mozilla:en- US:official&tbm=isch&source=univ&sa=X&ei=enyrUPbrIIn48gTR0YGoAw&ved=0CEcQsAQ&biw=1440&bih=796&sei=fXyrULX 4LI3W8gSpm4HQAQ • Ancient Chinese Counting Rods, (Google Images), https://www.google.com/search?q=ancient+chinese+counting+rods&hl=en&client=firefox- a&hs=Tww&tbo=u&rls=org.mozilla:en- US:official&tbm=isch&source=univ&sa=X&ei=4PmrUKqeIISs9ATjs4GgAQ&ved=0CDkQsAQ&biw=1440&bih=796&sei=5PmrU PCzEZKE9QTh6YCYDQ • Cramer’s Rule, Wikipedia®, last modified on 10 November 2012, http://en.wikipedia.org/wiki/Cramer%27s_rule • Renowned Mathematicians of Ancient China, Kaleidoscope-> Science and Invention Cultural China, 2007-2010, http://kaleidoscope.cultural-china.com/en/10Kaleidoscope2079.html • Matrices and Determinants, JJ O’Connor and EF Robertson, MCS St Andrews (UK), February 1996, http://www- history.mcs.st-and.ac.uk/HistTopics/Matrices_and_determinants.html .
Load more

Recommended publications
  • OECD Reviews of Innovation Policy Synthesis Report
    OECD Reviews of Innovation Policy CHINA Synthesis Report ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT in collaboration with THE MINISTRY OF SCIENCE AND TECHNOLOGY, CHINA ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT The OECD is a unique forum where the governments of 30 democracies work together to address the economic, social and environmental challenges of globalisation. The OECD is also at the forefront of efforts to understand and to help governments respond to new developments and concerns, such as corporate governance, the information economy and the challenges of an ageing population. The Organisation provides a setting where govern- ments can compare policy experiences, seek answers to common problems, identify good practice and work to co- ordinate domestic and international policies. The OECD member countries are: Australia, Austria, Belgium, Canada, the Czech Republic, Denmark, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Japan, Korea, Luxembourg, Mexico, the Netherlands, New Zealand, Norway, Poland, Portugal, the Slovak Republic, Spain, Sweden, Switzerland, Turkey, the United Kingdom and the United States. The Commission of the European Communities takes part in the work of the OECD. OECD Publishing disseminates widely the results of the Organisation’s statistics gathering and research on economic, social and environmental issues, as well as the conventions, guidelines and standards agreed by its members. © OECD 2007 No reproduction, copy, transmission or translation of this publication may be made without written permission. Applications should be sent to OECD Publishing: [email protected] 3 Foreword This synthesis report (August 2007 Beijing Conference version) summarises the main findings of the OECD review of the Chinese national innovation system (NIS) and policy.
    [Show full text]
  • Science Without Modernization: China's First Encounter with Useful and Reliable Knowledge from Europe Harriet T
    Science Without Modernization: China's First Encounter With Useful And Reliable Knowledge From Europe Harriet T. Zurndorfer Abstract This paper reviews how recent revisionist scholarship on the history of Chinese science and technology has recast the Jesuit enterprise in China. It argues that the Ming and Qing governments' efforts to control the Jesuit-transmitted knowledge in these fields stimulated ever-more interest among local scholars in Chinese traditions of mathematics and astronomy which culminated in the 18th century 'evidential research' movement. But because the scientific knowledge the Jesuits conveyed was already 'out-of-date' before their arrival in China, local scholars never had the possibility to make a complete reassessment of their own mathematical and astronomical practices. As the primary and -- at times the only -- translators of Western scientific thought to China, the Jesuits had an enormous historical impact on how Chinese scholars became trapped in a pre-Copernican universe where Chinese natural philosophy with its focus on metaphysical interpretations of the natural world remained entrenched until the 19th century. Introduction: The History of Chinese Science and Technology in Global Perspective and the 'Great Divergence' In 1603, the famous Chinese intellectual and Christian convert, Xu Guangqi (1562-1633) offered the local magistrate of his native Shanghai county a proposal outlining the methodology to measure the length, width, depth, and water flow of a river. Xu's document (later printed in his collection Nongzheng quanshu [Comprehensive Treatise on Agricultural Administration]; comp. 1639) 1 employed conventional surveying practices as well as calculating techniques based on the Pythagorean theorem. Although it is tempting to attribute Xu's achievement here as a direct consequence of his meeting the Jesuit Matteo Ricci (1552-1610) in Nanjing that same year, it is not certain from extant documentation that this encounter with the European was the defining influence on his water study.
    [Show full text]
  • Astronomy and Calendars – the Other Chinese Mathematics Jean-Claude Martzloff
    Astronomy and Calendars – The Other Chinese Mathematics Jean-Claude Martzloff Astronomy and Calendars – The Other Chinese Mathematics 104 BC–AD 1644 123 Jean-Claude Martzloff East Asian Civilisations Research Centre (CRCAO) UMR 8155 The National Center for Scientific Research (CNRS) Paris France The author is an honorary Director of Research. After the publication of the French version of the present book (2009), he has been awarded in 2010 the Ikuo Hirayama prize by the Académie des Inscriptions et Belles-Lettres for the totality of his work on Chinese mathematics. ISBN 978-3-662-49717-3 ISBN 978-3-662-49718-0 (eBook) DOI 10.1007/978-3-662-49718-0 Library of Congress Control Number: 2016939371 Mathematics Subject Classification (2010): 01A-xx, 97M50 © Springer-Verlag Berlin Heidelberg 2016 The work was first published in 2009 by Honoré Champion with the following title: Le calendrier chinois: structure et calculs (104 av. J.C. - 1644). This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
    [Show full text]
  • Papers Presented All Over World Inc
    THE GREAT WALL OF CHINA: The World’s Greatest Boundary Monument! John F. Brock, Australia Keywords: Ancient China, surveyors, Pei Xiu, Liu Hui, The Haidao Suanjing, Great Wall(s) of China, Greatest Boundary Monument. ”… in the endeavors of mathematical surveying, China’s accomplishments exceeded those realized in the West by about one thousand years.” Frank Swetz – last line in The Sea Island Mathematical Manual: Surveying and Mathematics in Ancient China. ABSTRACT It is said that the Great Wall of China is the only manmade structure on Earth which is visible from space (not from the Moon)! The only natural feature similarly identifiable from the outer reaches past our atmospheric zone has been named as Australia’s Great Barrier Reef. This Fig. 1 The moon from The Great Wall instead of natural wonder of the sea is vice versa which cannot actually occur !!! continuous while the Great Wall of China is actually made up of a series of castellated walls mainly erected along ridge lines causing major variations in the levels of its trafficable upper surface. Some of the barriers built are not formed from stone but from rammed earth mounds. The purpose for these walls was primarily to facilitate protection from hostile adjoining tribes and marauding hordes of enemy armies intent on looting and pillaging the coffers of its neighbouring wealthier Chinese Dynasty of the time. As the need for larger numbers of military troops became required to defeat the stronger opponents, which may sometimes have formed alliances, the more astute provincial rulers saw a similar advantage in the unification of the disparate Chinese Provinces particularly during the Ming Dynasty (1368-1644).
    [Show full text]
  • The Fundamental Cartographical Technology of Ancient China ─ Forward Intersection
    THE FUNDAMENTAL CARTOGRAPHICAL TECHNOLOGY OF ANCIENT CHINA ─ FORWARD INTERSECTION Zilan WANG1 Keling WANG Institute of History and Philosophy of Science University of Wuhan P.R.China Email: [email protected] Institute of Historical Geography University of Wuhan P.R.China Most available ancient Chinese maps were not based on field survey but were compiled indoor using direct or indirect travel and exploration records. The map preparation process can be roughly divided into the following steps. Firstly, the position of a geographical object is marked on the sketch map using its orientation and distance. The orientation data is based on the 8-orientation system in which the circumference is divided into 8 parts. The distance data is mainly based on the Chinese distance unit “Li”, but a smaller unit “Bu” will be used for detailed description. Secondly, the rectification by “intersection” method is carried out in order to minimize the errors in the relative positions of a geographical object caused by the intrinsic “roughness” of the aforementioned spatial model. This “intersection” rectification method, which is similar to the “forward intersection” in modern survey technology, was analyzed in this article from three angles: (1) the simulation study of the 2nd century B.C. survey map “Mawang Dui Map”, (2) the analysis of the traditional survey theory recorded in Zhou Bi Suan Jing and Jiu Zhang Suan Shu (including Liu Hui’s annotation of the latter), and (3) the new interpretation of the Fei Niao model proposed by Shen Kuo. In addition, travel records of “intersection” observation and the technique and historical background of forward intersection were found in related historical and geographical documents.
    [Show full text]
  • Absence of Geometric Models in Medieval Chinese Astronomy
    ABSENCE OF GEOMETRIC MODELS IN MEDIEVAL CHINESE ASTRONOMY JAYANT SHAH Abstract. In 718 A.D., Ch’¨ut’an Hsi-ta (Gautama Siddh¯artha), an Indian astronomer who was appointed an“astronomer royal” in the T’ang court compiled a compendium of omens and divina- tions, called K’aiy¨uan Chan-ching, analogous to Varahamihira’s Br. hatsam. hita. The 104th volume of this work, Chiu-chih li (Nine Upholders Calendrical System) on astronomy was entirely based on the Indian astronomy of the 7th century which in turn was based on the geometric astronomy of the Greeks. A few years later, the emperor asked I-hsing (Yixing in pinyin), a buddhist monk, an as- tronomer and a mathematician, to overhaul the traditional Chinese astronomy. He submitted an astronomical system, called Ta-yen li (Grand Expansion Calendrical System, Dayan li in pinyin) in 727 A.D. Only Ta-yen li was officially adopted. In the 13th century, a Persian astronomer submitted to Khubi- lai Khan an astronomical system, Myriad Year Calendrical System, based on the geometric Islamic astronomy. This too was not of- ficially adopted. Instead, Khubilai Khan ordered a major reform of the traditional Chinese system. The result was Shou-shih li (Granting the Seasons Calendrical System) which held sway over the Chinese astronomy until the arrival of the Jesuits in the 17th century. An analysis of the motion of the Sun and and the lunar paral- lax in Ta-yen li and Shou-shih li shows how little impact foreign imports had on Chinese astronomy. Geometric methods began to make inroads in Chinese astronomy only after the arrival of the Jesuits in the 17th century.
    [Show full text]
  • Chinese Mathematics and ICCM
    COMMUNICATION Chinese Mathematics and ICCM Editor’s Note: Notices invites occasional contributions, such as this piece, from its sister publications. Lizhen Ji Introduction distinguished Western math- China is big and growing, and Chinese mathematics is also ematicians such as Wiener, expanding and merging with world mathematics. What is Hadamard, Blaschke, and Os- special about the community of Chinese mathematicians? good were crucial for their How has Chinese mathematics evolved and interacted success. with the outside world? How will it impact the future of Modern Chinese math- mathematics and the global mathematics community in ematics reached another the world? minor golden age in the Though these questions are complex, one good way to 1950s and early 1960s. Then understand them is to take a look at an organization which political turmoil settled in. represents Chinese mathematicians and their friends and collaborators around the world: the International The History of ICCM Congress of Chinese Mathematicians (ICCM), which holds With the open door policy its seventh international conference this August in Beijing. in the 1980s, the Chinese economy and hence Chinese Chern in the early 1990s. A Glimpse at the History of Chinese Mathematics mathematics and sciences China has a long history, and Chinese mathematics also developed rapidly. By the has a long history. Though Chinese mathematics was di- 1990s the time was ripe rectly motivated by applications in astronomy, agriculture, to establish an international platform for mathemati- and commerce, there were systematic expositions of the- cians of Chinese descent and their friends to share and ories and results developed by Chinese people.
    [Show full text]
  • THE GREAT WALL of CHINA: the World's Greatest Boundary
    THE GREAT WALL OF CHINA: The World’s Greatest Boundary Monument! By John F. Brock Keywords: Ancient China, surveyors, Pei Xiu, Liu Hui, The Haidao Suanjing, Great Wall(s) of China, Greatest Boundary Monument. :”… in the endeavors of mathematical surveying, China’s accomplishments exceeded those realized in the West by about one thousand years.” Frank Swetz – last line in The Sea Island Mathematical Manual: Surveying and Mathematics in Ancient China. ABSTRACT It is said that the Great Wall of China is the only manmade structure on Earth which is visible from space (not from the Moon)! The only natural feature similarly identifiable from the outer reaches past our atmospheric zone has been named as Australia’s Great Barrier Reef. This Fig. 1 The moon from The Great Wall instead of natural wonder of the sea is vice versa which cannot actually occur !!! continuous while the Great Wall of China is actually made up of a series of castellated walls mainly erected along ridge lines causing major variations in the levels of its trafficable upper surface. Some of the barriers built are not formed from stone but from rammed earth mounds. The purpose for these walls was primarily to facilitate protection from hostile adjoining tribes and marauding hordes of enemy armies intent on looting and pillaging the coffers of its neighbouring wealthier Chinese Dynasty of the time. As the need for larger numbers of military troops became required to defeat the stronger opponents, which may sometimes have formed alliances, the more astute provincial rulers saw a similar advantage in the unification of the disparate Chinese Provinces particularly during the Ming Dynasty (1368-1644).
    [Show full text]
  • Ancient Chinese Mathematics (A Very Short Summary)
    Ancient Chinese Mathematics (a very short summary) • Documented civilization in China from c.3000 BCE. Un- til c.200 CE, ‘China’ refers to roughly to the area shown in the map: north of the Yangtze and around the Yellow rivers. • Earliest known method of enumeration dates from the Shang dynasty (c.1600–1046 BCE) commensurate with the earliest known oracle bone script for Chinese char- acters. Most information on the Shang dynsaty comes from commentaries by later scholars, though many orig- inal oracle bones have been excavated, particularly from Anyang, its capital. • During the Zhou dynasty (c.1046–256 BCE) and especially towards the end in the Warring States period (c.475–221 BCE) a number of mathematical texts were written. Most have been lost but much content can be ascertained from later commentaries. • The warring states period is an excellent example of the idea that wars lead to progress. Rapid change created pressure for new systems of thought and technology. Feudal lords employed itinerant philosophers1) The use of iron in China expanded enormously, leading to major changes in warfare2 and commerce, both of which created an increased need for mathematics. Indeed the astronomy, the calendar and trade were the dominant drivers of Chinese mathematics for many centuries. • The warring states period ended in 221 BCE with the victory of victory of the Qin Emperor Shi Huang Di: famous for commanding that books be burned, rebuilding the great walls and for being buried with the Terracotta Army in Xi’an. China was subsequently ruled by a succession of dynasties until the abolition of the monarchy in 1912.
    [Show full text]
  • Regiomontanus and Chinese Mathematics
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Ghent University Academic Bibliography Philosophica 82 (2008), pp. 87-114 REGIOMONTANUS AND CHINESE MATHEMATICS Albrecht Heeffer * ABSTRACT This paper critically assesses the claim by Gavin Menzies that Regiomontanus knew about the Chinese Remainder Theorem ( CRT ) through the Shù sh ū Ji ǔ zh āng (SSJZ ) written in 1247. Menzies uses this among many others arguments for his controversial theory that a large fleet of Chinese vessels visited Italy in the first half of the 15th century. We first refute that Regiomontanus used the method from the SSJZ . CRT problems appear in earlier European arithmetic and can be solved by the method of the Sun Zi , as did Fibonacci. Secondly, we pro- vide evidence that remainder problems were treated within the European abbaco tradition independently of the CRT method. Finally, we discuss the role of recre- ational mathematics for the oral dissemination of sub-scientific knowledge. * Post-doctoral fellow of the Research Foundation Flanders (FWO). An early draft of this paper was presented at the Symposium in Honor of Chikara Sasaki, Mathematical Sciences & Philosophy in the Mediterranean & the East , 4 – 7 August, 2009, Kamena Vourla, Greece, and benefited from constructive com- ments by Roshdi Rashed and Li Wenlin. 88 A. HEEFFER 1 Introduction The title of this paper is inspired by the section heading of Gavin Men- zies’s latest book 1434 (Menzies 2008, p. 147) titled Regiomontanus’s Knowledge of Chinese Mathematics . Menzies already stirred considerable controversy with his first work titled 1421 (Menzies 2002) in which he claims that the Chinese fleet circumnavigated the world during the Ming and travelled to parts of the world yet undiscovered by the Europeans, such as the Americas.
    [Show full text]
  • KUIL, Vol. 26, 2003, 429-474 the HISTORY of CHINESE
    KUIL, vol. 26, 2003, 429-474 THE HISTORY OF CHINESE MATHEMATICS: THE PAST 25 YEARS ANDREA EBERHARD-BRÉARD REHSEIS (CNRS), France • Ph. D. Program in History • The Graduate Center, CUNY JOSEPH W. DAUBEN Ph. D. Program in History • The Graduate Center, CUNY XU YIBAO Ph.D. Program in History • The Graduate Center, CUNY RESUMEN ABSTRACT El presente artículo presenta los más This paper presents the major accom- importantes logros de la investigacián plishments of research over the past quar- sobre historia de las matemáticas chinas en ter century in the field of Chinese mathe- el ŭltimo cuarto del siglo XX. Comienza matics and its history. We begin with a con una breve panordmica sobre el estado brief overview of the progress of our de conocimientos y las principales figuras knowledge of that history, and the major que realizaron las prirneras contribuciones figures who contributed the fundamental fundamentales antes de 1975 para después early works prior to 1975, and then exam- examinar más detenidamente las aporta- ine more carefully the achievements of the ciones Ilevadas a cabo durante el ŭltimo past quarter century, beginning with a cuarto de siglo: autores europeos, publica- general overview of the subject before ciones en inglés y, finalmente, la extraor- surveying in more detail the contributions dinaria produccián en chino, en su mayor made in the past twenty-five years, first parte tras la Revolución Cultural. by Europeans, then by scholars publishing in English, after which this survey turns to examine the extraordinary production of scholarship written in Chinese, most of it since the end of the Cultural Revolution.
    [Show full text]
  • Problem Solving Skills in Geometry of Chinese and U.S
    A Comparison of Math Teaching and Learning in China and the United States -: Problem Solving Skills in Geometry of Chinese and U.S. Students THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Mathematical Sciences in the Graduate School of The Ohio State University By Yaomingxin Lu Graduate Program in Mathematical Sciences The Ohio State University 2016 Dissertation Committee: Michael Battista, Rodica Costin Copyrighted by Yaomingxin Lu 2016 Abstract According to the TIMMS report, Chinese students tend to have better performance in solving geometry problems than U.S. students. What is the explanation for the superior mathematics achievement of Chinese students? What are the possible contributing factors? The purpose of this study is to compare and examine US and Chinese students’ problem solving skills in geometry and analyze the contributing factors through interviews with students from both countries. The interviews show that the Chinese students were more successful than the US students in creating auxiliary elements for helping them solve geometry problems as well as more comfortable switching to different problem solving strategies. This better performance in solving geometry problems may be due to Chinese teachers’ ability to apply their geometric conceptualizations flexibly in the classrooms because of their experience solving problems using different strategies as well as several non-school-related factors including things such as students’ self-expectation and efforts, family pressure, and cultural value. This kind of research will be useful to develop a deeper understanding of why Chinese students perform better in solving geometry problems compared with their American peers and the factors which contribute to their performances.
    [Show full text]