Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning.)
Average customer rating: 4.5 out of 5 stars
  • Guess the Profession of the Only Person Thus Far to Give this Book a One-Star Rating
  • Highly Recommended for Early Ed. Teachers
  • shows how important a profound understanding of fundamental mathematics is for teaching
  • Cure for Insomnia
  • The Key Differences Between Chinese and American Teaching Methods
Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning.)
Liping Ma
Manufacturer: Lawrence Erlbaum
ProductGroup: Book
Binding: Paperback

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ASIN: 0805829091

Book Description

Chinese students typically outperform U.S. students on international comparisons of mathematics competency. Paradoxically, Chinese teachers receive far less education than U.S. teachers--11 to 12 years of schooling versus 16 to 18 years of schooling.

Studies of U.S. teacher knowledge often document insufficient subject matter knowledge in mathematics. But, they give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education.


This book describes the nature and development of the "profound understanding of fundamental mathematics" that elementary teachers need to become accomplished mathematics teachers, and suggests why such teaching knowledge is much more common in China than the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts.


The studies described in this book suggest that Chinese teachers begin their teaching careers witha better understanding of elementary mathematics than that of most U.S. elementary teachers. Their understanding of the mathematics they teach and--equally important--of the ways that elementary mathematics can be presented to students, continues to grow throughout their professional lives.


Teaching conditions in the United States, unlike those in China, militate against the development of elementary teachers' mathematical knowledge and its organization for teaching. The concluding chapter of the book suggests changes in teacher preparation, teacher support, and mathematics education research that might allow teachers in the United States to attain profound understanding of fundamental mathematics.

Customer Reviews:

5 out of 5 stars Guess the Profession of the Only Person Thus Far to Give this Book a One-Star Rating.......2007-05-27

That's right: a teacher (undoubtedly an American teacher), and even worse, one working on a master's degree in education. And yet, she (to pick a gender to use) is unable to see any worth in this great book. Furthermore, her review illustrates one of the problems with many teachers today in the US: the lack of critical thinking skills, not to mention an apparent ignorance about research methodologies.

That reviewer complained that the author "neglects to even mention any cultural differences between the two societies that she is comparing" and saw that failure as a fallacy that undermined everything said in the entire book. How cultural differences would alter any of the valuable lessons that we can learn from this book about a better way of teaching mathematics in elementary school and the importance of teachers having an in-depth knowledge of the subjects that they are teaching is completely lost on me. Maybe that's because they would not make any difference!

Math is a universal language, and we should be able to learn something from other cultures who we already know are producing children who consistently outscore American children by a wide margin.

And guess what: one of the basic goals of cross-cultural studies is to find out if others are doing something better and, if so, whether their methods can be applied successfully to help us do something, like teaching mathematics, better. Of course there are some cultural differences between the US and China, but so what? The point is to examine other societies who are apparently doing a better job in some area and see what they are doing differently and what can we learn from them.

The fact that a teacher found this book "boring and not worth the paper that it is printed on" should tell those of you not working in the field of education how bad it already is in our schools and how much worse it is probably going to get in the future. I teach remedial mathematics at the college level. In case any of you reading my comments did not know it, many of our schools are, and for some time now have been, graduating kids from high school who cannot add and subtract integers because they do not understand the most basic facts about our number system and how it works. None of my students have even heard the term "base 10," which is what the "composing" and "decomposing" concepts used by the Chinese teachers relies so heavily upon, and is what determines the value of every number in the system that we use in everyday life (computers, of course, use base 2).

Is there any hope for improvement in the future? Frankly, I don't think so because we just keep throwing money at the problem (giving it to the same people who helped cause the problems), rather than doing those things that are necessary to bring about meaningful changes.

5 out of 5 stars Highly Recommended for Early Ed. Teachers.......2007-01-28

I am a college student who purchased this book for a class project. It was VERY HELPFUL. I used the chapter on division by fractions to teach my class ways to make it easier, and the reasoning behind the methods. It was so accurate on how American teachers teach, that anyone who will be teaching math to students should really review this book to learn helpful methods for students. I aced my lesson plan for the class I taught.

Topics in this book range from subtraction, to multiplication, division, representations of fractions, and more.
The case study comparisons between the Chinese teachers and the American teachers was shocking. A must read for anyone going into Elementary Education, or working in an Elementary School system.

5 out of 5 stars shows how important a profound understanding of fundamental mathematics is for teaching.......2007-01-16

Knowing and Teaching Elementary Mathematics is a book that compares and contrasts American and Chinese approaches to teaching elementary mathematics ie arithmetic and elementary geometry. The author argues that Chinese teachers have a more profound understanding of elementary mathematics than their American counterparts and provides pretty good evidence of this. While this aspect of the book is useful, the authors explanation of just what profound understanding of fundamental mathematics amounts to is much more useful. For example rather than using the technique of borrowing to subtract, the author recommends using something called decomposing a number which means understanding that, for example, the 2 in 23 is two tens so in 23 - 15 you move one ten from the 20 part and carry it over to the ones as a ten so 10 + 3 = 13 then you proceed to subtract 5 from 13. Of course the end result is the same but the student learns about the structure of numbers in the process ie that 23 = 2* 10 + 3 * 1. Anyway this is a very useful book. It is also a little bit embarrassing as I was not fully knowledgeable about some of the examples she used. For instance although I knew the process for computing (1 and 3/4 )/ (1/2) I couldn't for the life of me come up with a story to explain why you would want to do that. Anyway, this is a very eye opening book about the state of mathematics education in America and also just what it means to be proficient in elementary mathematics.

1 out of 5 stars Cure for Insomnia.......2006-12-14

Ma's book would put anyone to sleep. As a student working on a Masters in Special Education, this book was horrible. Basically, Ma compares Chinese teachers to American teachers in the area of Mathematics. She neglects to even mention any cultural differences between the two societies that she is comparing. This alone creates a fallacy for all of the generalizations that Ma makes about teachers from both countries. In summary, this book is long, boring and not worth the paper that it is printed on.

4 out of 5 stars The Key Differences Between Chinese and American Teaching Methods.......2006-09-23

For many years, I have heard about how Asian countries typically outperform America in tests relating to concepts in mathematics. I've often wondered why; I thought perhaps it's because testing is more rigorous in these countries or perhaps the students have more homework and are able to practice math more frequently. However, after reading this book, it appears the teaching method may make the biggest difference. Better teachers have probably had better experiences of being taught when they were students. This cycle continues on, therefore producing more competent students and perhaps fostering an interest in teaching in the future.
Much of the data contained in this book is based upon interviewing 23 American elementary-level teachers and 72 Chinese elementary-level teachers in regards to teaching processes. Each chapter deals with a different scenario: subtraction with regrouping, multi-digit multiplication, division by fractions, and relationship between perimeter and area. The point of each topic analysis is to see how the different teachers responded to each of these concepts.How would they teach it? Would they provide additional examples outside of the textbook? How would they correct a students mistake? I found Chapter 4's scenario particularly interesting: how would a teacher prove (or disprove) a student's unconventional new theory about area and perimeter?
Many excerpts from the teacher interviews are provided to show the differences between the understanding of the U.S. teachers and the Chinese teachers. The biggest problem with the American teachers that I noticed was that a fairly large majority of them were usually unsure of the rationale of why particular math concepts were carried out a certain way. Even when the math procedures were carried out correctly, the American teachers seemed much more unsure of their own knowledge than the Chinese teachers. The Chinese teachers usually provided more concise responses in regards to teaching the different types of material, as well as providing alternate ways to approach the problem.
The Chinese teachers most often showed a very deep understanding of the topic at hand, going above and beyond any of the American teachers' explanations. The most interesting observation is made by one of the teachers in Chapter 1; Tr. Chen mentions: "The operation of subtraction with decomposition (the Chinese term for subtraction with regrouping) is the application of several ideas rather than a single one. It is a package, rather than a sequence, of knowledge.". This "knowledge package" term is mentioned several times later on in this book, and I think it is an incredibly important indication of the difference between Chinese and American teaching methods. Every subject in mathematics, at the elementary level and higher levels, can be related to other important operations. For example, subtraction with regrouping should not be taught alone, as if it isn't relation to other concepts; it should be related to subtraction without regrouping, addition and subtraction as inverse operations, and so on. Many more examples of knowledge package diagrams are given in the book.
In conclusion, I find that "Knowing and Teaching Elementary Mathematics" would be a helpful book to read for anyone interested in wanting to improve their method of learning or teaching mathematics. For that matter, many of the techniques employed by the Chinese teachers interviewed could be applied to other subjects as well; integration of how one topic is directly related to others in a "knowledge package" is incredibly helpful in better understanding any subject.
The Tibetan Book of the Great Liberation: Or the Method of Realizing Nirvana through Knowing the Mind
Average customer rating: 4.5 out of 5 stars
  • A mistaken interpretation of Dzogchen and Tibetan Buddhism
  • backward-foreword
  • One of the best
  • The 4th book in the Tibetan Series by W.Y.Evans-Wentz
  • Ian Myles Slater on: Still Worth It, But Check Competition
The Tibetan Book of the Great Liberation: Or the Method of Realizing Nirvana through Knowing the Mind
C. G. Jung
Manufacturer: Oxford University Press, USA
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Binding: Paperback

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ASIN: 0195133153

Book Description

The Tibetan Book of the Great Liberation, which was unknown to the Western world until its first publication in 1954, speaks to the quintessence of the Supreme Path, or Mahayana, and fully reveals the yogic method of attaining Enlightenment. Such attainment can happen, as shown here, by means of knowing the One Mind, the cosmic All-Consciousness, without recourse to the postures, breathings, and other techniques associated with the lower yogas. The original text for this volume belongs to the Bardo Thodol series of treatises concerning various ways of achieving transcendence, a series that figures into the Tantric school of the Mahayana. Authorship of this particular volume is attributed to the legendary Padma-Sambhava, who journeyed from India to Tibet in the 8th century, as the story goes, at the invitation of a Tibetan king. Padma-Sambhava's text per se is preceded by an account of the great guru's own life and secret doctrines. It is followed by the testamentary teachings of the Guru Phadampa Sangay, which are meant to augment the thought of the other gurus discussed herein. Still more useful supplementary material will be found in the book's introductory remarks, by its editor Evans-Wentz and by the eminent psychoanalyst C. G. Jung. The former presents a 100-page General Introduction that explains several key names and notions (such as Nirvana, for starters) with the lucidity, ease, and sagacity that are this scholar's hallmark; the latter offers a Psychological Commentary that weighs the differences between Eastern and Western modes of thought before equating the "collective unconscious" with the Enlightened Mind of the Buddhist. As with the other three volumes in the late Evans-Wentz's critically acclaimed Tibetan series, all four of which are being published by Oxford in new editions, this book also features a new Foreword by Donald S. Lopez.

Customer Reviews:

3 out of 5 stars A mistaken interpretation of Dzogchen and Tibetan Buddhism.......2005-01-02

This text has now been published as "Self-Liberation Through Seeing With Naked Awareness" translated by John Myrdhin Reynolds and published by Snow Lion. This edition by Evans-Wentz is basically a misinterpretation of Tibetan Buddhism in general and of Dzogchen in particular. In the book "Self-Liberation Through Seeing With Naked Awareness" over forty pages are given to a detailed discussion of Evans-Wentz and Jung's basic misunderstandings. This alone is well worth reading so you can make up your own mind before (if) you decide to get the Evans-Wentz version. I have found the translation by John Myrdhin Reynolds to be far superior and truly inspirational.

4 out of 5 stars backward-foreword.......2004-07-12

Having returned to this marvelous work recently after an incident in my life required it, I was shocked to be reminded of the disturbing foreword, which detracts from the majesty of the actual work and Evans-Wentz's accompanying interpretations.

Without dwelling too long on the foreword, written by Donald S. Lopez, Jr., let me say that it strikes me as one of the most long-winded, derogatory and self-serving forewords I have ever seen in a book; not to mention the fact that the foreword is advertised on the cover of this edition. Donald Lopez insults Evans-Wentz on every page and goes on to tear down Jung, as well.

There are genuine reasons for why marvelous works by men such as W.Y. Evans-Wentz stay in print, and they go far beyond the bruised egos of stoic/pedantic academics like Lopez. When so-called Buddhist scholars, such as Lopez and Thurman, project themselves as arrogant intellectuals, it contradicts everything that Evans-Wentz stood for.

Oxford University Press should be ashamed for pulling in a voice so anti-thetical to the spirit of this work. The work, itself, is awesome and is hindered only by the hypercritical Lopez touch.

5 out of 5 stars One of the best.......2004-05-06

This is one of the earliest and still one of the best volumes to come out of the still-intact Tibetan region into the English language. Lots of Voltage.
It's interesting to see in these reviews how many people want to show off what they know.

Best Wishes

5 out of 5 stars The 4th book in the Tibetan Series by W.Y.Evans-Wentz.......2003-11-27

This is the forth and final book in the Tibetan series from W.Y.Evans-Wentz. Although this book can be used as a stand-alone book it is certainly not best read that way. Basically this is part of a developing series. The first book in the Tibetan series - The Tibetan Book of the Dead, is the fundamental book of the series which describes Buddhist philosophy, psychology and metaphysics. It is the best translation out there and the original! The second book in the series is called Tibets Greatest Yogi Milarepa and is the story of a great yogi who puts into practice most of what we learn from The Tibetan Book of the Dead. It is through the story of Milarepa that we learn more about The Tibetan Book of the Dead. In the story of Milarepa the yogi studies the Seven Books of Wisdom of the Great Path as taught to him by his gurus. Tibetan Yoga and Secret Doctrines, the third book in the series, is an expansion that explains those wisdoms and describes the yoga that is used to achieve them.

The Tibetan Book of the Great Liberation is a three act book which ties together everything learned from the other three books. Essentially the start of the book develops a clearer understanding of the metaphysics associated with the first three books in the form of a general introduction. The book then lays out the premise for a type of yoga practice called the Supreme Path or Mahayana, that was created to serve as an INSTANT ENLIGHTENMENT yoga. It is mostly psychological. The middle section of the book is devoted to the guru Padma-Sambhava who brought this yoga to Buddhists in the eighth century. The latter part of the book expounds on that yoga in a full translation.

Make no mistake about it. This is the ORIGINAL and best work because this was the man who brought the work to the occident! These texts are ancient and old but have served millions since their inception. The work that Evans-Wentz has done here is substantial if not some of the most important Tibetan Buddhist concepts ever seen by the occident - all directly translated by master gurus whom which Dr. W.Y.Evans-Wentz was a student for years.

There is nothing wrong with the translation. Forget those who seek to play down the originals so that they can sell their new version. This book has stood the test of time. It was first published in 1954! The original book in the series was published in 1921! Evans-Wentz was in Tibet at the turn of the century learning under these gurus! He is held is highest esteem by Oxford University for his endeavors!

*** The other books in the series are - The Tibetan Book of the dead - Tibets Greatest Yogi Milarepa - Tibetan Yoga and Secret Doctrines - all before this one, the final book in the Tibetan Series. ***

5 out of 5 stars Ian Myles Slater on: Still Worth It, But Check Competition.......2003-11-27

The title text of this collection of translations has recently appeared in a significantly clearer and better-annotated translation, as "Self-Liberation Through Seeing With Naked Awareness." Like the other three books in W.Y. Evans-Wentz's "Oxford Tibetan Series," it suffers from a dependence on Tibetan translators working at time when few clear guidelines for translating technical terms had been developed, and from Evans-Wentz's own lack of familiarity with Mahayana Buddhism and its various schools. (Which apparently has not prevented it from achieving its own canonical status with some readers; a process not unknown in the history of translations, from the Christian adoption of the Septuagint in place of its Hebrew original, to some Chinese -- and Tibetan -- renderings of Buddhist Sanskrit texts.)

As Lopez points out in his introduction to this new edition (part of an end-of-the-century reissue of the series, in which the publisher formally acknowledges over a half-century of additional scholarship), Theosophy and Hinduism are the real points of departure. There is a commentary to the translation offered by C.G. Jung, which is of great importance to students -- but of Jung, not of Tibetan Buddhism. The historical significance, and sometimes impressive literary quality, of the translation series is enduring; its value as a set of primary sources is not.

However, a large section of the book is given over to an (abridged) translation of one of the traditional biographies of the *Lotus-Born Guru*, the "Apostle to the Tibetans." In western terms, it is a mix of popular hagiography (like "The Golden Legend"), heroic romance, and supernatural thriller. So far as I have been able to determine, it is the only English-language version of this particular text (there are other Tibetan treatments of the subject, a number of which have been translated), and it makes fascinating reading, simply as a piece of story-telling.

The translation of the story has extensive, and sometimes obsolete, annotations which attempt to tie down the places and times mentioned, but which also recognize that portions, at least, are intended to be symbolic or allegorical (which does not mean that the original audience would not have regarded them as literally true, as well). Padma-Sambhava, besides introducing advanced forms of Buddhist Yoga, is supposed to have written, and concealed for future generations, a number of important texts, including, besides the one translated as "The Great Liberation," the so-called "Tibetan Book of the Dead" (Evans-Wentz's catchy, but potentially misleading, title). He also appears as a major character in some versions of the Tibetan "Gesar" epic.

The presence of this fascinating piece of Tibetan literature may account for the interesting fact that Snow Lion, the publisher of the competing "Self-Liberation Through Seeing With Naked Awareness," offers this book in its catalogue as well (as of Summer 2003).

Those who find this portion of the book interesting will probably also enjoy the traditional "biography" of a Tibetan holy man, in "Tibet's Great Yogi Milarepa," another volume edited by Evans-Wentz. (It is a companion volume in the Oxford Tibetan series). It presents itself as its hero's own account of his progression from black magician (to avenge his family) to Enlightenment. (There are several editions of the translation available; the 1999 Oxford paperback reprinting, uniform with the present volume, including a new introduction, should be in print at this writing.)
Knowing Words: Wisdom and Cunning in the Classical Traditions of China and Greece (Myth and Poetics)
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    Knowing Words: Wisdom and Cunning in the Classical Traditions of China and Greece (Myth and Poetics)
    Lisa Raphals
    Manufacturer: Cornell University Press
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    Knowing Practice (Studies in Ethnographic Imagination))
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      Knowing Practice (Studies in Ethnographic Imagination))
      Judith Farquhar
      Manufacturer: Westview Press
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      Book Description

      This book examines the theory and practice of traditional medicine in modern China. Farquhar describes the logic of diagnosis and treatment from the inside perspective of doctors and scholars. She demonstrates how theoretical and textual materials interweave with the practical requirements of the clinic. By showing how Chinese medical choices are made, she considers problems of agency in relation to different forms of knowledge. Knowing Practice will be of value not only to anthropologists interested in medical practice but also to historians and sociologists interested in the social life of technical expertise and traditional teachings.
      Knowing China
      Average customer rating: 5 out of 5 stars
      • To know China objectively.(From a young Chinese boy)
      Knowing China
      Gregory C. Chow
      Manufacturer: World Scientific Publishing Company
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      Customer Reviews:

      5 out of 5 stars To know China objectively.(From a young Chinese boy).......2004-06-05

      First of all, I want to point out that there is indeed few to have this kind of provilige like experienced Chow to talk about China.

      With Knowing China, you can see much of China by the historical and cultural perspective and many current controversial issues that China is now facing. Of course, Chow gives you convincible analysis and his specific view.

      As a professor of Economics, Chow not only sees China from the historical trajectory, but also See china from future perspective, perhaps with his piercing rational expectation.

      Particularly, I changed my view through it upon the birth control policy in China as a suffered boy born in late 1970's. Chow uses the theory of economic growth with simulation and wild interpretation of utility concludes that there is no nessesary to conduct that policy.

      In the traditional Chinese culture, or in the point view of Confucius, since Chow was two (may be three) generation older than I so that I have to receive the his view unconditionally. But my acceptence after reading this is through convincible explanation but not enforcable way, I mean, it's very objectively written.

      This book is very accesible (in contrast to Chow's professional works) and can be read widely. Even though this is an introduction for the non-Chinese readers, I still recommend it for Chinese, especially those who love China but not know how to.
      Knowing Practice: The Clinical Encounter in Chinese Medicine (Studies in the Ethnographic Imagination)
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        Knowing Practice: The Clinical Encounter in Chinese Medicine (Studies in the Ethnographic Imagination)
        Judith Farquhar
        Manufacturer: Westview Pr (Short Disc)
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        Knowing, Naming and Negation: A Sourcebook on Tibetan Sautrantika (Translations in Indo-Tibetan Buddhism)
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          Knowing, Naming and Negation: A Sourcebook on Tibetan Sautrantika (Translations in Indo-Tibetan Buddhism)
          Anne Klein
          Manufacturer: Snow Lion Publications
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          ASIN: 093793822X

          Book Description

          This is a challenging book on the nitty-gritty issues of Sautranika philosopy, the basis of Madhyamika epistemology.
          Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States.(Review) (book reviews): An article from: American Scientist
          Average customer rating: Not rated
            Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States.(Review) (book reviews): An article from: American Scientist

            Manufacturer: Sigma Xi, The Scientific Research Society
            ProductGroup: Book
            Binding: Digital

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            ASIN: B0008GTQXI
            Release Date: 2005-07-28
            Knowing China [A book review from: Journal of Asian Economics]
            Average customer rating: Not rated
              Knowing China [A book review from: Journal of Asian Economics]
              B. Bachner
              Manufacturer: Elsevier
              ProductGroup: Book
              Binding: Digital
              ASIN: B000RR2X42

              Book Description

              This digital document is a journal article from Journal of Asian Economics, published by Elsevier in 2005. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

              Description:
              Knowing the business environment: the use of non-market-based strategies in Chinese local firms.(Company Profile): An article from: Ivey Business Journal Online
              Average customer rating: Not rated
                Knowing the business environment: the use of non-market-based strategies in Chinese local firms.(Company Profile): An article from: Ivey Business Journal Online
                Mingfang Li , and Haiwei Zhou
                Manufacturer: Thomson Gale
                ProductGroup: Book
                Binding: Digital

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                ManagementManagement | Business & Investing | HTML | Formats | e-Docs | Formats | Books
                ASIN: B000E1N462
                Release Date: 2005-12-27

                Book Description

                This digital document is an article from Ivey Business Journal Online, published by Thomson Gale on November 1, 2005. The length of the article is 2686 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

                Citation Details
                Title: Knowing the business environment: the use of non-market-based strategies in Chinese local firms.(Company Profile)
                Author: Mingfang Li
                Publication: Ivey Business Journal Online (Magazine/Journal)
                Date: November 1, 2005
                Publisher: Thomson Gale
                Page: 1(5)

                Article Type: Company Profile

                Distributed by Thomson Gale

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                2. Labor Relations in the Public Sector, Third Edition (Public Administration and Public Policy)
                3. Logistics & Supply Chain Management: creating value-adding networks (3rd Edition) (Financial Times Series)
                4. Man, Economy, and State with Power and Market (Scholars Edition)
                5. Managing Cultural Differences, Sixth Edition: Global Leadership Strategies for the 21st Century (Managing Cultural Differences)
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                7. Mathematics for Economists
                8. Media Now: Understanding Media, Culture, and Technology, 2008 Update
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                10. Modernity at Large: Cultural Dimensions of Globalization (Public Worlds, V. 1)

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