Running Head: GREENER COMPLEXITY Why Always Greener on the Other Side? The Complexity of Chinese and U.S. Mathematics Education Thomas E. Ricks Louisiana State University [email protected] ABSTRACT: Researchers have noted that both China and the U.S. seem to be striving to copy aspects of the other’s educational system. In an attempt to understand this phenomenon, the complexities of mainland China’s educational factors were juxtaposed against those of the US to develop theory suggesting that China’s complexity currently occurs mostly at the supra-individual level (familial, class cohorts, coherent lessons, professional development cooperatives, etc.), while the US’s complexity is manifest primarily by enabling the individual student. China envies U.S. student creativity, independence, curiosity, and innovation, while the US seeks to adopt the integrated features of China’s educational system.

Keywords: China, complexity, cross-culture comparison, mathematics education, reform, U.S. Introduction China and the United States (U.S.)—two major world superpowers—are increasingly perceived as global competitors not only for natural resources and world markets but in the area of education. Along with the growing mantra that educational excellence is vital for economic prosperity and national security, the rise of international testing has facilitated the scrutiny of each country’s educational establishment by researchers, the popular media, and policymakers (Biggs & Watkins, 2001; Clarke, Keitel, & Shimizu, 2006; Fan & Zhu, 2004; Hiebert, et al., 2003; Huang & Bao, 2006, Huang & Li, 2009, F. Lin & Tsao, 1999; Stevenson, Chen, & Lee, 1993). Unfortunately, conglomerating statistical data masks pertinent details about how students in different countries approach mathematics (Cai, 2004), and simple comparisons of international test scores belie the more complex nature of the underlying educational systems (Cai, 2000). This study sought to move past superficial indicators of educational excellence to develop a

framework for understanding why both China and the U.S. seem to be trying to copy certain features of the other’s educational system. Many researchers have pondered this paradoxical place-swapping (Cai, 2008; Tienken, 2008; Tienken & Canton, 2009; Wong, Han, & Lee, 2004; Zhao, 2009a, 2009b); it is like each country’s educational system is trying to adopt features of the other (Paine, 1997). This curious situation is reminiscent of the U.S. idiom: “The grass is always greener on the other side of the fence” (meaning that one—not satisfied with his or her current allotment—often envies the supposedly ‘fairer green pastures’ of others). In an effort to help understand this phenomenon, this chapter connects each country’s educational strengths and weaknesses to the complexity of its education to argue that both China and the U.S. are gravitating to the other’s strengths. The Study Theoretical Framework of Complexity This study uses the theoretical perspective of complexity—a new paradigm increasingly used in social systems research—to describe and compare Chinese and U.S. educational systems, (Davis & Simmt, 2003; Davis & Sumara, 2001; Davis, Sumara, & Kieren, 1996; Ricks, 2009b). I used complexity because it is one of the few perspectives available to scholars to describe holistic and integrated practices. Complexity is the study of complex systems—emergent and adaptive systems that develop as multiple agents interact in ways that generate supra-agent phenomena, which are phenomena that exist above and beyond the attributes of any of the system’s agents (Johnson, 2001)—and the way these systems interact with their surrounding (sub-)systems. Colloquially, complexity is the study of when, where, what, how, and why certain wholes are greater than the sum of their parts. As the educational system in any nation consists of overlapping, intertwined, and nested social systems, complexity theory offers educational

researchers a unique way to identify, describe, and understand such holistic phenomena (Davis & Simmt, 2003). Complexity is a reaction against the dominant scientific paradigm of reductionism that reduces phenomena to their constituent parts through dissecting, fracturing, sub-dividing, etc. Unfortunately, reductionism has failed to adequately explain much of the natural world because many phenomena cease to exist once reduced to their individual components (Anderson, 1972). When collections of individual agents (e.g., bacteria, bees, or people) interact, they often produce larger collective phenomena that exhibit novel behaviors and properties not manifest by the original collection of agents: a new entity emerges through this collectivization: “Under certain circumstances agents can spontaneously cohere into functional collectives—that is, they can come together into unities that have… potential realities that are not represented by the individual agents themselves” (Davis & Simmt, 2003, p. 141). Complex system boundaries are also difficult to identify because the system is always in a state of dynamic equilibrium and nestled within larger systems (Davis, Sumara, & Simmt, 2003). Complex systems are themselves learning entities that can adapt to environmental pressures in surprising, unpredictable, and sometimes haunting ways—evidencing intelligence at the new, higher-ordered, structural level (Ricks, 2009a, 2009b). They resist being linearly defined and are highly robust. For example, people self-organize into families, neighborhoods, societies, and cultures; bees, termites, ants, and other social insects form stable hives and colonies; bacteria develop collectively into colonies that can creatively solve problems through shared cognition—all of these larger structural systems exhibit definable characteristics that supercede the capacities of the individual agents which make them up (Johnson, 2001; see also Ben-Jacob, 1998; Shapiro, 1998). Most educational research operates under a reductionist

mentality; there have been calls by mathematics education researchers to embrace more holistic methods (e.g., Cai, 2008; Cobb & Yackel, 1995). This study is just such an attempt. This cross-cultural comparison study of Chinese and U.S. educational systems used Glaser’s (1965) four-part constant comparative method (comparing, integrating, delimiting, and writing) to develop theory for wider application; the constant comparative method is good at developing rather than testing theory because the constant comparative method “is concerned with generating and plausibly suggesting (not provisionally testing) many properties and hypotheses about a general phenomenon” (p. 438, emphasis in original). Data for this study is drawn from a variety of sources, consistent with constant comparative methodology: (a) the literature, (b) various videotaped student/teacher interviews, videotaped classroom lessons, and videotaped professional development (including Chinese teaching research groups and model lessons)—collected in both Chinese (Beijing, Tianjin, Hangzhou, Shanghai, and Chengdu) and U.S. cities1, and (c) the researcher’s life experience (an especially pertinent piece of constant comparative data). In the constant comparative method, such a wide data net augments theory creation; I used the constant comparative methods’ inherent “flexibility [to] aid the creative generation of theory” (p. 438) that consists of two basic complex levels of educational entities: (1) individual agents and (2) systems made of individual agents (supra-individual). Results: The Complexity of China’s and the U.S.’s Educational Systems I describe a complexity-based framework that illuminates the respective strengths and weaknesses of China’s and the U.S.’s educational establishments by connecting them to the quality of the complexity at either the individual or supra-individual level. We can categorize the U.S. educational system as a loosely-coupled, decentralized complex system whose main focus is to educate by enabling the individual pupil (Davis & Simmt, 2003; Weick, 1976, 1982).

China’s educational system, by contrast, has a more centralized network of integrated complex systems that educate by conforming students to the supra-individual (Huang & Li, 2009; Ministry of Education, 2003). This complex framework similarly highlights each nation’s educational weaknesses: China’s sidelining of student individuality for the supra-individual and the U.S.’s dedication to decentralization that stifles possible supra-individual growth The U.S.’s Focus on the Individual The U.S. educational system educates by enabling the individual student’s natural capacities. Educational environments provide generous educational resources, tailored curricula, student-centered pedagogies, realistic views of mathematics, and abundant opportunities to continue learning. These flexible external factors cater to the needs of individuals to nurture creativity, critical thinking, innovation, and independence. Even the U.S. teacher tends to work as an individual (Paine & Ma, 1993). Educational resources. The U.S. has built “one of the most developed educational systems in the world” (J. Chen & Mu, 2010, p. 129), pouring great expense into state-of-the-art facilities that sport spacious, technology-filled classrooms with low student/teacher ratios, large libraries, and high per-pupil expenditure. The U.S. spends a higher percentage of its gross domestic product on education than China (Leung, 1995), allowing for smaller class sizes than China (Bloom, 1984; Cai, 2004, 2008; Huang & Li, 2009; Leung, 2005), and hence greater instructional contact time for each individual student; this promotes more individual learning than in higher ratio classrooms (Dahar & Faize, 2011). Even U.S. parents are better resource providers than Chinese parents, being “less interested in their children’s specific academic achievement than in their children’s general cognitive development so they… provide experiences that foster… cognitive growth rather than academic excellence… stress[ing]

independence… and acceptance of diversity” (Cai, 2003, p. 90). There is also a greater emphasis on pre-school education (Stevenson & Stigler, 1992; X. Wang et al., 2011). The U.S.’s relaxed educational environment enables U.S. students to participate in the learning process with far less stress than their East Asian counterparts by “experiencing and enjoying mathematics” in pleasurable ways (Leung, 1995, p. 313; see also Cai & Wang, 2010; Leung, 2001; L. Li, 2011; Young, 2010). Tailored curricula. Because U.S. education emphasizes the individual student becoming over his or her knowing, curricula are modified to fit the needs of the individual child (Xie & Carspecken, 2008). The U.S. does not have a national curriculum (Cai & Wang, 2010). U.S. educational policies are also based on principles that emphasize equitable education for every child (NCTM, 2000); individual diversity is highly valued and supported. Decentralized U.S. educational policies give great power to local administrators and teachers to make accommodations, especially for gifted/talented or special needs students because “the individual is of prime importance” in the U.S. educational process (Leung, 2001, p. 44). Such flexibility allows teachers “to help students explore and generate knowledge by themselves” (Cai & Wang, 2010, p. 283). Student-centered. Most classroom pedagogy is based on differentiation strategies that seek to tailor instruction to the diverse needs of individual students (Leung, 2001; Leung, 2008). The U.S. employs a rigorous tracking system that separates students into homogenous abilitygrouped class environments that de-emphasizes the diversity of the group for maximum singular pupil gain (Darling-Hammond, Ancess, & Ort, 2002). Student-centered, U.S. classrooms focus on constructing individual cognition through the development of individual autonomy, creativity, problem-solving, critical thinking, social skills, adaptability, and flexibility (Cai & Wang, 2010).

Real-world mathematics. The U.S. sports a broader view of mathematical learning than China; the U.S. emphasizes real-world problem solving and recognizing/extending patterns more than the Chinese (Cai, 2004). Leung (2005) described how this approach caters to the individual: Many Western mathematics educators regard mathematics in essence as the process of dealing with certain aspects of reality. In consequence, the process of ‘doing mathematics’ that the individual regards as appropriate is seen as more important than learning the established structure of mathematics. (p. 211) U.S. teachers use more concrete problems that allow students to “directly participate in many hands-on activities where students can physically manipulate” objects and to “to explore the relationship between mathematics and their own life experience by providing extensive real-life examples and tactile experiences in the class” (Cai & Wang, 2010, pp. 280, 283). U.S. mathematics teachers also stress the “practical function of mathematical knowledge” more than Chinese teachers (Cai & Wang, 2010, p. 271). Creativity. The U.S. approach nurtures student creativity, generating more mathematically creative students than the Chinese (An & Wu, 2008; Cai, 2008; J. Li, 2004). U.S. teachers believe that “an effective teacher should be a good listener” to student thinking and use individual student questions as material for whole-class discussion to promote student participation and collaboration (Cai & Wang, 2010, p. 278). Lesson enactment develops as an organic process and cannot be predicted in advance (Leung, 2001, p. 44). The U.S. classroom environment stresses original thinking more than in Chinese classrooms (Young, 2010). The highly technological environment in the U.S. engenders “creativity, including creative mathematical thinking” (Clements & Sarama, 2008, p. 178). U.S. students learn to tolerate deviations from the norm, to challenge authority and conventional wisdom, and to take intellectual risks in problem-solving (Cai, 2008). Students engage in activities that promote independent leadership, active participation, group projects, innovative ideas, and presentations

(Cai & Wang, 2010). Peer interaction. U.S. teachers support student-peer interaction and class participation more than Chinese teachers (Cai, 2008; Cai & Wang, 2010), preparing individuals for rapid integration into post-education careers by developing students’ interpersonal skills, problem solving capacity, creativity, and team work spirit (You & Jia, 2008). Individual class activities like “in-class participation, seminar presentations and individual research projects, common practice in elementary schools in North America, are largely unheard of in the Chinese classroom—even in most universities” (Young, 2010). U.S. students also engage in a variety of extra-curricular and informal educational activities beyond the classroom that further develop their individuality and social skills, including sports, clubs, work, play, and interactions with siblings and friends—much more so than their Chinese counterparts who live in mostly singlechild families, sometimes raised by grandparents (as many parents seek employment in the bigger cities), and who focus most of their energies on schoolwork (Cai, 2003, 2004; Cai & Hwang, 2002). These opportunities help U.S. children develop into confident individuals that can transit into a variety of larger collectives. Continued learning opportunities. The U.S. also has a rich history of higher education to serve the post-secondary individual graduate: Harvard was founded 1636 as New College, the College of William and Mary in 1693; Yale University in 1701 as the Collegiate School, etc. The U.S. currently has over 4,300 functioning universities and colleges; 17 out of the top 20 universities world-wide are located in the U.S., and half of the top 100 universities are American. China, by contrast, has only recently founded universities (the first was in 1888); the top Chinese university ranks 49th. Chinese higher education is also more hierarchical and elitist (Epstein, 1980, 1986). But what probably sets the U.S. apart the most from China is the percentage of its

population that graduate from college—almost 25% to China’s 6% (Bauman & Graf, 2003; Zhu, 1999). What about China’s high ranking on international assessments? In arguing that the U.S. places a stronger emphasis on education as enabling the individual student than China, one might wonder: What about Chinese students’ superior mathematics test scores on standardized assessments? Doesn’t stronger content knowledge indicate that China is “enabling” their individual students as much as—or more than—the U.S.? The short answer is no, for two reasons: (1) international tests only measure a part of student mathematical competence (Kilpatrick, Swafford, & Findell, 2001), and (2) a closer look at Chinese mathematics classrooms verifies that their culture emphasizes the individual conforming to the collective, rather than the other way around. Although strong content knowledge does “enable” students, this study examined the manner in which China and the U.S. educate; Chinese students gain their strong (albeit, limited) content knowledge through China’s supra-individual focus. For example, although Chinese students outperform U.S. students on routine symbolic manipulation, computation, and abstraction, the U.S. students match or outperform Chinese students on concrete, open-ended, and visualization problem-solving tasks, as well as on mathematical problem-posing (Cai, 2000, 2003, 2004; Cai & Hwang, 2002; Harmon et al., 1997); and “when solving process-open tasks, U.S. students had higher mean scores than did Chinese students” (Cai, 2008, p. 159). Considering that Chinese children are exposed to algebraic generalization and pattern prediction at an earlier grade than U.S. students (Cai, 2004), it makes sense that Chinese students outperform U.S. students on international assessments stressing routine, symbolic, and computational problems (Cai, 2000; Cai & Hwang, 2002). But “if the analysis is limited to U.S. students using symbolic (algebraic or arithmetic)

representations, there is no mean difference between U.S. and Chinese students' performance” (Cai, 2008, p. 156). So claiming that Chinese students have ‘stronger’ content knowledge is not accurate—it depends on the type of tasks being assessed. Higher Chinese international mathematics scores reflect a cultural tendency to prefer abstract strategies over more concrete ones rather than any superiority in mathematical ability (Cai, 2004). Additionally, U.S. students are more likely to use correct strategies than Chinese students, but become entangled in the computation—with which the Chinese are more proficient—and thus score lower because international tests just look at cumulative correct answers (Cai & Hwang, 2002). Thus, U.S. students’ preference for concrete or semi-abstract strategies places them at a disadvantage on international tests. U.S. students are very competitive against Chinese students on problem-posing, mathematical exploration, and generative thinking (Cai & Hwang, 2002); U.S. students are more willing to take risks and experiment when confronted with a perplexing problem (Cai, 2008). On international comparisons, researchers found that U.S. students posed (qualitatively) more complex extension problems, posed (quantitatively) more non-extension problems, and developed more (mathematical) rule-based problems, than did Chinese students (Cai & Hwang, 2002). The U.S. competes very well against China on other measures of international mathematics competence (both are ranked at or near the top globally in the Word Mathematical Olympiads, for example). Not surprisingly, producing students who are strong in symbolic manipulation and skillful with computation is not as valued in the increasingly technological world as it once was; as Cai (2008) admits: “The most important qualities we can help our students develop are the abilities to think independently and critically, to learn, and to be creative” (p. 159). Unlike China, the U.S.:

…respects individual talents, supports divergent thinking, tolerates deviation, and encourages creativity; a system in which the government does not dictate what students learn or how teachers teach; and a culture that does not rank or judge the success of a school, a teacher, or a child based on only test scores in a few subjects determined by the government. (Zhao, 2009a, p. vi) In addition to limited performance on international assessments, China stresses the conformity of the individual to the collective (Cai & Wang, 2010) through integration, harmonious behavior, and compliance (Leung, 1995, 2001). China has a centralized—not decentralized—educational system, and a nationally mandated curriculum (Cai, 2004; Huang & Li, 2009; Ministry of Education, 2003). Chinese pedagogy is characterized by surface-learning (You & Jia, 2008). For example, Chinese pedagogy encourages students to recite the teacher’s words exactly even if the student’s own depiction is mathematically accurate, to follow fixed problem-solving steps, and to detail solutions in a rigid format (Leung, 1995). Chinese students are more likely to use teacher-taught conventional strategies than experiment on their own, and often leave test items blank rather than risk independent thought (the U.S. students, however, are very willing to guess or take other risks in answering questions) (Cai, 2008)! There are fewer investigation, open exploration, or generalization problems in China (Leung, 1995). Uniform teaching and assessment generates an “ethos of competition” that pressures students and teachers, and helps to “reinforce state control of people through the education system” (Leung, 2008, p. 991). Despite studies that show that the Chinese pedagogical approach engenders submissive and passive learners, Chinese teachers still believe this teacher-centered lecture style yields active and creative learning later in life (Cai & Wang, 2010). It would be difficult for Chinese teachers, in classes of 40-plus students, “to monitor the progress of all the students if they were doing different tasks and proceeding at different paces, and so the teacher had to resort to whole-

class instruction” (Leung, 1995, p. 314). Chinese teachers do not listen as much to student questions to guide instruction, do not utilize students’ direct physical participation in lessons or student-peer interaction, and closely follow teaching scripts (Cai & Wang, 2010, p. 279). They also do not relate the mathematics as much to real life situations. (Leung, 2005, p. 205). Chinese mathematics classes are teacher-, rather than student-, centered (Cai & Wang, 2010). The Chinese system places heavy workloads and immense stress on students, which further limit opportunities to explore intellectual ideas and stifles independence (Cai & Wang, 2010; You & Jia, 2008). The current Chinese system emphasizing passing examinations greatly burdens both teachers and students and maintains an ideology of subservience to the State (J. Y. Lin, 1995). The pressure to perform is almost overwhelming, limiting students’ exploration, creativity, and curiosity—so much so that “very often, the insistence on hard work becomes [such] a burden for East Asian students [that] many students dislike or even hate the learning” (Leung, 2001, p. 42). Chinese students lack the flexibility to rapidly integrate into new environs and exhibit an “inability of individuals to take the initiative” (Young, 2010). Although China is quickly catching up to the West in the quantity and quality of its educational facilities, it is still years behind the type of education that would compete with U.S. schools (Hou, 2010). China does not yet spend even half of what the U.S. spends per pupil; and the recent, rapid educational development in China has only made funding issues worse (You & Jia, 2008). Despite passing standardized exams and even graduating from Chinese universities, Chinese graduates are entering a “derivative, manufacturing-based economy, which is unable to innovate core technology, lacks major research and development projects—and lags far behind in creative sectors like marketing and design” (Young, 2010; see also Greenspan, 2008).

In brief, although China has stellar performance on major international comparisons of content capability, a more fine-grained, detailed analysis challenges the view of Chinese content superiority. Further, Asian educators, researchers, and policy-makers feel that “the United States does a better job of nurturing students' creativity than Asian countries do. Some Chinese leaders openly express their dissatisfaction with K-16 education for just giving students knowledge, but not the ability to think critically” (Cai, 2008, p. 159; see also Zhang, Yan, Dong, & Zhou, 2009). Because of this, I argue that the U.S. strength lies in enabling the individual pupil. Sensitivity to individual students’ needs is lost in the Chinese push to memorize mathematical rules and procedures, by large class sizes, and pressure for examinations because “it is the obligation of the individual to fit into the social structure” (Leung, 2001, p. 44; see also Leung, 1995, 2008). The Chinese Focus on the Supra-Individual Despite not promoting individual student creativity, innovation, or autonomy quite like the U.S., China’s educational system does strengthen the supra-individual collective more than the U.S., leading to a different set of educational strengths that the U.S. envies, including: a unified curriculum that facilitates teacher collaboration and development of a firm teaching knowledge base, demanding textbooks, a culture of rigorous expectations for student study, strong familial support, teachers’ profound understanding of fundamental mathematics, coherent lessons, de-privatized teacher practice, and stable professional development (Fan & Zhu, 2004; Hiebert, et al., 2003; Huang & Bao, 2006; Huang & Li, 2009; F. Lin & Tsao, 1999; Ma, 1999, Paine, 1997; Stevenson, Chen, & Lee, 1993; Stigler & Hiebert, 1999). As Leung (2008) explained: One manifestation of this social orientation of the East Asians in the area of education is the unified nature of the expectation on students. In an individual orientation culture [like the U.S.], there are often calls for an individualized curriculum or tailoring of the standard curriculum to suit the needs of students of

different inclinations and aptitudes. [A] centrally administered uniform examination expects individuals to adjust themselves to the requirements of an orthodox curriculum, which is more consistent with a social orientation philosophy. (pp. 987–988) The Chinese Confucian culture—one example of China’s strong supra-individual phenomena—encourages Chinese students to excel by bringing “honour to one's parents, family and ancestors”; additionally, “academic achievement is much more important for doing well in society. …This sends a message to students” (Leung, 2001, p. 43; see also Wong, 2000). Chinese parents have higher educational expectations for their children than U.S. parents (Cai, 2004; Leung, 1995; Wong, 2008), buy more mathematics textbooks for their children, are better monitors of their children’s progress, and “play a more positive role than do …US parents.” (Cai, 2003, p. 87). Chinese children also enter school with deeper mathematical understandings (Han & Ginsburg, 2001; Siegler & Mu, 2008). Note that a culture of high academic and familial expectations is an example of a supra-individual phenomenon (existing above and beyond the individual student), requiring students to conform to these socially-oriented attitudes rather than nurturing or enabling students’ natural inclinations. Further, J. Li (2004) has noted that whereas Western researchers consider extrinsic motivating factors to not be as powerful an influence on positive learning outcomes as intrinsic motivation (which seems true for Euro-American children), Chinese students “enjoy… learning just as much and did better when their task was chosen by… mothers or trusted peers” (p. 128). I further describe in more detail three other Chinese supra-individual educational influences: class, lessons, and professional development. Class. In the U.S., a ‘class’ is a temporary subject-specific gathering of students aimed at making education efficient and affordable, without any purposeful attempt to harness social power for group learning (Ricks, 2007). In China, however, ‘class’ takes on a whole different

meaning—a class is a collective cohort of students that typically stay together throughout the day as a single unit and advance together throughout the grades (Park & Hannum, 2001; Yang & Ricks, 2011). The class even exercises as a highly collective unit in rhythmic synchronization (Ricks, 2009b)! Further, the teachers that teach this class also advance through several grades with the class cohort; studies indicate such prolonged contact matters for student achievement, especially with less-experienced teachers (Park & Hannum, 2001). There is no diversification of curriculum at primary or junior secondary levels, nor ability-grouping in China (Liang, 2001; Park & Hannum, 2001), allowing for focused collective effort at the class level. The U.S. does not have anything comparable, as students move independently through the subjects based on personal preference and ability level. Although there is some stability in U.S. classes based on tracking and grade-level advancement, there is not the developed camaraderie that exists in the Chinese classes; U.S. classes do not form cohorts and U.S. teachers rarely if ever advance through the grade levels with a particular group of students. The collective Chinese classes also offer fewer management problems for Chinese teachers (Cai & Wang, 2010). Lessons. Cross-cultural studies indicate that Chinese lessons are more instructionally, psychologically, and socially coherent than U.S. lessons (Cai & Wang, 2010; Ma, 1999; Perry, 2000; Stigler & Perry, 1988; Stevenson & Stigler, 1992; Wang & Murphy, 2004); Chinese teachers can clearly articulate the core concept of the lesson and how the resultant tasks relate to this core concept. The U.S.’s “fragmented school curriculum” (Tienken, 2008, p. 4) spawns correspondingly piece-meal, disconnected lessons with up to 30% prior review (Kilpatrick, Mesa, & Sloane, 2006), that are fraught with management problems, and have little substantive content investigation (“A mile wide and an inch deep” is a common descriptor of U.S. lessons). Chinese lessons, by contrast, focus on a single content topic with purposeful variation that gives

Chinese students a much better grasp of the central ideas of the lessons. Focusing on a few cognitively-engaging problems allows Chinese teachers to carefully think about the tasks they will use in their lesson. Chinese teachers study the textbook more than U.S. teachers and integrate it into their lessons (Cai & Wang, 2010). U.S. teachers tend to pick problems much more randomly. U.S. lessons lack cognitively-difficult or complex problems, and even the subject itself is disconnected: In [Chinese] curricula, … mathematics is seen more as an integrated whole than as subject matter that can be parsed by topic area without overt integration. This curricular parsing is the same for weak and strong students in the United States. The integration is left up to the student, a task many find difficult or fail to complete on their own. (Kilpatrick, Mesa, & Sloane, 2006, p. 3) Further, lessons are typically multi-day experiences, not the hit-and-miss fragmentary approach of U.S. lessons. Devoting one whole lesson—and sometimes several lessons—to a central content idea allows for the depth needed for students to really dig in and think about the topic. In addition, Chinese lessons engage students with fewer problems, allowing students to spend more time on each problem (Liao & Cao, 2010; Stigler & Hiebert, 1999). Chinese lessons are also more interconnected (content-wise) (Cai & Wang, 2010). Professional development. Although prospective Chinese teacher training is weaker than in the U.S. (at least in terms of content and contact hours of the teacher preparation programs), professional development in China quickly helps Chinese teachers to surpass U.S. teachers’ abilities (Chen & Mu, 2010; Ma, 1999). The Chinese school is also structured to help with professional development, a required part of teachers’ promotional advancement as they participate in school-based research (Huang & Bao, 2006; Ma, 1999). Chinese teachers feel comfortable talking about their individual lessons to peers (Paine, 1997). Paine and Ma (1993) acknowledge that “Chinese teachers… have a decades-long tradition and well-articulated

structure for teachers collaborating” (p. 675). Chinese professional development is year-round and continuous at every level; Chinese teachers are able to attend at least one form of professional development at least weekly (An & Kulm, 2010; Leung, 1995). Chinese professional development helps teachers, administrators, researchers, teacher developers, and policy makers communicate and collaborate to solve the pressing problems of Chinese education. Said Paine (1997): “Teachers in China are members of multiple groups— formal, informal, and even across distance. Together these groups construct and maintain a culture of teaching which encourages teachers in particular ways” (p. 81). Chinese professional development is systematic and nested: grade-based, school-based, school-district-based, citybased, and even national. Grade- and school-based meetings typically involve the collaborative creation and discussion of lessons (An & Kulm, 2010); school-based professional development also involves selected teachers demonstrating a public lesson to observing colleagues (Paine & Ma, 1993; Park & Hannum, 2001; Yang & Ricks, 2011). School- and district-based meetings involve the collaborative observation and discussion of school-based public lessons as well as model lessons by master teachers to a random group of school-district-based students. City and national events usually showcase “invited top teachers to demonstrate effective lessons to a randomly selected class of students from the host elementary school” (An & Kulm, 2010, p. 48; see also Paine & Ma, 1993). Teachers who are not able to attend have access to these demonstration lessons and accompanying lesson plans via websites (An & Kulm, 2010). There are also more subtle aspects of assisting teachers’ communication and collaboration; for example, the clustering of Chinese teachers’ offices by subject matter promotes collaboration (Paine & Ma, 1993). This more robust environment of professional development leads to Chinese teachers

who possess a profounder understanding of fundamental mathematics and place a greater emphasis on conceptual knowledge than do American teachers; they connect ideas to prior knowledge and stress students’ proficiency with computational skills (An, Kulm, & Wu, 2004; Ma, 1999; Mok, 2006). Chinese teachers use student errors as a starting-point for further inquiry, promoting a climate of openness to discuss mistakes during the struggle to learn mathematics. Because American teachers interpret errors as an indication of a failure to learn, mistakes are discouraged and hidden, often leading to student embarrassment (Santagata, 2004; Schleppenbach, Flevares, Sims, & Perry, 2007; Stevenson & Stigler, 1992; Wang & Murphy, 2004). Chinese professional development focuses on issues related to daily teaching practice, mostly the creation, implementation, and refinement of lessons, often in teaching research groups (Paine & Ma, 1993). Chinese professional development is also based on current content interests that motivate Chinese teachers to attend, participate actively, and take the learning back to their classrooms—it is not some passing fad as often seen in the U.S., or an occasional one-day workshop (An & Kulm, 2010; Yang & Ricks, 2011). Finally, Chinese professional development opportunities are varied and rich. Some of these include: (1) participation in exemplary lesson development (a form of Chinese lesson study called ‘keli’) or in teaching research groups, a mandatory part of promotion and tenure, (2) collaboration by university professors and district supervisors to coordinate model lessons taught by invited ‘master teachers’ to a random class of students in the presence of the district’s math teachers, and (3) sharing common office spaces and planning times to facilitate in-school collaboration (Huang & Bao, 2006; Liang, 2001; Ma, 1999; Park & Hannum, 2001; Yang & Ricks, 2011). Chinese teachers’ instructional workload is lighter than U.S. teachers’, allowing

for greater attention to professional development (Leung, 1995; Sargent & Hannum, 2005). Chinese teachers have more time (almost four times as much!) to participate in professional development than U.S. teachers (An & Kulm, 2010). While visiting China, I noticed the lesson capture equipment prevalent in teaching laboratories dedicated to professional development, complete with two-way mirrors, (remotecontrolled) camera equipment, in-house editing software, and specialized ceiling microphones. Communication is a central component of all professional development in China (An & Kulm, 2010). China also has a position I call a university liaison, which does not exist in the U.S. The closest we have is a ‘math coach’, or perhaps a lone and zealous university mathematics professor who attempts to coordinate activities. The Chinese university liaison is a dedicated link between university theory and actual school implementation of theory in practice. Chinese university liaisons also meet as a group—a further level of networked supra-individual collaboration. Additionally, the Chinese have dedicated teaching-universities apart from their research institutions, with teaching-university professors working in groups with selected schools on professional development. These are non-existent in the United States. Another form of Chinese professional development not apparent in the U.S. educational system is the organization of teaching contests and teaching exhibitions (Y. Li & Li, 2009). The Chinese teachers seek to emulate these outstanding individual teachers because they are “the model of the collective. They represent and embody a common orientation which all teachers are to pursue. In a sense they are like a magnetic force that attracts and calls teachers of the whole country to work together” (Paine & Ma, 1993, p. 682). The U.S., by contrast, does not have networked supra-individual educational structures (Paine, 1997). For example, the U.S. teacher is not given the time for professional development.

U.S. teachers work in extreme isolation, severely limiting communication, collaboration, or shared thinking. The U.S. teacher, when attempting collaboration, rarely moves past the collection stage into collective work (e.g., joint activity work, see Stein & Brown, 1997). The U.S. does not have a sustained, coherent, or effective professional development program. The reasons for this are diverse, including lack of time, isolation, no expectation for continued learning, ignorance of how to use professional development time, little administrative support, and high teaching contact hours with students. Additionally, unlike the Chinese who view beginning teachers as novices, the U.S. academy graduates “certified” (and hence, “competent”) teachers, rarely to interact with them again. The U.S. does not have a system for recognizing or rewarding good teaching (except for looking at standardized test scores, a poor way of ranking teachers). Although class sizes are smaller, the U.S. teacher teaches more students than other countries, placing a greater burden on them. Funding provides the resources and incentive to conduct more systematic initiatives in the U.S., such as summer courses with follow-up research. These are, however, the exception rather than the norm and are not sustainable once funding stops. The one-day workshop is the typical example of U.S. professional development: fragmented, unconnected to real practice, temporally disjoint, and not done with colleagues over several years. U.S. teachers—protected by the tenure system—often settle into a comfortable groove of continuing the status quo. New generations of teachers, brought up under this culture, also perpetuate the status quo (Stigler & Hiebert, 1999). Chinese professional development is not plagued by the issues lamented by U.S. scholars about U.S. professional development (An & Kulm, 2010). U.S. professional development efforts “collectively do not form a cohesive and cumulative program… much of the time and money invested in such programs, however, is not used effectively” (Kilpatrick,

Swafford, & Findell, 2001, p. 431) By contrast, China has the mechanisms to allow networking communication between educational entities, especially video equipment, professional development, dedication of time and resources to improving teaching, various types of lesson study, similar curricula to aid teacher discussion, etc. Communication occurs across a variety of channels: between colleagues teaching the same material, across grade levels, with teachers from other subjects, across schools, cities, and the entire nation (An & Kulm, 2010). The U.S. has nothing comparable; all supra-individual complexity is primarily limited to the class in the form of temporary student groups or whole class discussions. In the U.S., outsiders often attempt to reform the practice of insiders; however, in China, all levels of professional development are insider-organized (An & Kulm, 2010; Davis & Simmt, 2003; Kilpatrick, Swafford, & Findell, 2001). Chinese professional development is thus much more effective than U.S. models (An & Kulm, 2010). In summary, the theoretical framework of complexity illuminates the strengths and weaknesses of both the Chinese and U.S. educational systems. The individualistic U.S. culture has produced an educational system focused on developing the capacities of individuals by nurturing students’ innovation, creativity, curiosity, and autonomy—to such an extent that supraindividual complex systems rarely emerge2. By contrast, China’s collective culture generates productive, stable, and networked supra-individual collectives (class cohorts, teaching research groups, etc.) that are the envy of the West. China’s collective mentality, however, has limited the development of the individual pupil, despite the Chinese pupil’s strong content manifestation in certain areas (An & Kulm, 2010). Discussion Complexity theory helps suggest why China and the U.S. may each be attempting to

adopt certain features of the other’s educational system (Tienken & Canton, 2009; Zhao, 2009a). Each nation is striving to adopt the strong complex aspects of the other’s system, in which they themselves are weak: The U.S.—strong in educating by enabling the individual—is trying to adopt the supra-individual influences of China; China—already strong in its networked suprastudent influences—is trying to adopt the U.S.’s individual emphasis. China envies U.S. student creativity and innovation, while the U.S. envies the holistic and robust interconnected educational networks of the Chinese system that yield sustainable professional development, motivation for students’ hard work, and (apparently, especially to politicians, policy-makers, and parents) higher international test scores. The U.S. seeks China’s supra-individual features. The U.S. is striving to modify its educational system to adopt some of the supra-individual principles manifest by the Chinese. For example, because “U.S. curriculum materials are less focused and more repetitive, and U.S. curriculum policy is less authoritative, less specific, and less consistent” (J. Wang & Lin, 2005, p. 3) than those in China, many in the U.S. are pushing for a “common core curriculum” to help teachers across the country better communicate, cooperate, and jointly think about teaching in new collective ways (NCTM, 2010). Some believe that a more focused curriculum—supported by peer collaboration—will yield more focused and content-based U.S. lessons (NCTM, 2006). Cai (2008) reported “In the United States, several recent reports call for learning from Asia because it is believed that Asian countries like China, India, and Singapore are much more effective in mathematics and science education, thus posing a major threat to global competitiveness of the United States” (p. 159). The U.S. is also striving to develop department, school, and district-based learning communities that exhibit the sustained networks seen overseas in China (NCTM, 2000). The principle is to increase the connections between curriculum points,

between teachers, between schools/districts/universities. Many U.S. states are also pushing to drop teachers’ tenure protection to improve performance. China seeks the U.S.’s individual focus. China recognizes that their students are far behind U.S. students in terms of individual capacity for creative and independent thought, although Chinese students perform better in general on international tests (Lu & Wang, 2008; J. Wang & Lin, 2005). They are seeking to increase expenditure for education, shrink class sizes, adopt a less teacher-centered and more progressive (some would say: ‘constructivist-based’) pedagogy, make education more equitable for all Chinese, decrease examination pressures, diversify curriculum, and allow more students into college by allowing the national university examination to be taken multiple times and opening more universities (Kong, & Gimmestad, 1999; S. Li & Yang, 2008; Wong, Marton, Wong, & Lam, 2002). In the U.S., academics is seen as a parallel process to living; in modern China, academics—once the pathway to economic prosperity—is to be tempered with other life-enriching experiences like extra-curricular activities, work experience, and internships (K. Y. Chen, 1981; S. Wang & Lu, 2008). Some feel that China’s one-child policy has created a generation of coddled youth illprepared for the harsh realities of market-driven economies (Tschang, 2007; Tsui & Rich, 2002). One Chinese principal I interviewed (renowned for turning low performing schools into high performing schools) said two major obstacles to Chinese educational reform are the sociallyharmful but usually mandatory one-child policy and the excessive emphasis on examinations. China seeks to “undo the damages of testing and standardization” (Zhao, 2009a, p. vi). China’s one-time national college entrance examination is being modified into an exam that can be retaken multiple times. This change would have an enormous impact on Chinese secondary education which has historically been geared to prepare students to pass the examination:

The National Conference is demanding changes in the [university] admission standards that would include qualifications other than the one-time examination [such as] greater emphasis on students' creativity and the ability to solve practical problems… These changes may have tremendous impact on the curriculum structure of both secondary schools and postsecondary institutions; heretofore, curricula have been designed to strive for students' achievement in examinations rather than in creative and practical skills. (Kong, & Gimmestad, 1999, p. 88) China is specifically seeking to “decentralize curriculum and textbooks, diversify assessment and testing, and encourage local autonomy and innovations in order to cultivate creativity and well-rounded talents.” (Zhao, 2009a, p. vi). Further, China is striving to re-orient their traditionally elite-oriented educational system to help the general masses—to focus on the needs of every individual, rich or poor, Han or minority (Kong, & Gimmestad, 1999). China is becoming more open to Dewey and child-centered learning (Su, 1995, p. 319). Conclusions As the global village shrinks and pressure to improve teaching and learning mounts, cross-cultural comparisons offer intriguing new possibilities for such improvement (An, Kulm, & Wu, 2004; Cai, 2004; Cai & Hwang, 2002; Kaiser, 1999; Robitaille & Travers, 1992; Stigler & Perry, 1988; Wolcott, 1999; Xie & Carspecken, 2008). Researchers have commented that both China and the U.S. seem to be trying to adopt the educational practices of the other (Tienken, 2008; Tienken & Canton, 2009; Zhao, 2009a, 2009b). This study has applied the theoretical framework of complexity to attempt to understand this grass-is-greener-on-the-other-side phenomenon. In particular, this study has highlighted that China’s educational system is characterized by strong supra-individual phenomena that overshadows individuality. The U.S. does not have well-developed supra-individual phenomena because U.S. classes are collections rather than collectives of students, U.S. lessons are fragmentary, and the U.S. still struggles to sustain any meaningful professional development system. However, the U.S. has developed an

education system that enables individual students’ development of creativity, curiosity, innovation, and autonomy to the envy of the Chinese. This study suggests that China and the U.S. appear to be copying the complex strengths (while avoiding the weaknesses) of the other in order to augment their own shortcomings. Complexity offers a framework to explain how and why each country is striving to copy certain features of the other’s educational system. Further, if each nation judiciously picks and chooses which parts of the other’s system to integrate into its own, it is reasonable to expect that both will benefit. The danger comes when populations panic and attempt rapid, unthoughtful integration— proverbially ‘biting off more than they can chew.’ As Leung (2001) advised: In considering adopting the practices from a different cultural tradition, one has to thoroughly analyze the underlying values to see whether they are compatible with the values in one's own culture. Wholesale adoption rather than adaptation is usually not desirable. (p. 47) As long as China and the U.S. respect the complex mathematics education strengths they offer their students, I see no harm for either to selectively adapt their own educational system based on the successful experience of the other country. Appropriate integration of certain cross-cultural features should provide each country with innovative and promising ways forward without jeopardizing the cultural strengths for which each system is known (Wong, Lin, & Watkins, 1996). Improving the weaknesses through the experience of one’s neighbor is wise, as long as the process is seen as a temporary and experimental attempt until its adaptation is deemed successful. Let us open up the pasture gates, welcome our neighbor’s foraging upon our own local successes, and gratefully graze upon the greener stretches on the other side. ENDNOTES The two U.S. cities are kept confidential to honor the requests of the research participants. The cities are located near Salt Lake City, Utah and Atlanta, Georgia. 2 The only possible exceptions being the U.S. professional educational organizations, like the National Council of Teachers of Mathematics (NCTM), or teacher unions. 1

REFERENCES An, S., & Kulm, G. (2010). How Chinese in-service elementary mathematics teachers gain knowledge from professional development. Journal of Mathematics Education (English Version), 1(1), 41–57. An, S., Kulm, G., & Wu, Z. (2004) The pedagogical content knowledge of middle school math. teachers in China and the U.S. Journal of Mathematics Teacher Education, 7, 145–172. An, S., & Wu, Z. (2008). Developing and assessing pre-service teachers' knowledge of mathematics teaching. In L. D. Miller, & S. R. Saunders, (Eds.), Proceedings of the US-Sino Workshop on Mathematics and Science (pp. 111–119). Murfreesboro, Tennessee. Anderson, P. W. (1972, August, 4). More is different. Science, 177(4047), 393–396. Bauman, K. J., & Graf, N. L. (2003). Ed. attainment: 2000. U.S. Census Bureau C2KBR-24. Ben-Jacob, E. (1998). Bacterial wisdom, Gödel’s theorem & creat. genomic webs. Physica A, 248, 57–76. Biggs, J. B. & Watkins, D. A. (2001). Insight into teaching the Chinese learner. In D. A. Watkins, & J. B. Biggs (Eds.), Teaching the Chinese learner (pp. 277–300). Hong Kong/Melbourne: C.E.R. Centre. Bloom, B. S. (1984). The 2 sigma problem. Educational Researcher, 13(6), 4–16. Cai, J. (2000). Mathematical thinking involved U.S. and Chinese students’ solving of process-constrained and process-open problems. Mathematical Thinking & Learning, 2(4), 309–340. Cai, J. (2003). Investigating roles in students’ learning of mathematics from a cross-national perspective. Mathematics Education Research Journal, 15(2), 87–106. Cai, J. (2004). Why do U.S. and Chinese students think differently in mathematical problem solving? Journal of Mathematical Behavior, 23, 135–167. Cai, J. (2008). International assessment as a means for improving students’ learning. In L. D. Miller, & S. R. Saunders, (Eds.), Proceedings of the US-Sino Workshop (pp. 155–162). Murfreesboro, Tennessee. Cai, J., & Hwang, S. (2002). Generalized & generative thinking in U.S. and Chinese students’ mathematical problem solving & problem posing. Journal of Mathematical Behavior, 21(4), 401– 421. Cai, J., & Wang, T. (2010). Conceptions of effective mathematics teaching within a cultural context. Journal of Mathematics Teacher Education, 13(3), 265–287. Chen, K. Y. (1981). Chinese education. World Education Monograph Series, Number Two. Chen, J., & Mu, Z. (2010). The cross-national comparison of pre-service math. teacher ed. and curriculum structure. Journal of Mathematics Education (English Version), 1(1), 119–136. Clarke, D. J., Keitel, C., & Shimizu, Y. (2006). Mathematics classrooms in twelve countries: The insider’s perspective. Rotterdam: Sense Publishers. Clements, D. H., & Sarama, J. (2008). Mathematics and technology. In L. D. Miller, & S. R. Saunders, (Eds.), Proceedings of the US-Sino Workshop (pp. 178–183). Murfreesboro, Tennessee.

Cobb, P., & Yackel E. (1995). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. In D. T. Owens, M. K. Reed, & G. M. Millsaps (Eds.), Proceedings of the Seventeenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 3–29). Columbus, OH: ERIC/CSMEE Publications (ERIC Document Reproduction Service No. SE057176). Dahar, M. A., & Faize, F. A. (2011). Mis-allocation of student teacher ratio, class size and per student expenditure. International Research Journal of Finance and Economics, 62, 94–110. Darling-Hammond, L., Ancess, J., & Ort, S. W. (2002). Reinventing high school. AERJ, 39(3), 639–673). Davis, B., & Simmt, E. (2003). Understanding learning systems. Journal for Research in Mathematics Education, 34, 137–167. Davis, B., & Sumara, D. (2001). Learning communities: Understanding the workplace as a complex system. New Directions for Adult and Continuing Education, 92, 85–95. Davis, B., Sumara, D., & Kieren, T. E. (1996). Co-emergence, cognition, curriculum. Journal of Curriculum Studies, 28, 151–169. Davis, B., Sumara, D., & Simmt E. (2003). Complexity and collectivity. In Proceedings of the 2003 Complexity and Ed Research Conf, October 16–18 (pp. 217–230). Edmonton, Canada. Epstein, I. (1980). Review: The Dewey experiment in China. Comparative Education Review, 24(3), 438– 440. Epstein, I. (1986). Reformatory education in Chinese society. Comparative Criminology Offender Therapy and International Journal of Criminology, 30(2), 87–100. Fan, L., & Zhu, Y. (2004). How have Chinese students performed in mathematics? A perspective from large-scale international mathematics comparisons. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics (pp. 3–26). Hackensack, NJ: World Scientific. Glaser, B. G. (1965). The constant comparative method. Social Problems, 12, 436–445. Greenspan, A. (2008). China Vs. America? Learning Strategies in the 21st Century. The Globalist. Retrieved 28 March 2011 from: http://www.theglobalist.com Han, Y., & Ginsburg, H. P. (2001). Chinese and English mathematics language: The relation between linguistic clarity and mathematics performance. Mathematical Thinking and Learning, 3(2-3), 201220. Harmon, M., Smith, T. A., Martin, M. O., Kelly, D. L., Beaton, A. E., Mullis, I., Gonzalez, E. J., & Orpwood, G. (1997). Performance assessment in IEA’s Third International Mathematics and Science Study (TIMSS). Chestnut Hill, MA: Boston College, TIMSS International Study Center. Hiebert, J., Gallimore, R., Garnier, H., Givvin, K. B., Hollingworth, H., Jacobs, J. et al (2003). Teaching Mathematics in Seven Countries: Results from the TIMSS 1999 Video Study. Washington, DC: NCES.

Hou, H. (2010). A comparison of the career and technical education programs in US community college and a Chinese institution (Unpublished doctoral dissertation). National-Louis University, Chicago, IL. Huang, R., & Bao, J. (2006). Towards a model for the teacher professional development in China: Introducing Keli. Journal of Mathematics Teacher Education, 9, 279–298. Huang, R., & Li, Y. (2009). Pursuing excellence in mathematics classroom instruction through exemplary lesson development in China. ZDM Mathematics Education, 41, 297–309. Johnson, S. (2001). Emergence. New York: Scribner. Kaiser, G. (1999). International comparisons in mathematics education under the perspective of comparative education. In G. Kaiser, E. Luna & I. Huntley (Eds.), International comparisons in mathematics education (pp. 1–15). Philadelphia, PA: Falmer. Kilpatrick, J., Swafford, S., & Findell B. (2001). (Eds.), Adding it up: Helping children learn mathematics. National Research Council: National Academy Press. Kilpatrick, J., Mesa, V., & Sloane, F. (2006, November). U.S. algebra teaching and learning viewed internationally. Paper presented at the 2nd IEA International Research Conference, Brookings Institution, Washington, DC. Kong, X., & Gimmestad, M. (1999). ERIC review: U.S. community colleges and China’s counterpart institutions. Community College Review, 27(3), 77–91. Leung, F. K. S. (1995). The mathematics classroom in Beijing, Hong Kong and London. Educational Studies in Mathematics, 29, 297–325. Leung, F. K. S. (2001). In search of an East Asian Identity in mathematics education. Educational Studies in Mathematics, 47, 35–51. Leung, F. K. S. (2005). Some characteristics of East Asian mathematics classrooms based on data from the TIMSS 1999 Video Study. Educational Studies in Mathematics, 60(2), 199–215. Leung, F. K. S. (2008). In the books there are golden houses: mathematics assessment in East Asia. ZDM Mathematics Education, 40, 983–992. Li, J. (2004). A Chinese cultural model of learning. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics (pp. 124–156). Hackensack, NJ: World Scientific. Li, L. (2011). East or West, Nothing Is Perfect. Beijing Review, 8. Retrieved March 28, 2011 from: http://www.bjreview.com.cn/quotes/txt/2011-03/04/content_337484.htm# Li, Y., & Li, J. (2009), Mathematics classroom instruction excellence through the platform of teaching contests. ZDM Mathematics Education, 41(3), 263–277. Li, S., & Yang, Y. (2008). Reform in the process of teaching development. In L. D. Miller, & S. R. Saunders, (Eds.), Proceedings of the US-Sino Workshop (pp. 126–132). Murfreesboro, Tennessee.

Liao, S., & Cao, Y. (2010). The structure of mathematics lessons in China. Journal of Mathematics Education (English Version), 1(1), 27–40. Liang, X. (2001). China: Challenges of Secondary Education. Washington, D.C.: World Bank. Lin, J. Y. (1995). The Needham Puzzle: Why the industrial revolution did not originate in China. Economic Development and Cultural Change, 43(2), 269–292. Lin, F., & Tsao, L. (1999). Exam maths re-examined. In C. Hoyles, C. Morgan, & G. Woodhouse, (Eds.), Rethinking the Mathematics Curriculum (pp. 228–239). Philidelphia: Falmer Press. Lu, S., & Wang, S. (2008). The research process, testing, and revision of the mathematics curriculum standard of Full-time Obligatory Education in China. In L. D. Miller, & S. R. Saunders, (Eds.), Proceedings of the US-Sino Workshop (pp. 23–27). Murfreesboro, Tennessee. Ma, L. (1999). Knowing and teaching elementary mathematics. Hillsdale, NJ: Erlbaum. Ministry of Education, P. R. China. (2003). Mathematics curriculum standards for normal senior high schools. Beijing: People’s Educational Press. Mok, I. (2006). Teacher-dominating lesson in Shanghai. In D. J. Clarke, C. Keitel, & Y. Shimizu (Eds.), Mathematics classrooms in 12 countries (pp. 87–98). Rotterdam: Sense Publishers. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence. Reston, VA: Author. National Council of Teachers of Mathematics. (2010). Making it happen: A guide to interpreting and implementing Common Core State Standards for Mathematics. Reston, VA: Author. Paine, L. W. (1997). Chinese teachers as mirrors of reform possibilities. In William K. Cummings & P. G. Altbach (Eds.), The challenge of Eastern Asian education (pp. 65-83). Albany: State University of New York Press. Paine, L. W., & Ma, L. (1993). Teachers working together: A dialogue on organizational and cultural perspectives of Chinese teachers. International Journal of Educational Research, 19(8), 667-778. Park, A., & Hannum, E. (2001). Do teachers affect learning in developing countries? Evidence from matched student-teacher data from China. Paper presented at the Rethinking Social Science Research on the Developing World in the 21st Century, Park City Utah, June 7-11, 2001. Perry, M. (2000). Explanations of mathematical concepts in Japanese, Chinese, and U.S. first- and fifthgrade classrooms. Cognition and Instruction, 18(2), 181-207. Ricks, T. E. (2007). The mathematics class as a complex system (Unpublished doctoral dissertation). University of Georgia: Athens, GA. Ricks, T. E. (2009a). Juxtapositional pedagogies in mathematics methods courses. In S. L. Swars, D. W.

Stinson, & S. Lemons-Smith, (Eds.) Proceedings of the Thirty-First Annual Meeting, PME-NA (Vol. 5). Atlanta, GA: Georgia State University. Ricks, T. E. (2009b). Superbugs and ailing schools: What bacterial colonies can teach us about education. Education Week Commentary, published on-line, July 6, 2009. Robitaille, D.F., & Travers, K.J. (1992). International studies of achievement in mathematics. In D.A. Grouws (Ed.), Handbook of mathematics teaching and learning (pp. 687–709). New York: Macmillan Publishing Company. Santagata, R. (2004). “Are you joking or are you sleeping?” Cultural beliefs and practices in Italian and U.S. teachers’ mistake-handling strategies. Linguistics & Education, 15, 141–164. Sargent, T. & Hannum, E. (2005). Keeping teachers happy: job satisfaction among primary school teachers in rural Northwest China. Comparative Education Review, 49(2), 173–204. Schleppenbach, M., Flevares, L. M., Sims, L., & Perry, M. (2007). Teachers’ Responses to Student Mistakes in Chinese and U.S. classrooms, The Elementary School Journal, 108(2), 131–147. Siegler, R. S., & Mu, Y. (2008). Chinese children excel on novel mathematics problems even before elementary school. Psychological Science, 19(8), 759–763. Shapiro, J. (1998). Thinking about bacterial populations as multicellular organisms. Annual Review of Microbiology, 52, 81–104. Stein, M. K., & Brown, C. A. (1997). Teacher learning in a social context. In E. Fennema & B. S. Nelson (Eds.), Math teachers in transition (pp. 155–191). Mahwah, NJ: Erlbaum. Stevenson, H. W., Chen, C., & Lee, S.-Y. (1993). Mathematics achievement of Chinese, Japanese, and American children: Ten years later. Science, 259, 53–58. Stevenson, H. W., & Stigler, J. W. (1992). The learning gap. NY: Summit Books. Stigler J. W., & Hiebert, J. (1999). The teaching gap. NY: Free Press. Stigler, J. W., & Perry, M. (1988). Mathematics learning in Japanese, Chinese, and American classrooms. New Directions for Child Development, 41, 27–54. Su, Z. (1995). A critical evaluation of John Dewey's influence on Chinese education. American Journal of Education, 103(3), 302–325. Tienken, C. H. (2008). Rankings of national achievement test performance and economic strength: Correlation or conjecture? International Journal of Education Policy and Leadership, 3(4), 1–15. Tienken, C. H., & Canton, D. C. (2009). National curriculum standards: Let’s think it over. Journal of Scholarship and Practice, 6(3), 3–9. Tschang, C. (2007). China’s college graduate glut. China Economic Review. Retrieved 15 October 2011 from: http://www.businessweek.com/globalbiz/content/jun2007/gb20070605_780984.htm Tsui, M., & Rich, L. (2002). The only child and educational opportunity for girls in urban China. Gender

and Society, 16(1), 74–92. Wang, J., & Lin, E. (2005). Comparative studies on U.S. and Chinese mathematics learning and the implications for standards-based math. teaching reform. Educational Researcher, 34(5), 3–13. Wang, X., Liu, C., Zhang, L., Luo, R., Glauben, T., Shi, Y., Rozelle, S., & Sharbono, B. (2011). College education and the poor in China. Working paper 213, Phi Delta Kappan, 63(10), 673–676. Retrieved 15 October 2011 from: http://iis-db.stanford.edu/pubs/23081/213__College_Education_and_the_Poor_in_China.pdf . Also available from Asia Pacific Education Review, 2011. Wang, S., Lu, S. (2008). Research process, changes and implementation of mathematics curriculum standards for senior high schools in China. In L. D. Miller, & S. R. Saunders, (Eds.), Proceedings of the US-Sino Workshop on Mathematics and Science Education: Common Priorities that Promote Collaborative Research, (pp. 49–53). Middle Tennessee State University, Murfreesburro, TN. Wang, T., & Murphy, J. (2004). An examination of coherence in a Chinese mathematics classroom. In: L. Fan, N.-Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 107–123). Singapore: World Scientific Publishing Company. Wolcott, H. F. (1999). Ethnography: A way of seeing. Walnut Creek, CA: AltaMira. Weick, K. E. (1976). Educational organizations as loosely coupled systems. Administrative Science Quarterly, 21(1), 1–19. Weick, K. E. (1982). Administering education in loosely coupled systems. Phi Delta Kappan, 63(10), 673–676. Wong, N. Y. (2000). Mathematics education and culture: The “CHC” learner phenomenon. Retrieved 8 October 2011 from http://www.math.admu.edu.ph/tsg22/wong.htm Wong, N. Y. (2008). Confucian heritage culture learner’s phenomenon: from “exploring the middle zone” to “constructing a bridge”. ZDM, 40(6), 973–981. Wong, N. Y., Han, J. W., & Lee, P. Y. (2004). The mathematics curriculum: towards globalisation or Westernisation? In L. Fan, N. Y. Wong, J. Cai & S. Li (Eds.), How Chinese learn mathematics: perspectives from insiders (pp. 27–70). Singapore: World Scientific. Wong, N. Y., Lin, W. Y., & Watkins, D. A. (1996). Cross-cultural validation of models of approaches to learning: An application of confirmatory factor analysis. Educational Psychology, 16(3), 317–327. Wong, N. Y., Marton, F., Wong, K. M., & Lam, C. C. (2002). The lived space of mathematics learning. Journal of Mathematical Behavior, 21, 25–47. Xie, X., & Carspecken, P. F. (2008). Philosophy, learning and the mathematics curriculum. Sense Publishers: Taipei.

Yang, Y., & Ricks, T. E. (2011). Chinese lesson study: Developing classroom instruction through collaborative school-based Teaching Research Groups. Unpublished manuscript. You, Z., & Jia, F. (2008). Do they learn differently? An investigation of the pre-service teachers from US and China. Teaching and Teacher Education, 24, 836–845. Young, R. M. (2010). Creative education: China vs. United States. Retrieved 28 March 2011 from: http://breakthroughgen.org/blog//2010/07/ creative_education_china_v_uni-print.html Zhang, L., Yan, W., Dong, B., & Zhou, Z. (2009). The comparison study of Chinese and American secondary school students’ knowledge structure. Frontiers of Education in China, 4(2), 286–297. Zhao, Y. (2009a). Catching up or leading the way? ASCD. Zhao, Y. (2009b). Preparing global citizens. London, England: SSAT. Zhu, M. (1999). The views and involvement of Chinese parents in their children’s education. Prospects, 29, 233–238.