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Introduction
Since the early 1970s, constructivism has fundamentally transformed the understanding of mathematics and its learning and teaching (Steffe & Kieren, 1994). Mirroring the paradigm change in epistemology that perceives knowledge as interpretive and socially constructed (Van de Ven, 2007), traditional conception and practice vis-Ă -vis what mathematics is, how it should be learned, how it should be taught and so on, have been re-scrutinized. No longer being a set of universal truths, mathematics is understood to be socially constructed, life-related, and culturally important (Cobb, Yackel, & Wood, 1992). In light of constructivism, mathematics knowledge is not a fixed body of procedures and rules, but a growing and changing science of quantity and patterns, and the practice of mathematics involves experimentation, reasoning, and argumentation (National Research Council, 1990).
In school mathematics education, mathematics learning is no longer considered the mapping of the external world into the internal cognition of students via simple drill and rote memorization (Cobb, 1994). Instead, students are perceived as actively constructing the meaning of mathematical concepts via active interactions. Teachersâ roles are expected to change from knowledge providers to facilitators, provocateurs, and questioners, who need to create an interactive environment, that is, a constructivist mathematics classroom, for students to model mathematically their lived worlds (Fosnot, 2005).
Different from traditional classrooms, constructivist classrooms should offer original curriculum materials, seek and value studentsâ input, provide student-centered learning activities, and conduct authentic assessment of student learning (Brooks & Brooks, 1993). Ideally, constructivist mathematics classrooms should be like a workshop, a mini society, a community of learners, in which students are actively engaged in authentic mathematical activities, discourses, and reflections (Fosnot, 2005).
This constructivist vision for teaching and learning has impacted mathematics education to a great extent. One of the prominent influences can be found in the setting of mathematics curriculum standards in the U.S. Since the 1980s, education reform has been characterized by the development and adoption of curriculum standards at all levels of policymaking and governance (Fuhrman, 1999; Smith & OâDay, 1991). In such an era, constructivism continued to nourish school mathematics education. It culminated in the milestone document, the Curriculum and Evaluation Standards for School Mathematics (for short, the N.C.T.M. Standards) (National Council of Teachers of Mathematics (N.C.T.M.), 1989). The N.C.T.M. Standards (1989), grounded in constructivism, placed a greater emphasis on fostering studentsâ conceptual understanding, reasoning, problem-solving, and communication. To this end, students need to actively interpret, organize, and construct the meaning of situations with mathematical modeling (Fosnot, 2005).
The N.C.T.M. Standards provided students and teachers a coherent and consistent roadmap. A common set of targets of knowledge and skills was specified for students to achieve, and the sequence of content areas was detailed for teachers to follow. In line with the N.C.T.M. Standards, many states in the U.S. developed mathematics curriculum standards that were constructivist-oriented and implemented standards-based reform curricula, in the hope of transforming instructional practices and enhancing academic achievement (Schoenfeld, 2004).
Since the first decade of this century, the Federal Government of the U.S. has been nationalizing curriculum standards benchmarked against challenging international ones. Arne Duncan, the then U.S. Secretary of Education, declared that ââŚthe notion that we have 50 different goalposts is absolutely ridiculous. If we accomplish one thing in the coming years â it should be to eliminate the extreme variation in standards across Americaâ (Duncan, 2009, para. 2). In 2010, the Common Core State Standards came into being (Common Core State Standards Initiative, 2010). Further efforts were made to develop a curriculum based on the Common Core State Standards, since innovating the curriculum has been the primary approach to inciting large-scale educational change for decades (Cohen & Hill, 2000; Darling-Hammond, 1990; Fullan & Pomfret, 1977; Stenhouse, 1975).
Even though standards and curriculum could be developed at the national level, it is local school districts and buildings, however, that determine the extent those instruments of reform succeed (Ogawa et al., 2003). China might be a potential site to examine how an innovative curriculum reform could be implemented nationwide and possibly enable instructional transformation. Interestingly enough, as the U.S. casts an appreciative eye over Chinese mathematics education (Asia Society, 2005; Stevenson & Stigler, 1994), China has grown increasingly dissatisfied with its own education and instead looks to the developed countries, particularly the U.S., as the role model for reform. Notably, following in the footsteps of the Western constructivist-minded reformers, China has embarked on a constructivist standards-based mathematics curriculum reform since the late 1990s.
Troubled basic education in China
Educational reform, according to Ginsburg and colleagues (Ginsburg et al., 1990), focuses on changing one or more of the following aspects of educational systems:
In basic education in China, âreformâ has been a buzzword since 1949. Seven rounds of nationwide educational reform was carried out until 1992 (Chen, 1999). On average, every 5 years there was a new round of curriculum reform. Even though some achievements were made, serious setbacks also occurred, for policies were constantly oscillating between whether education should be for economic development or for ideological integrity, for social equality or for efficiency, and/or for maximizing human capacity or for growing intellectuals (Tsang, 2000).
Previously, many reform efforts had been exerted in changing the curriculum and pedagogy. Yet, after many attempts, Chinese parents were disappointed to see that problems were persistent. Heavy examination pressure remained which haunted children, students were overloaded with testing in many subject areas, and teaching still relied on direct instruction with few interactions. One simple fact testifies to this observation. The Ministry of Education (M.O.E.) in China ordered to ease studentsâ burdens (jianfu) 49 times from 1985 to 2000, however, the workload of students has only increased (Liu, 2007). Peopleâs dissatisfaction grew ever stronger with Chinaâs highly test-centric schooling.
In the late 1990s, two domestic and international factors paved the way for another round of educational reform in China. Firstly, China underwent rapid political, social, and economic transformation. As China changed from a primarily socialist planned economy to a market economy, growing consensus was reached with regard to the significance of education in advancing economic development, addressing social equity, and improving the qualities of human resources. Very possibly, there could be less resistance to and ambivalence about the direction of the reform. Secondly, in the meantime, China was expected to become a member of the World Trade Organization (W.T.O.) (China officially joined in late 2001) and face fierce competition with developed countries in the global market. The authorities stressed the imperativeness of reforming out-of-date basic education that suffocated the nationâs originality and creativity, and impeded its development in science and technology.
Owing to Chinaâs unique relations with the West in history, the West not only serves as the source for its inspirations, but also stirs up feelings among the Chinese people. âLearning from the Westâ, âchasing the Westâ, and âbeating the WestââŚthese lofty slogans can always magnetize and energize Chinese society. Thus, the reference to globalization and competition with developed countries could effectively displace societyâs frustration with actual problems, and mobilize genuine support for the educational reform.
The Chinese central authorities began exploring the possibility of having another round of educational reform in 1996 (Huang, 2004). Under a new and soon to be widespread banner, suzhi jiaoyu, or âeducation for improving the qualities of students,â the Action Plan for Invigorating Education in the 21st Century (hereinafter referred to as âthe Action Planâ) was formulated by M.O.E. and ratified by the State Council in 1999 (Guan & Meng, 2007). In order to greatly improve the education, suzhi, of the whole Chinese nation, the Action Plan spelled out the goals that should be realized in the realm of moral, intellectual, physical, and art education, early childhood education, and education for children with disabilities and ethnic minorities. Despite its vagueness, and danger of engendering and justifying social inequality, one key purpose of suzhi jiaoyu was to develop the competencies of children rather than focus on exam success, consequently leading to the revitalization of the nation. A subsequent policy document, the Decision to Strengthen the Educational Reform and to Foster Full-scale Qualities-oriented Education (hereinafter referred to as âthe Decisionâ) (M.O.E., 1999), marked the official launch of the eighth wave of comprehensive educational reform in China.
The Decision set forth goals in such aspects as educational equity, educational decentralization and privatization, promotion of lifelong learning, and internationalization and globalization (Guan & Meng, 2007). In all its sincerity, the Decision placed an emphasis on the need to substantially overhaul the national curriculum framework in response to the above issues. It directed that a new framework be remolded in line with advanced curriculum theories, and required that educational goals be reoriented and objectives redefined, curricular contents be updated, accessible, related to real life, and promote higher-order thinking, and instruction be explorative, heuristic, and child-centered. The Decision stated that the curriculum should consist of three tiers of management at the national, local, and school levels.
Development and implementation of the National Mathematics Curriculum Standards
The preparation stage (1999â2001)
The first move was to replace the old teaching outlines with curriculum standards. In China, the teaching outlines were documents that outlined the sequence, scope and depth of knowledge of each subject area at each grade level, which teachers, students, and textbook writers should stick to. New curriculum standards were to set minimum expectations for teaching and learning. The task of designing new curriculum standards for 18 subject areas from Grades 1 to 9 started in March 1999. M.O.E. called up an expert group that consisted of 15 university professors, several Grade 1â9 mathematics teachers, and a number of mathematicians, publishers, and teacher trainers. The group explored a wide range of issues. For instance, they identified the problems in the current curriculum, researched the reform practices of developed countries, and envisioned mathematics for the next century. After a dozen revisions, the group produced the trial version of the National Mathematics Curriculum Standards for Grades 1 to 9 (for short, the N.M.C. Standards) in February 2000 and sent out 40,000 copies for feedback in March of that year (China Education Network, 2005). Also, the N.M.C. Standards (Trial) was officially published in June 2001 (M.O.E., 2001). Between the creation of the trial version and its official publication, textbook series with newly added content were piloted in more than 40 schools in Beijing, Guangdong, and Xinjiang. Different from the previous âone outline, one set of textbooksâ policy, the central authorities allowed having multiple textbook series written in accordance with the Standards. Altogether, eight sets of textbooks were adopted for the elementary level, and six for the secondary level.
The pilot stage (2001â2004)
In September 2001, the beginning of the new school term, the N.M.C. Standards were tried out in 42 experimental counties selected by M.O.E. Before that, backbone teachers (âmainstayâ teachers, the selected core teachers with potential), principals, and teacher trainers selected from these regions were brought to the national training centers for multiform professional development activities by a number of trainers. The developers of the N.M.C. Standards directly administered over 40-hours of training for those backbone teachers who would themselves become reform demonstrators back in their own regions (Yuan, 2005). One year later, about 520 province-level pilot programs, or 18% of all the counties in China, were established and started using the N.M.C. Provincial authorities were in charge of all reform-related activities under the supervision of M.O.E. Until September 2003, more than 1,400 counties, nearly 50% of all counties, participated in the reform.
Full implementation (2005â2010)
In the years that followed, the r...