Introduction
The world is much smaller than it used to be in many different ways. Comparative education is a process that looks at the different educational traditions in one country or culture and then compares those traditions to the educational traditions in other cultures—this is a way of developing educational theory, and a method for utilising the vast amounts of data now available to glean new insights (Bignold and Gayton, 2009). These processes look at the many issues associated with education and try to draw parallels and examine differences between different cultures and the educational experiences offered by each culture (Bignold and Gayton, 2009). Although many of these educational experiences deal with pedagogy and with teacher characteristics in the classroom, they can also be used to build stronger bridges within various intercultural groups and communities (Bignold and Gayton, 2009).
Culture in Education
One of the fundamental concepts of comparative education is the drive to establish global frameworks for children, regardless of culture (Bignold and Gayton, 2009; Voogt and Roblin, 2012). Through their search for a better understanding of culture and educational practices, experts in this field are able to lay the groundwork for new institutional educational practices, as well as a better understanding of student needs outside of the student’s individual cultural sphere (Bignold and Gayton, 2009; Voogt and Roblin, 2012).
British Curriculum in Mathematics
For the British educational system, learning takes place in a number of stages (Shuayb and O'Donnell, 2008). Wolfram (2014) writes that the British system has become too much like the American system of learning maths—that the British system is now relying heavily on rote learning and standardised testing to assess students and to discover how the country, as a whole, is faring in mathematics (Wolfram, 2014). Because the country as a whole is also relying heavily on standardised testing, there is an increasing need for British instructors to “teach to the test,” so to speak (Wolfram, 2014; Gilroy, 1992). According to the British government, the standards for primary school mathematics include number and place value, number addition, subtraction, multiplication, and division, measurement and geometry (Gov.uk, 2015). Each year, teachers delve further into these topics for the primary school curriculum (Gov.uk, 2015).
Gilroy (1992) notes that teacher training in England and Wales changed significantly during the early 1990s, and the British government was then given unprecedented control over the ways that teacher training was carried out in this time (Gilroy, 1992). This control by the British government was arguably a turning point for British curricula, especially in maths and sciences; after the British government tried to maintain control over the education of teachers, it was only a matter of time before the government retained control over the curriculum that these teachers taught their students and the ways that these students are assessed for their capabilities (Gilroy, 1992; Wolfram, 2014). Gilroy (1992) marks this shift as extremely significant, insofar as the future of the British curriculum was concerned. Wolfram (2014) suggests that the current British educational system promotes learning by rote, rather than learning through understanding and comprehension.
Shanghai Curriculum in Mathematics
The Shanghai curriculum in mathematics is focused differently than the British curriculum. Where the British curriculum is extremely focused on rote learning and understanding the steps taken to solve a particular problem, the Shanghai method of learning maths focuses much more on the process of solving the problem (Lin, 2007). However, Shanghai has not relied on the old style of learning to teach children mathematics; instead, Shanghai and the teachers in the city have begun to use a hybrid method for teaching mathematics, blending the strengths of the Shanghainese curriculum with the strengths of the western curriculum (Cai and Nie, 2007; Lin, 2007; Han, 2006). In the Shanghai system, students are lined up in even rows to facilitate learning; they are expected to give their full attention to the instructor, as well (Wolfram, 2014). Shanghainese students are expected to give their full attention to learning and are expected to perform highly in math and sciences (Wolfram, 2014).
There are aspects of the British and American system that are very prominent in the Shanghai system today—for instance, the students are allowed calculators once they reach an accepted level of proficiency—but they are taught their mathematical concepts differently from a very young age (Cai and Nie, 2007; Lin, 2007; Han, 2006). Shanghai students are encouraged to engage with mathematical concepts differently than western students, and as a result, they begin their foundational learning with a number of benefits (Li et al., 2008; Cai and Nie, 2007). According to Lim (2007), “All Shanghai schools subscribed to one major curriculum document, the Shanghai City Primary and Secondary Mathematics Curriculum Standard (2004). The document is divided into two parts. The first part outlines the theoretical framework, the aims and objectives, the structures and implementation of the general primary and secondary education in Shanghai. The second part is Characteristics of Mathematics Teaching in Shanghai subdivided into five sections: (a) introduction to the theoretical framework of the curriculum, (b) aims and objectives, (c) curriculum design, (d) content and demand, and (e) curriculum implementation” (Lim, 2007). Students are first asked to revise concepts with variation, use precise language, and implement their understanding in their everyday lives.
The Shanghai students also begin their mathematical learning much earlier than students, especially with conceptual mathematics (Lim, 2007). Some research also suggests that language plays a significant role in the ability of Shanghainese children to understand mathematical concepts earlier than other children, although this remains out of the scope of discussion for this particular report (Lim, 2007; Li et al., 2008). However, language does play a particularly significant role in education and learning, especially when considering comparative education (Lim, 2007; Li et al., 2008).
Similarities between Curricula
One of the interesting things about the Shanghai curriculum and the British curriculum is that the two sets of leaders that are responsible for curricula in both locations are borrowing information and practices from each other. In Shanghai, for instance, there is a much more relaxed attitude to learning maths than there has ever been before; this is due in no small part to the fact that the Shanghai government opened its doors to the western world in the past few decades (Wolfram, 2014). Some of the disciplinary practices that cause discomfort in the western world are gone in China, some still remain, and the Shanghai children that are learning maths in Shanghai are still subject to significant pressures (Yang, 2009; Leung et al., 2006).
Although the British curriculum has been separate from the Shanghai curriculum—the borrowing has certainly been one way up to this point—recent strides in Shanghai primary school mathematics has led to the British engaging with the Shanghainese in hopes of producing better maths and science students in the future (Wolfram, 2014). Wolfram (2014) notes, for instance, that the British hope to utilise a number of teaching practices used commonly in Shanghai to better British pupils in the maths classroom, including the teaching of multiplication tables more efficiently and at a younger age. Lim (2007) notes that Shanghainese students tend to be fluent in their multiplication tables, while Li et al. (2008) note that the texts in the West and the East treat rote memorisation very differently—the western texts expect it, while eastern texts promote conceptual understanding.
Differences between Curricula
Along with the growing number of shared educational theories between Shanghai and the U.K., there is a growing number of differences. Some of these differences are small—seemingly insignificant—but they can result in the overall lack of achievement for children in the western mathematics system. Li et al. (2008) report on the differences between Western and Eastern concepts in primary school mathematics, stating, “Ninety-eight percent of the Shanghainese sample correctly answered 4 items indicating conceptions of equality and provided conceptually accurate explanations. In contrast, only 28% of the U.S. sample performed at this levelU.S. teacher preparation textbooks rarely interpreted the equal sign as equivalence. On the contrary, Chinese textbooks typically introduced the equal sign in a context of relationships and interpreted the sign as ‘balance,’ ‘sameness,’ or ‘equivalence’ and only then embedded the sign with operations on numbers” (Li et al., 2008). While the Li et al. (2008) study focuses on an American text and a Chinese text, it is important to note that a close reading of Shuayb and O'Donnell (2008) does not demonstrate any conceptual distinction drawn in this particular area. There are a plethora of small examples of differences between Shanghainese textbooks and teachings and British teaching methods—these may seem small at first, but they add up to a significant set of cultural differences that set the British children at a disadvantage from a relatively young age (Li et al., 2008; Cai and Nie, 2007; Lin, 2007; Han, 2006; Shuayb and O'Donnell, 2008). Although some of the curriculum seems to note that the British system relies on rote learning, the Shanghai system also relies on rote learning. The emphasis in the Shanghai system is different, however—focusing on important concepts and attempting to ingrain them in the learner for future mathematical success.
Strengths of Curricula
Britain
The British curriculum is not weak in every aspect of mathematics teaching, although it has slipped in recent years (Shuayb and O'Donnell, 2008). Maths teaching in Britain is focused on ensuring that students are able to perform as necessary in their tertiary education; for many students, however, the maths education that they receive in primary and secondary school is the only maths education they ever receive. For these students, the maths education that is provided in school is sufficient; it gives them the information that they need to function appropriately in society. British teaching does focus heavily on test-taking in many ways, but not as much as American mathematics teaching focuses on test taking; instead, the British system has tried to balance the test-taking and assessment portion of the western tradition of education with a more reasoned approach (Shuayb and O'Donnell, 2008). Britain has a strong tertiary school system as well, which is important; there is a long tradition of strong academics in the country, which can provide an excellent basis for good educational traditions and a good educational future (Shuayb and O'Donnell, 2008).
Shanghai
Shanghai has undoubtedly been performing extremely well on global mathematics exams in recent years, especially for the younger students (Wolfram, 2014). There are elements of the program that are extremely strong—for instance, students in Shanghai often have an excellent grasp of the multiplication tables at a very young age, which makes doing higher level maths much easier for them in the long run. They also have a tendency to engage with material on both a rote learning level and a conceptual level; teachers mark all their students’ work very quickly, which means that students get very quick feedback on their successes and failures (Wolfram, 2014). Wolfram (2014) also suggests that parent involvement is extremely important—the Shanghainese families just value mathematics and mathematical learning at a much different level than British families do, for a variety of cultural reasons (Wolfram, 2014). All the literature on child development suggests that parental involvement is fundamentally important for child success—children have a much more difficult time succeeding in things like maths without parental support and involvement (Wolfram, 2014).
Weaknesses of Curricula
Britain
The British curriculum relies too much on both rote memorisation and on standardised testing, and these problems have become obvious in various assessments designed to compare the abilities of students from a number of different countries (Wolfram, 2014). Wolfram (2014) writes, “The problem is not the difference between Britain and Shanghai – which education minister Elizabeth Truss visited on a fact-finding mission last week – but the worldwide difference between maths in education and maths in the real world: everywhere, we are teaching largely the wrong maths. Here's why. In the real world we use computers for calculating, almost universally; in education we use people for calculating, almost universally” (Wolfram, 2014). Britain’s curriculum, according to Wolfram (2014), is too disconnected from real life—students feel no connection to maths, and they do not understand why they have to learn maths. When students are disconnected from a subject, it does not bode well for their learning and participation in this subject. The disconnect and apathy with maths is linked back to insufficient learning and understanding at a primary school level (Wolfram, 2014).
Shanghai
Despite the terrible reputation Britain has somehow gleaned for being a system full of rote memorisation, the early years of the Shanghainese school system are also full of rote memorisation (Weale, 2014). Weale (2014) describes the crossover between Shanghai as focusing on producing students who are able to take orders from an instructor and ask no questions—the students are not encouraged to laugh, communicate, or problem solve in the classroom, particularly the younger students (Weale, 2014). Wolfram (2014) suggests that the early rote learning is the reason why many Chinese children can go on to succeed—they already have the basics that they need on a fundamental level to understand things like higher level maths and coding (Wolfram, 2014). However, Weale (2014) suggests that perhaps the Shanghai model is not as strong as many professionals seem to think—it is a bubble, Weale (2014) suggests, that is bound to burst, because it puts too much pressure on children and creates a cultural, emotional, and educational pressure cooker.
Discussion and Conclusions
References
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