Toward An International Mathematics Curriculum

Toward An International Mathematics Curriculum Nell Wackwitz Texas State University Mathematics Department 15 November 2015  Introduction There are several aspects in the world today, which are moving the countries of the world toward an international mathematics curriculum. Some of these influences include globalization, real-time communication, international examinations, and twenty-first century research. Globalization is an inevitable part of our world today. As a concept, globalization refers both the to fact that the world is growing smaller and that, at the same time, the increased consciousness of the world is growing larger (Cai & Howson, 2013). More than this, we come to understand globalization as a new way of living, which affects every facet of life: the ways we shop, the ways we eat, the ways we interact with others. Societies across the globe have developed progressively closer contact over the past several centuries, but within the past two decades, the pace of collaboration and cooperation has increased overwhelmingly (Apple Developer Library, 2014). Jets, enormous cargo ships, and instant capital flow: all these have made the world interdependent, one nation on the other. More importantly, in our world today, ideas circulate more freely than ever before (Cai & Howson, 2013). As a result, many academics treat these international globalization trends as both inevitable and welcome. Whether we want globalization or not, this movement is not waning (Dello-Iacovo, 2009). Real-time communication occurs on an epic scale from one side of the earth to the other. The World-Wide Internet has enabled us to have almost instantaneous communication with people from many other countries throughout the world. With essentially real-time video streaming, people around the world can watch a concert or listen to a lecture, at almost the same time, so that these events become shared aspects of a worldwide culture. Scientists and everyday people together watch as a new photograph is projected millions of miles to Earth from the moon Kerberos as it orbits around Pluto (Wall, 2015). More and more people in third-world countries are enjoying free email, free texting services, and audio-visual abilities. Most people in the world have access to social websites and research-oriented networks, such as Facebook, Twitter, Research Gate, and Academia.edu. People have acquaintances around the globe, with whom they communicate daily (Cai & Howson, 2013). Moreover, the “people of the world are inextricably linked in such a way that local happenings are shaped by events happening around the globe” (Cai & Howson, 2013, p. 954). The terrorist attacks in Paris on 13 November 2015 are a case in point. Support for Paris came almost instantly from around the globe, including pledges of solidarity and allegiance from Pope Francis, United States President Obama, British Prime Minister Cameron, and millions of people from around the world who changed their Facebook profile photos to the French flag, and who spread the word on Twitter with #PrayForParis and #PrayForTheWholeWorld in communal support of the Parisian people (Walmsley, 2015). An event thousands of miles away affected the lives of caring people around the globe. This is indeed real-time communication on an epic level. Further, there are international exams, such as the Trends in International Mathematics and Science Study (TIMSS) and the Organisation for Economic Coöperation and Development’s (OECD) Programme for International Student Assessment (PISA), which bring countries together via serious competition (Cai & Howson, 2013; English & Kirshner, 2015; Pinar, 2014; Sagun & Corlu, 2014; Siregar, 2015). The TIMSS occurs at (the United States equivalent of) grades 4 and 8, while the PISA tests secondary students at an average age of 15. The TIMSS, in 2011, included 52 countries; and the PISA, in 2012, comprised 65 countries. Very often, the curricula of the countries, which score well on these examinations, are emulated by other countries (Cai & Howson, 2013). However, it is important to note that a “country wishing to use TIMSS data to improve its mathematics teaching must … [determine] … the varying cognitive demands of the individual items” (Howson, 2002, p. 123). Further, according to the World Bank, the Organisation for Economic Coöperation and Development has at its center an economic rather than an educational emphasis (World Bank Group, 2015). Cai & Howson (2013) state that an excellent performance on the PISA means only that a particular country is developing a “qualified workforce that will be competitive in a globalized economy” (p. 955). Thus, international exams are only one way to compare the educational merits and curricula of diverse countries. Mathematics and education researchers and many research-oriented publications in mathematics education, for instance the International Journal of Educational Development and the International Journal of Science and Mathematics Education, are now written and published on an international scale (Pinar, 2014). There are programs, lead by universities and other professional organizations, seeking to network with colleagues across the world in one academic language (Fraser & Ikoma, 2015). For example, the International Mathematics Union (IMU) is a non-profit, non-governmental organization, which is “devoted to promoting the development of mathematics, in all its aspects, across the world” (IMU, 2015, p. 3). In 1908, the International Congress of Mathematics, held in Rome, established the International Commission on Mathematics Instruction (ICMI). Its initial goal was to analyze the similarities and differences in international secondary mathematics education. Eventually, the ICMI produced a tome containing 187 volumes and 310 reports from 18 countries (IMU, 2015). Finally, in 1968 and every four years thereafter, the ICMI presented an International Congress on Mathematics Education (ICME), wherein mathematics educators from all over the world could come together to discuss and learn from one another (IMU, 2015). For these and many other reasons, the citizens of the world are moving toward a mathematics curriculum, which is international in scope, and which is highly adaptable to varied cultures, countries, socioeconomic statuses, and student needs (Apple Developer Library, 2014). International curriculum It is necessary to define this international curriculum, to which we refer in this article. There are three general levels of curriculum: the intended, the implemented, and the attained (Cai & Howson, 2013, p. 951). The intended is the material carefully gathered and delineated by researchers; it is what the instructor wants the students to learn. The Common Core States Standards for Mathematics (CCSSM) curriculum of the United States is an example of an intended curriculum (Burke & Marshall, 2010; Common Core initiative, 2015). The CCSSM offers no syllabi; neither does it suggest a textbook. In other words, the intended curriculum is an outline with suggestions for any country to use. An implemented curriculum includes the pedagogy the teacher uses to present the intended curriculum; it is what the teacher teaches. Finally, the attained curriculum is the knowledge the students gain through instruction; it is what the student actually learns. We generally determine the attained curriculum via exams or some other form of assessment. For the purposes of this paper, the term curriculum will refer, unless specified otherwise, to the intended curriculum. Thus, an international curriculum is one, which is international in capacity, and which uses the curriculum materials developed by mathematics education researchers. It follows that, in different countries, this same type of curriculum could be developed and taught in many different ways, using many different syllabi, texts, methods, and assessments; and it can be designed for many and varied types of cultures, learning styles, and students (Bagnall, 2015; Gravemeijer & Rampal, 2015). Fieldwork Education As an example of an international curriculum, it is interesting to explore the curricula developed by a company like England’s Fieldwork Education, which developed two international curricula: the International Primary Curriculum (IPC) and the Middle Years International Curriculum (MYIC) (World Class Learning Group Limited, 2015). In the early 1980s, Shell Oil Company wanted a suitable curriculum for the English-speaking children of the Shell employees stationed around the world; thus, two British headmasters, David Playfoot and Martin Skelton, started Fieldwork Education in 1984. Playfoot and Skelton spent four years developing the IPC and later the MYIC. The IPC, as the first curriculum developed, was the result of years of trials and rigorous improvements, international-mindedness, and personal development. In 2013, Fieldwork Education became part of the World Class Learning (WCL) Group, which joined with Nord Anglia Education to form a massive program, covering in excess of 16,000 schools in more than 100 countries (Nord Anglia Education, 2013; World Class Learning Group Limited, 2015). As of the fall of 2015, the IPC was used in schools in more than sixty-six countries, and incorporated approximately 250,000 English and non-English-speaking children. Fieldwork Education is an ever-expanding assortment of schools across Asia, Europe, the Middle East, and North America. The IPC remains in development today, to ensure a current and highly relevant curriculum, which continues to evolve. “No one can properly predict the nature of work that will be available for today’s primary age children by the time they are adults” (World Class Learning Group Limited, 2015). Many of the jobs they will have simply do not yet exist, especially in the fields of technology and science. Figure 1 shows that the principle of the IPC is to focus on personal, academic, and international learning that will prepare children, wherever they may live, for the future. The basic skills include personal learning goals that emphasize adaptability, resilience, cooperation, and respect and which, as a result of progressive skill development, help children to become able and inspired learners. The international context is not just an extension of the curriculum in the IPC. International-mindedness is part of all IPC learning, to ensure that children grow up with a very clear global understanding. See Figure 1 (Nord Anglia Education, 2013; Siregar, 2015; Tamer, 2015; World Class Learning Group Limited, 2015). International Baccalaureate Not every student in the world today has the opportunity to attend a school with an international curriculum, like that of the Fieldwork Education schools. However, in more than 70 countries around the world, including the countries in the European Union and most of the countries in Africa, many secondary students have the opportunity to achieve an International Baccalaureate (IB) certification with their high school diploma. The IB offers an internationally accepted university qualification, which gives these students consideration for admission in some of the top universities in the world (International Baccalaureate Organization, 2015). The IB curriculum was developed in the early 1960s, and it aims not only to provide an appropriate academic curriculum, but also to “support geographic and cultural flexibility and to promote international understanding while preserving the students’ own cultural identity” (Hayden & Wong, 1997, p. 349). The IB curriculum runs concurrently with the curriculum of the country in which the high school is located (Doherty & Shield, 2012). Thus, students in countries around the world are having the benefit of an international high school curriculum, regardless of the views of their country concerning an overall international curriculum (Doherty & Shield, 2012, p. 417). Figure 2 illustrates the levels and interconnections of the International Baccalaureate’s curriculum. TIMSS and PISA Countries are coming together internationally to compare curricula and compete with one other on international exams. A curriculum that works in one country is worthy of examination and possible imitation by other countries. Tests like the TIMSS and the PISA, among other things, rank countries in their mathematics ability. Fifty-two countries took part in the 2011 TIMSS. TIMSS scores are on a scale from 1 to 1000, with a mean of 500, and a standard deviation of 100. The TIMSS organizes mathematics assessment around two dimensions: (1) a content dimension, specifying the subject matter to be assessed; and (2) a cognitive dimension, specifying the cognitive or thinking processes to be assessed. At grade 4, TIMSS assesses student knowledge in three content domains: number, geometric shapes and measures, and data display. At grade 8, TIMSS assesses student knowledge in four content domains: number, algebra, geometry, and data and chance. At both grades (and across all content domains), TIMSS assesses students’ mathematical thinking in three cognitive domains: knowing, applying, and reasoning (English & Kirshner, 2015, p. 8; Provasnik et al., 2012, pp. 1-4). Countries with the top rankings on the 2011 8th-grade TIMSS examination are shown in Table 1 (Provasnik et al., 2012, p. 9). Table 1. 2011 Grade 8 TIMSS mathematics scores for the top 20 countries Country Mean Score Rank Republic of Korea 613 1 Singapore 611 2 China 609 3 Japan 570 4 Russian Federation 539 5 Israel 516 6 Finland 514 7 United States 509 8 England 507 9 Hungary 505 10 Australia 505 11 Slovenia 502 12 Lithuania 502 13 Italy 498 14 New Zealand 488 15 Kazakhstan 487 16 Sweden 484 17 Ukraine 479 18 Armenia 467 19 Romania 458 20 (Provasnik et al., 2012) Sixty-five countries participated in the 2012 PISA, which represented “more than 80% of the world’s economy,” with China scoring in the first position (Organisation for Economic Coöperation and Development, 2014, pp. 5, 8). The PISA, like the TIMSS, has a 1000-point scoring scale, with a mean of 500 and a standard deviation of 100. The PISA assesses the degree to which 15-year-old students have obtained the essential knowledge and skills that are fundamental for their future, in making contributions in the their own countries and to the world. The PISA focuses on mathematics, and especially on problem solving, by examining how well students can deduce from what they know toward situations which are unusual, both academically and in labor force settings (Organisation for Economic Coöperation and Development, 2014, pp. 2-3). In fact, the mathematics portion of the PISA uses paper and pencil, because students have to solve some critical-thinking type of problems which require skills, which are said to be the very skills the world’s children need to succeed in a new worldwide culture (Cai & Howson, 2013; English & Kirshner, 2015). “Modern societies reward individuals not for what they know, but for what they can do with what they know” (Organisation for Economic Coöperation and Development, 2014, p. 3). Table 2. 2012 PISA mathematics scores for the top 20 countries Country Mean Score Rank China 613 1 Singapore 573 2 Republic of Korea 554 3 Japan 538 4 Liechtenstein 536 5 Switzerland 535 6 The Netherlands 523 7 Estonia 521 8 Finland 519 9 Canada 518 10 Poland 518 11 Belgium 515 12 Germany 514 13 Viet Nam 511 14 Austria 506 15 Australia 504 16 Ireland 501 17 Slovenia 501 18 Denmark 500 19 New Zealand 500 20 (Organisation for Economic Coöperation and Development, 2014) The top countries in the world on the 2011 PISA exam are shown in Table 2 (Organisation for Economic Coöperation and Development, 2014, p. 6). It is interesting to notice that the top-ranked countries on the PISA are different than the top-ranked countries on the TIMSS. In some cases, this is due to countries not participating in both exams. However, many countries, like England and the Czech Republic, both of which score vastly different on the two exams. China and Singapore scored about one standard deviation above the mean score of the PISA. It is important to study and analyze carefully the curricula of these countries, one quite large and diverse, and the other smaller and considerably poorer. One might ask if a high ranking on the PISA or the TIMSS is an important goal for the countries in the world? In order to achieve a higher ranking worldwide on the TIMSS and the PISA, will these countries have to develop a more centralized educational system, similar to those counties whose scores on the TIMSS and the PISA greatly outshine the rest of the world? The remainder of this paper will explore these questions and try to determine if international ranking on examinations is the best focus to bring the countries of the world closer to an international curriculum. There are two readily identifiable questions: 1) How do the mathematics education researchers of the world devise a test, based on Resnick’s (1987) higher-order critical-thinking skills, which is possible to give to hundreds of thousands of students (p. 3)? 2) How do we test a student’s ability to think independently, to be self-motivated, to be creative, and to learn to think critically? Until higher-order thinking skills are measurable en masse, the world will be limited to tests like the TIMSS and the PISA. As far as financial success is concerned, international research shows evidence that there is a strong positive correlation between the quality of schooling, measured by students’ performance on achievement tests such as the TIMSS or the PISA, and robust economic growth within that country (Wößmann, 2007). Is financial success or student learning the objective for the ultimate international curriculum? Wealth and world standing According the World Bank’s rankings, in 2014 the United States (US) was the richest nation in the world, followed closely by China and Germany (Figure 3) (World Bank Group, 2015). Yet, China and Germany consistently score near or at the top of the PISA and TIMSS rankings, whereas the US is behind many other countries when ranked via these exams (English & Kirshner, 2015; Sagun & Corlu, 2014; Siregar, 2015). A county’s wealth does not seem to correlate with the mathematics’ achievement of its students on international exams. Citizens of the world need to think critically across many cultural boundaries and need to acquire problem-solving skills (World Bank Group, 2015). For these and many other reasons, mathematics curricula should be internationalized, highly adaptable to varied cultures, countries, and socioeconomic statuses (Apple Developer Library, 2014). “There may be a limit to the number of good factory jobs in the world, but there is no limit to the number of idea-generating jobs in the world” (Friedman, 2006, p. 308). According to Friedman, we are moving toward a global economy, wherein countries like China and India can participate with the European Union as equals (Friedman, 2006, pp. 288-289). In fact, China was one of the countries prepared to bail out Greece from its 2015 financial crisis (Keating, 2015). Perhaps it would be enlightening to examine the mathematics attainment and curricula, of the countries that scored at or above the mean on the 2012 PISA (Table 3). Table 3. Countrya Ranking on 2014 World Bank GNP Ranking on 8th-grade 2011 TIMSS Ranking on 2012 PISA Internationalized Standards China 2 3 1 No Singapore 36 2 2 No Korean Republic 13 1 3 No Japan 3 4 4 Yes Lichtenstein 151 10 5 No Switzerland 20 19 6 Yes The Netherlands 17 14 7 Yes Estonia 104 12 8 No Finland 41 7 9 Yes Canada 11 13 10 Yes Poland 23 --b 11 No Belgium 25 16 12 Yes Germany 4 15 13 Yes Viet Nam 55 -- 14 No Austria 28 -- 15 No Australia 12 20 16 Yes Ireland 44 -- 17 Yes Slovenia 64 21 18 No Denmark 34 -- 19 Yes New Zealand 54 24 20 Yes Czech Republic 51 11 21 No France 6 17 22 Yes England 5 9 23 Yes Iceland 114 18 24 No Russian Federation 10 5 34 No United States 1 8 36 No aAll countries listed have centralized educational systems and national mathematics standards except the US; b-- indicates that the country did not participate in the 2011 8th-grade TIMSS. (Organisation for Economic Coöperation and Development, 2014; Provasnik et al., 2012; Siregar, 2015; World Bank Group, 2015) United States of America Notice that the United States scored more than one standard deviation below Korea, the top country in the 2011 TIMSS. Still, the US ranked 8th on the 2011 mathematics TIMSS. However, the US ranked 36th in the world on the mathematics portion of the PISA. What happened between the ages of 13 (for the 8th-grade TIMSS) and 15 (for the PISA) to lower the United States’ worldwide ranking so dramatically? Certainly, the TIMSS is a more basic, content-related exam when compared with the more challenging PISA, where critical-thinking questions abound (Cai & Howson, 2013, pp. 953-954). Further, the US has been unsuccessful at developing a national mathematics curriculum for all states. In Figure 4, one can see that the Common Core State Standards for Mathematics (CCSSM) has come closest to being accepted (Common Core initiative, 2015; Schoenfeld, 2014). Briefly, the United States’ CCSSM curriculum not only stresses conceptual understanding but also stresses organizing principles, such as place value and the properties of integers, some of the big ideas in mathematics (Common Core initiative, 2015). Further, current research in mathematics education informs these standards (Common Core initiative, 2015; Schmidt & Houang, 2012). The knowledge and skills students need to be prepared for mathematics in college and in life, the big ideas which are the underpinnings of the CCSSM, are connected throughout the standards (Common Core initiative, 2015). One thing, which differentiates the CCSSM curriculum from the curricula of countries, which score well on the TIMSS and the PISA is that the CCSSM does not have a multiculturalist-international underpinning (Schmidt & Houang, 2012). The few states in the USA which have not accepted the Common Core do have state-wide standards which are comparable to the ideals of the Common Core (Akbuga, 2014; Reys, 2014). One example is the Texas Essential Knowledge and Skills (TEKS) (Regional Educational Laboratory Southwest, 2008; Texas Education Agency, 2015). Should the USA adopt an international perspective in setting national standards of education? According to the Heritage Foundation (2010), states’ rights will be violated, and American education will suffer if the United States has even a national curriculum (Burke & Marshall, 2010, p. 10). Moreover, proponents of the 2010 Elementary and Secondary Education Act will not be able to deliver national standards and assessments “because they will fail to address the critical problems of power and incentive structures in public education today” (Burke & Marshall, 2010, p. 4). However, national standards continue to be the trend of an ever-expanding federal role in education. Further, according to Akbuga (2014), without some kind of centralization, American “students continue to experience radically different educational experiences depending on the kind of school students attend and its neighborhood” (p. 4). Furthermore, the U.S. Board on International Comparative Studies in Education (1990) identified several reasons why the USA should participate in working toward an international curriculum, including understanding of multicultural education systems and enhanced mathematics education research (Bradburn & Gilford, 1990). These facts, together with the information on the other countries in the world, most of which have centralized mathematics curriculum, leads to the conclusion that eventually, in order to keep up internationally, the US will have a national mathematics standard. A National Public Radio (NPR) announcement on 20 November 2025 stated the results of the latest Open Doors report from the Institute of International Education (IIE). Nearly one million students from other countries are studying in US colleges and universities, the largest rate of growth in over 35 years. Additionally, the number of US students studying abroad is at an all time high (IIE, 2015; Turner, 2015). A local example is Texas State University. Figure 5 illustrates the flags of the every country of all the students, who are attending Texas State University as of the fall of 2015. As one can easily see, Texas State is home to students from around the globe (Office of Student Diversity and Inclusion - Texas State University, 2015). Professors of Texas State students must adapt their curriculum to be inclusive for a diverse population who are entering their classes. The world is moving toward an international mathematics curriculum. Yet, “when we looks at the American education system, we realizes that it is broad, complicated, organizationally fragmented, and decentralized” (Akbuga, 2014, p. 2). Should the US adopt an international perspective in setting national standards of education? Countries such as Great Britain, France, Japan, Sweden, Germany, Turkey, and Russia, where education is governmentally centralized, have accepted national standards, and are participating in the development of an international curriculum (Hannaway, 2015; IMU, 2015; Tahirsylaj, Brezicha, & Ikoma, 2015; Tamer, 2015). The Heritage Foundation is fighting the trend toward a US national mathematics curriculum; and some states, including Texas, are fighting with them (Burke & Marshall, 2010). However, Noah (1989) asserted that Americans need to maneuver away from their natural distaste of national standards in mathematics (p. 21). According to the National Education Association (NEA) (2015), “standards promote equity by ensuring [that] all students are well prepared to collaborate and compete with their peers in the United States and abroad” (NEA, 2015). “The consequences of not having a national mathematics standard, and focusing exclusively on local and state autonomy, has led to de facto national standards that private agencies, such as textbook publishers and educational testing services, establish” (Noah, 1989, p. 19). Further, an intended curriculum is a design of what one feels is important to cover in a particular subject. “Through the curriculum and our experience of it, we choose what to remember about the past, what to believe about the present, and what to hope for and fear about the future” (Pinar, 2014, p. 522). If individual states, rather than a centralized governmental agency, determine the standards, the United States will not ever be able to present a common front when competing with other countries in mathematics (Akbuga, 2014; Common Core initiative, 2015; English & Kirshner, 2015; NEA, 2015; Siregar, 2015). Without a centralized national mathematics standard, the US will be left behind as other countries join their own national standards into one international intended curriculum (Akbuga, 2014; Siregar, 2015; Tamer, 2015; Tseng, 2014). Conclusion “The world's education systems vary widely in terms of structure and curricular content. Consequently, it can be difficult for national policymakers to compare their educational systems with those of other countries or to benchmark progress towards national and international goals” (United Nations educational scientific and cultural organization (UNESCO) & UNESCO Institute of Statistics, 2014). Countries have been competing for centuries, and competing in mathematics is nothing new. Tests developed for one country are not necessarily valid for another country. Nevertheless, common learning goals worldwide spell the inevitability of an international curriculum. Teachers must teach students to think critically about diverse, complex mathematical ideas necessary to deal with the world of tomorrow. Students need to learn in a setting where there are not always answers to every problem, where there is uncertainty, “where it is necessary to find order when only chaos is apparent” (Resnick, 1987, p. 3). The world is becoming politically and economically smaller. In 1993, twelve countries in Europe formed a charter creating the European Union. There are now twenty-eight countries, with seven more nearing admission, in the European Union (European Union, 2014). In countries around the world, at disparate levels and in varied subjects, national curricula are moving toward one, which is international in scope (Wößmann, 2007, p. 271). The movement toward an international curriculum is happening one family at a time, one school at a time, one country at a time. As time passes, schools in other countries join in the movement (World Class Learning Group Limited, 2015). These movements toward internationalization are lead by teachers and parents in schools with international curricula, at conferences and colloquiums by university professors, with world-wide competitive examinations, and among private industry (World Class Learning Group Limited, 2015). Change toward an internationalized curriculum is already coming. The field of mathematics, at every level, is a part of this international shift (IMU, 2015; Tamer, 2015). For these and many other reasons, mathematics curricula is becoming globalized, highly adaptable to varied cultures, countries, and socioeconomic statuses (Apple Developer Library, 2014). Someday, all the countries of the world, including the United States, will be caught up in this already occurring whirlwind of activity, toward a workable international mathematics curriculum.  References Akbuga, E. (2014). The comparison of the American and the Turkish education systems. Summary Report. Texas State University Mathematics Department. Apple Developer Library, T. (2014). About internationalization and localization. Retrieved from https://developer.apple.com/library/mac/documentation/MacOSX/Conceptual/BPInternational/Introduction/Introduction.html Bagnall, N. (2015). 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