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A Cross-Cultural Comparison of Brazilian and American Mathematics Curricula

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A Cross-Cultural Comparison of Brazilian and American Mathematics Curricula Running Head: A CROSS CULTURAL COMPARISON A cross-cultural comparison of Brazilian and American mathematics curricula by Larissa Berry A capstone project submitted in partial fulfillment of graduating from the Academic Honors Program at Ashland University May 2013 Faculty Mentor: Dr. Jason B. Ellis, Associate Professor of Curriculum and Instruction Reader: Dr. David Kommer, Chair and Professor of Curriculum and Instruction I ABSTRACT The study of mathematics tends to hold reputation as being universal language of studies, meaning mathematical literacy sustains value worldwide. However, mathematics cannot be determined universal by mathematical literacy alone. It is the curricular development in education that lays the groundwork in deciding what mathematical knowledge is of most value which in turn sets the tone for mathematical literacy. Specifically, the development of the scope and sequence of mathematics standards in education frame the content and order in obtaining mathematical literacy and are examined in this thesis between two different countries, Brazil and the U.S. The outcome of comparing mathematics standards of both Brazil and the U.S. is discussed with some minor curricular differences, but also with an overall cohesiveness in mathematical literacy which may indicate universality in mathematics in the two countries which could potentially translate worldwide. 1 INTRODUCTION As the education system has become more and more refined, finding what is considered most literate in a given subject matter falls almost directly on the scope and sequence of the curriculum. It holds particularly true when comparing similar curricula of mathematics education among countries around the globe. Particularly, in this study, Brazil and the United States are the countries in focus. This study intends to provide a curricular analysis of the similarities and differences between American and Brazilian numeracy benchmarks, starting with pre- kindergarten up to high school expectations. A curricular analysis was performed to identify discrepancies between mathematics indicators in the Brazilian and American school curricula up to 12th grade. These discrepancies within the mathematics indicators illustrate the potential differentiation of education philosophy regarding the knowledge of mathematics. However, in doing this analysis I also hoped to find an overall trend of similarities between the two curricula. This would favor the notion that mathematical literacy is attainable despite minor sequential differences. From an educator’s standpoint, being able to confidently determine that mathematics can be translated across cultural and linguistic barriers is useful in that it allows for a greater delivery of services to students of diverse backgrounds. Having the ability to communicate successfully through the use of numerical symbolism and structure on an international level is quite profound. In today’s society more than ever before, globalization and international interaction has become so prevalent that discovering a universal language such as mathematics to utilize, share ideas, and collaborate on projects would be very advantageous, and a vital component in interpreting information. Educators must be aware of such potential when enlightening their students of the 2 endless opportunities within the realm of mathematics. Thus, international communication could be amplified by finding a common fold in curricula of mathematics education. After studying in Brazil and having experienced learning math in another language, I became interested in discovering how much mathematics actually measured up as a universal language. In the beginning, I had very little experience with the Portuguese language and yet I was able to interpret and understand the mathematical calculations and proofs being displayed on the board in front of me. I then realized that although I was unable to comprehend most of the linguistic interpretation of the math content, I was able to learn the material by means of mathematical notation and symbolic formulations. REVIEW OF THE LITERATURE Westbury (2013) defined curriculum as “an authoritative prescription for the course of study of a school or system of schools” (p. 1). Curricula often times are constructed on the basis of existing practices of teachers or possibly the context of texts being used in the classroom. Because all curricula develops as a result of ideas about what should be taught and learned, it is most apparent that the curricula thrives from the question “what knowledge is of most worth?” Westbury (2013) stated that: The curriculum is necessarily a part of all of the sociological and cultural ambiguities within societies. As such, the scope and nature of the curriculum are viewed as critically important for teachers, parents, cultural critics, interest groups, and the employers of the graduates of the school. As the curriculum as an idea is seen through the eyes of all such groups, it becomes a mirror that reflects different visions of the society and culture, and the tensions within the society around, say, the proper nature of the work of schooling and/or status-attainment and employment possibilities. As a result inevitable and unresolved differences of viewpoint characteristically surface around all discussions of the curriculum as a symbol of both a normative order for education and of the quality and character of what schools are understood as doing. (p. 5) 3 As such, having control of the curriculum is a powerful force. The school curriculum indirectly affects and shapes the influential directions in a society such as social, cultural, political, and economic entities. Understanding how liberating or conserving, good or evil the indoctrination can be of the curriculum elevates the importance of its overall establishment. Specifically, the structure of the curriculum can and may very well define academic success (Hewitt, 2006). For example, a mathematics curriculum which emphasizes the importance and relevancy of simple arithmetic skills such as addition and subtraction has the ability to position students to achieve well in particular lessons pertaining to more complex problem solving. Because the basic steps in ensuring the students understand adding and subtracting are the main focus, the structure of the curriculum allows for development in other areas that require similar processes such as multiplication and division. The role of public interest in curriculum planning is of direct interest if what Hewitt discusses is true. Kirst and Walker (1972) observed that: By and large, curriculum decisions are based, not on quantitative decision techniques or even on a plethora of objective data, but rather on the resolution of conflicts among various groups and individuals with competing values. A mapping of the leverage points for curriculum policy-making in local schools would be exceedingly complex. U.S. State departments and boards of education have also played a traditional, but varying, role in setting and enforcing minimum curriculum standards. During the last decade, the U.S. Government has also become a very powerful influence on curriculum development, mainly through the large sums of money spent through the National Science Foundation and the Office of Education. These two sources of funds for curriculum planning are relatively new and thus not fully dependable. The role of the local lay community in curriculum change appears to be minimal. Most of the groups generating curricular alternatives are also important sources of demands for curriculum change. Despite the difficulties of systematic curriculum policy-making, efforts in this direction are virtually certain to increase. (p.28) Through the 1970’s, race, culture, and socioeconomic status came to the foreground of debate in curriculum design and policy. Boyd (1978) observed “with the mediation of social and 4 ethnocultural class conflicts in public schools, policy makers face political problems when adjusting school curricula. These problems are created by the simultaneous needs for the curriculum to maintain and change society” (p. 577). What Boyd (1978) described as maintaining society calls into question the idea of minimal curricular requirement, or rather, what is of most worth in terms of curriculum that a child needs to leave school with at the end of formal K-12 education? Adaptation, on the other hand, is an entirely different concept. Ediger (1994) has discussed how curriculum, in the broadest sense, can be adaptive. Ediger (1994) noted that curriculum design plays a vital role in the progression of the optimal learner. In terms of objectives that hold expected fulfillment, the student must be the focal point in the construction of the curriculum. Specifically, an emphasis on teaching and learning modifications must be made with the student in mind. Quality design in the curriculum guides students to optimally attain material. The sequence of the curriculum holds effect for the learner quite intuitively. Most traditionally, teachers fulfill the role in determining the sequence or order of the students’ attaining objectives. The logical selection arranges the objectives in such a way that the complexity and harmonious balance of each benchmark pertains to the student with relativity and cohesion. Conversely, the curriculum may be devised with teacher-student collaboration. This process requires situational learning of attainable objectives because the student is empowered to select the sequence in which the material is taught
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