In the United States, bilingualism is a crucial issue that must be addressed. Although bilingualism has no clear cut definition yet, Shenker (no date) provides one appropriate definition of bilingualism. According to him, bilingual children are “are those… who speak/have been spoken to in two (or more) languages in the home since birth and who are spoken to in only one or both of those two languages at school. ” (Shenker, no date).
These children may also be spoken in one language at home but acquired (or is exposed to) a second-language when they start attending school. There is a common misperception that bilingual children are more unsuccessful academically than monolingual children. However, researches show that bilingual children have superior performances than their monolingual counterparts. Perhaps the first one to radically change this perception is the study done Peal and Lambert in 1962.
They conducted research regarding the premise that bilingualism causes retardation. However, their conclusion proved otherwise. They found that experiences from two cultures provide bilingual children an advantage such as increased mental dexterity and superior ability to think abstractly than that experienced by monolinguals (Peal & Lambert, 1962). Other researches show an association between bilingualism and greater cognitive flexibility and awareness of language (Cummins & Culutsan, 1974; Diaz, 1983; Hakuta & Diaz, 1984).
Moreover, bilingual children were proven to have more effective controlled processes. Although their study was conducted among adults only, they generally concluded “that controlled processing is carried out more effectively by bilinguals and that bilingualism helps to offset age-related losses in certain executive processes” (Bialystok, Klein, Craik, & Viswanathan, 2004). Because of their greater cognitive flexibility, bilingual children outperform their monolingual counterparts in virtually almost every subject including mathematics.
Nevertheless, bilingual children, including their parents, still do not have the confidence to learn and interact with others. This is due to a punishment in the early 1900s where bilingual children are severely punished for speaking their home language. Although researches have found that bilingual children have greater cognitive flexibility than monolingual children, none has yet been undertaken investigating what practice can be used in teaching bilingual children to interact with other people.
Thus, the purpose of this study is to investigate what teaching practice can be used in teaching bilingual children, in which they can improve not just their understanding of the project but also their interaction with other people. Statement of the Problem Mathematics is considered as one of the most difficult subjects to understand. Students have difficulty applying the basic computational skills to a more complex mathematics or science (Seceda & dela Cruz, n. d. ). Researchers argue that this difficulty in understanding the concepts of mathematics is due to most educators’ strict observation to procedure (Schoenfeld, 1988).
Although there is a steady rise in students’ achievement scores in mathematics since the early 1980’s (Seceda, 1992) showing that educators are successful in teaching basic computational skills to students, they have been less successful in teaching the students when to apply the skills they have taught (Dossey, Mullis, & Jones, 1993; Dossey, Mullis, Lindquist, & Chambers, 1988; Mullis, Dossey, Foertsch, Jones, & Gentile, 1991; Mullis, Dossey, Owen, & Phillips, 1993; Seceda & dela Cruz, n. d. ). Thus, it is important that educators should focus in teaching mathematics for understanding to students rather than in observing strict procedures.
However, one must note the fact that teaching for understanding does not just concern the mainstream or majority students. As Seceda and Cruz emphasize that “teaching for understanding concerns more generally all students including those with diverse social backgrounds. It is believed that mathematics involves considerable use of English, especially word problems” (Seceda & dela Cruz, n. d. ). Due to this belief, it only follows that children who are studying English as a second-language (or second language learners) have difficulty in studying mathematics.
In this context, the term “bilingual children” means students who are second-language learners. Most schools in the United States teach mathematics in a “procedural” manner. That is, when students solved a particular mathematical problem in an unconventional way (the computations are not presented in the algorithm taught by the teacher), their solutions are marked incorrect and will be drilled further (Seceda & dela Cruz, n. d. ), even though their solutions meant that they understand the problem but resolved to write their solution in their own way.
In so doing, bilingual children, feeling that they cannot understand and cannot be understood, are being left out in classroom conversations. When teaching and learning is continued in this manner, this will eventually lead to the bilingual children’s failure in mathematics, adding to the conventional belief that bilingual children cannot engage in mathematics. Another consequence of teaching mathematics in a “procedural” manner is that children begin to perceive that mathematics makes no sense (Seceda & dela Cruz, n. d. ).
This perception will increase children’s capacity to understand something which is not sensible, not practical and not applicable using with the outside world (that is, world outside the classroom). In this paper, the author investigated which educational practice is best to apply in teaching mathematics for understanding to bilingual children. Two educational theories will be examined — Pask’s Conversation Theory and Landa’s Algo-Heuristic Theory. Furthermore, the study aims to find which practice can help students not just understand mathematics but to have confidence in solving problems and in interacting with others. Research Questions
The study specifically aims to: 1. compare Pask’s Conversation Theory and Landa’s Algo-Heuristic Theory; and 2. examine which one of these two is best to apply in teaching mathematics for understanding to bilingual children. Significance of the Study Results of the study will help educators find the best way to teach mathematics in which bilingual children will be able to understand and apply outside the classroom. In general, results of the study will help in finding the best way to teach children who are limited English proficient in such a way that these children can understand and apply the lessons with other activities.
Moreover, the study will help teachers train their students with confidence. Overview of the Paper In Chapter 2, a review of literature is provided. In this chapter, the definition of bilingualism is discussed. Researches undertaken on bilingual children’s cognitive development are provided. Then bilingual education is defined according to literature. Historical background on the evolution of bilingual education (1800s-1900s) is also provided. The author also discusses emotional, linguistic and academic issues bilingual education is concerned with. Mathematics education is also discussed in this chapter.
Theories applied in mathematics teaching are discussed. Problem solving is given importance in the discussion on mathematics education. Cognitive background information on addition, subtraction multiplication and division is also given which provides as basis for the word problems given to the participants of the study. Finally, in this chapter, researches done involving mathematics and bilingualism are provided. Chapter 3 provides the theoretical framework used in the study. The first part discusses Pask’s Conversation Theory and the second part discussed Landa’s Algo-Heuristic Theory.
Chapter 4 provides the methodology used for obtaining the results needed. This section explains the research design the study used. Sample, sample setting, procedure and data collection and analysis are discussed. The sample and sample setting for the study is discussed in the first part. In the second part, the author explained the procedures done from the pre-assessment stage to the classroom setting to the final assessment stage. The third part discussed how the data was collected and analyzed. In Chapter 5, results obtained from the experiment are discussed.
The students’ scores obtained in the pre-assessment, addition and subtraction, multiplication and division, and final assessment examinations are shown in the first part. In the second part, results from the interview are discussed. Finally, Chapter 6 concludes the paper. The first part summarized the main findings discussed in Chapter 5. The second part gives recommendations for the teachers on how to teach mathematics for understanding to bilingual students. The third part provides limitations for the study as well as recommendations for future researches that can be carried on from this study.
CHAPTER 2 REVIEW OF LITERATURE Bilingualism Bilingualism has no clear-cut definition yet but Shenker (no date) provided a definition in terms of young children. According to Shenker (no date), bilingual children are “are those… who speak/have been spoken to in two (or more) languages in the home since birth and who are spoken to in only one or both of those two languages at school. ” (Shenker, no date). These children may also be spoken in one language at home but acquired (or is exposed to) a second-language when they start attending school.
Bilingual children were perceived to have less advantageous situations than monolingual children. This perception was radically changed in 1962 by Peal and Lambert. Peal and Lambert (1962) conducted a research regarding the premise that bilingualism causes retardation. Their study reached the conclusion that experiences from two cultures provide bilingual children with greater benefits than that experienced by monolinguals such as increased mental dexterity and superior ability to think abstractly (Peal & Lambert, 1962). Other researches prove that bilingual children have superior performances than their monolingual counterparts.
Researches show an association between bilingualism and greater cognitive flexibility and awareness of language (Cummins & Culutsan, 1974; Diaz, 1983; Hakuta & Diaz, 1984). Moreover, bilingual children were proven to have more effective controlled processes. Although their study was conducted among adults only, they generally concluded “that controlled processing is carried out more effectively by bilinguals and that bilingualism helps to offset age-related losses in certain executive processes” (Bialystok, Klein, Craik, & Viswanathan, 2004).
Bilingual Education Despite having many researches proving that bilingual children provide greater than (or at least at the same level as) the monolingual children, there is constant debate whether to provide bilingual children with bilingual education or programs that focus uniquely on acquiring English. Bilingual education is the teaching of all subjects in school using two different languages — English and Spanish or Chinese depending which is the native language of the student. Definition
According to Ovando, Combs and Collier (2006) bilingual education is not a single uniform program or a consistent methodology for teaching language minority students. Bilingual education includes a number of different program models with a number of distinct goals. Other programs may promote the development of two languages for bilingualism and biliteracy while others use the students’ first language so that students may better learn English. Some bilingual education programs preserve an indigenous or heritage language as an ethnic, cultural, or community resource.
There are programs that aim to incorporate students into the mainstream of society (Baker 2001). Thus, as Cazden and Snow (1990) stress, bilingual education is “a simple label for a complex phenomenon” since not all programs necessarily “concern the balanced use of two languages in the classroom” (Baker, 2001). (Throughout this paper, the terms L1 and L2 to denote the child’s language, L1 for their native language and L2 for the language they are acquiring. )
The inseparable connection between language and culture brings bilingual programs to include historical and cultural components associated with the languages being used. As Ulibarri (1972) says: In the beginning was the Word. And the Word was made flesh. It was so in the beginning and it is so today. The language, the Word, carries within it the history, the culture, the traditions, the very life of a people, the flesh. Language is people. We cannot conceive of a people without a language, or a language without a people. The two are one and the same.
To know one is to know the other (p. 295). Historical Background Discussing the historical background of bilingual education in the United States indicates that there is a cyclical pattern with regard to language policies and programs (Korschun, 2006). Furthermore, studying the origins of bilingual education helps to understand its present undertakings and its future effectiveness. There are few references that account the history of bilingual education. In this paper, I rely predominantly on Ovando et al’s account of the history of bilingual education.
The 1800s. Contrary to the common perception in the United States, schools in the United States use for instruction multiple languages other than English during the eighteenth and nineteenth centuries. Because of the increasing establishments of homesteads of different groups of different languages and countries of origin in US territories, a general sense of geographical and psychological openness existed. Some communities were self-sufficient and agrarian based while some were ethnic pockets in urban areas (Ovando, 1978b).
According to historical records, many schools in the nineteenth century, both public and private, used languages other than English for instruction. In fact, during this century, following the annexation of the Territory of New Mexico, a school’s curriculum may use either Spanish or English or even both as medium for instruction (Leibowitz, 1971). In 1900, at least 600,000 children in US received part or all of their schooling in German in public and parochial schools (Crawford, 2004; Ovando &Wiley, 2003; Kloss, 1977; Tyack, 1974). Many other states passed laws providing for schooling in languages other than English (Crawford, 1992, 2004).
Some public schools provided bilingual or non-English-language instruction during the second half of the nineteenth century. The 1900s. Between 1900 and 1910, over 8 million immigrants were admitted to the United States majority of which came from Europe (Stewart, 1993). Because of this, the struggle for power to control institutions became imminent. One solution to this power struggle focused on schools. This solution came in the form of “Americanizing” all immigrants. By 1919, 15 state laws had been passed calling for English Only instruction (Higham, 1992).
During the first half of the twentieth century, many schools already implemented the English dominant instruction which was impelled by many factors such as the standardization and bureaucratization of urban schools (Tyack, 1974), the need for national unity during the two world wars, and the desire to centralize and solidify national gains around unified goals for the country (Gonzalez, 1975). In fact, from World War I to the 1960s, language-minority students were severely punished whenever they used a language other than English in the classroom, or even on the playground.
This policy continued until the 1950s resulting to an enormous loss of many indigenous languages (Crawford, 2004; Ovando & Wiley, 2003). The consequence of this action is still visible today. The ambivalence of language-minority parents toward bilingual education reflects fears that their children will be punished for using a language other than English (Arias & Cassanova, 1993). The early 1920s saw yet another restrictive immigration laws. These immigration laws, passed by the US congress, created a national-origins quota system. These extremely restrictive laws discriminated against eastern and southern Europeans and even excluded Asians.
This resulted to fewer numbers of new immigrants while second-generation immigrants dropped the use of their native languages. Moreover, bilingual education disappeared for nearly have a century in US public schools (Crawford, 1992a). Indigenous groups whose land was eventually assimilated into the United States suffered even more repressive experiences. They endured more discrimination than any other language-minority groups. From the 1850s to the 1950s, native Spanish speakers in Texas and California were taught in English Only instructions while Mexican Americans in Texas segregated to other schools.
This discrimination only stopped when segregation was ruled illegal. Even though the US government initially recognized the language rights of the Cherokees in an 1828 treaty, records show that many other American Indian groups suffered an oppression of their native languages and cultural traditions which also applied to the Cherokees during that period. In 1879, American Indian children were sent to boarding schools, where they were punished for using their native language.
As mentioned earlier, this resulted to the loss of languages of many indigenous groups. In North America, 210 out of 300 original languages remain. In the United States, it is only 175. Of these languages, only 18 are still being passed on to the children, namely, Hawaiian (in Hawaii), Siberian Yupi’k, Central Yupi’k (in Alaska), Cocopah, Havasupai, Hualapai, Yaqui, Hopi, Navajo, Tohono O’odham, Western Apache, Mescalero, Jemez, Zuni, Tiwa, Keresan, (in Arizona and New Mexico), Cherokee (in Oklahoma), Choctaw (in Mississippi) (Krauss, 1996).
Reyhner (1996) emphasized the importance of stabilizing and restoring indigenous languages: Many of the keys to the psychological, social, and physical survival of humankind may well be held by the smaller speech communities of the world. These keys will be lost as languages and cultures die. Our languages are joint creative productions that each generation adds to. Languages contain generations of wisdom, going back into antiquity.
Our languages contain a significant part of the world’s knowledge and wisdom. When a language is lost, much of the knowledge that language represents is also gone (p. 4). Aside from the fear of severe punishment, this repression of non-English-languages also resulted to the lack of foreign-language skills among the US populace. This became evident when the need for military and civilian personnel who were proficient in many languages during World War II. Because of this, a radical change happened.
US personnel returning overseas helped convince the government of the importance of multiple language resources (Pena, 1976a). The United States’ increasing need to compete for international status and power, influenced by the cold war mentality and the Soviets’ launching of Sputnik, led to an increasing need to expand their foreign-language skills. In 1958, the National Defense Education Act was approved providing federal money for the expansion of foreign-language teaching.