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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.

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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. 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.

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