A two-way bilingual classroom provide second language learning and enriching academic and sociocultural experiences for both language minority and language majority students. Academic Issues. Bilingual education is developed mainly because children must be kept from falling behind academically (Ovando, Combs, & Collier, 2006). The emotional and linguistic issues discussed in the preceding sections thus far build directly into the key goal of helping each child reach his full educational potential.

The use of the first language of language minority students in classrooms is not a new one. As concluded in a 1951 meeting of international experts, “It is axiomatic that the best medium for teaching a child is his mother tongue” (United Nations Educational, Scientific and Cultural Organization, 1953, p. 11). This is one of the primary justifications of the 1968 Bilingual Education Act. Language minority students in the United States do not start on an equal footing with their language majority peers. Thus, both the content (e. g.

math, science, social studies, etc. ,) and processes (e. g. cooperative learning holistic assessment, culturally compatible classroom practices, etc. ,) must be made appropriate for them. Bilingual education helps students to keep up with the subject areas with instruction in their first language and at the same time catch up with the English needed to function socially and academically in English dominant classroom settings (Ovando, Combs, & Collier, 2006). The catch-up challenge becomes even more critical in middle school and high school.

In these levels, the curricula are more structured with less emphasis on learning by doing and more emphasis on abstract language. However, we must consider that the principal aim of bilingual education at all grade levels is to provide academic experiences in a language that the student can understand. In this way, the students become well educated while at the same time learning English. As mentioned earlier, mathematics is perhaps one of the most (if not the most) difficult subjects to teach.

Mathematics education is developed to study theories and practices that would help mathematics educators teach mathematics to students. Today, mathematics is increasingly becoming difficult to some students. Although most students know the procedures on how to solve specific problems, they still fail to understand the facets that mathematics really teaches. Many researches are devoted to studying how mathematics can be taught effectively, in which students do not only learn how to operate equations but manipulate any problem that comes their way.

Carpenter and Peterson (1988) studied how children learn mathematics from instruction. The researchers integrated the perspectives on teaching mathematics and research on children’s thinking and problem solving strategies. According to them, students do not enter the classroom in a “blank state”, that is, in a state wherein they do not know anything. They already have knowledge — some are correct, some are incorrect. Thus, educators should determine the prior knowledge that these children have and then focus on developing what these children know.

Davis and McGowen (2007) reiterated Carpenter and Peterson’s (1988) practice of teaching mathematics. They called this practice “formative assessment”. According to them, formative assessment is “a kind of assessment that uses the data acquired to adapt instruction to better meet student need” (Davis & McGowen, 2007). Although, there are many other studies investigating which practice is best to apply in teaching mathematics, few has been undertaken regarding teaching mathematics to bilingual students.

Therefore, this study aims to determine which practice is best to apply in teaching mathematics to bilingual students. Due to time constraints, only two current educational theories will be compared — Pask’s Conversation Theory and Landa’s Algo-heuristic Theory. These theories will be further explained in the succeeding sections. But first, we will discuss some famous educational theories that are used in teaching mathematics. Later on, in the discussion part, we will compare these theories to Pask’s and Landa’s theories by studying their differences and similarities.