A Study On The Interaction Among Language,Knowledge And Strategies In Mathematical Problem-Solving

The "bilingual instruction" in China at present is in essence content-based instruction (CBI). Content-based instruction began to gain prominence in the1980s and it was defined as the integration of particular academic subject with language teaching aims. With the experience of more than twenty years, CBI has won more and more supports from scholars and experts and is gradually becoming one of the popular language teaching methods. The rapid economic development of China and its further integration into the international community increasingly address the need for intellectuals with not only language proficiency but also professional knowledge in certain academic or scientific fields. Therefore, content-based instruction has drawn considerable attention in our educational circle.According to the basic notion of content-based instruction, language cannot be learned separately from substantive content and rather, it should be combined with concrete subject content. Meanwhile, for the current English teaching in China, the general knowledge in language textbooks seems inadequate to learners’ cognitive needs, which should be made full use of to facilitate language development and broaden the sphere of knowledge as well. However, foreign language learners differ greatly from children in terms of the acquisition of language and knowledge. Children gain knowledge and language almost simultaneously, for language is the prime medium of interaction through which adults transmit to children the great store of knowledge, but at the same time, children become capable of learning language because they have already acquired the fundamentals of cognition. This way,"language and cognition are related interactively, supporting and boosting each other"(Mutsumi Imai,2012). By contrast, in CBI, foreign language learners gain knowledge from the tool of a second language. The question is that can foreign language learners gain knowledge as well as second language proficiency when neither of them is adequate? Therefore, before implementing CBI, a prime question should be figured out, that is, what is the impact of second language proficiency on academic performance in CBI and how second language proficiency, content knowledge and thinking strategies interact.Based on the theories concerning the relationship between language and thought, content-based instruction, bilingualism and other relevant empirical studies, the present study has adopted both quantitative and qualitative methods and all senior one students in one high school in Shanghai have been recruited as research population for the present study. In order to ensure the reliability and validity of the study, the subjects are grouped according to their Maths and English competence represented by their performance in senior high school entrance examination and they are given a maths test written in English. This study aims to investigate how second language exerts impacts on learners’ problem solving process and thinking strategies which are adopted to tackle problems and thus this study can explore the interaction among second language proficiency, thinking strategies and content knowledge. The main findings of the present study are as follows:Firstly, positive correlations are found between students’ English proficiency and mathematical problem solving in this study. English proficiency plays a paramount role in the performance of the test. However, significant difference of test performance is only found between the English high and English low or English intermediate group, while the performances of English low or English intermediate groups do not differ significantly.Secondly, students are common in turning to strategies for help when they have difficulties no matter what level of English proficiency or mathematical competence students have. These strategies are helpful for problem solving, but they are not perfectly safe all the time, especially when the reading text is very difficult.Thirdly, students with intermediate level of maths competence seem to meet with the most difficulties, compared with the other students who have the same level of English language proficiency.