The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes (original) (raw)
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In 1613 the official-scholar LI Zhi-zao (李之藻) of the Ming Dynasty, in collaboration with the Italian Jesuit Matteo RICCI (利瑪竇), compiled the treatise Tongwen Suanzhi (同文算指). This is the first book which transmitted into China in a systematic and comprehensive way the art of written calculation that had been in common practice in Europe since the sixteenth century. This paper tries to see what pedagogical lessons can be gleaned from the book, in particular on the basic operations in arithmetic and related applications in various types of problems which form the content of modern day mathematics in elementary school education.
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In China, the importance of quality mathematics education has never been called into a question, whereas numeracy as a general capability that is more than the mastery of mathematical knowledge and skills is seldom discussed in the literature about Chinese schools and education systems or considered in teaching practices, presenting an overall picture that numeracy development seems to be missing from Chinese education or considered as a tacit outcome automatically produced by the acquisition of mathematical knowledge. This issue may stem from the linguistic differences between English language and non-English language that render the interpretation of numeracy distorted and further evolve into a whole situation in China as a result of the longstanding debate on the essence of numeracy and the heavy emphasis laid on mathematics education rather than numeracy development as a whole. In this paper, the nature of numeracy is discussed by referring to a number of classic literature works, with special attention to clarifying the relationships between numeracy and mathematics that can be confused at a conceptual level.
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The Base of Math in The Chinese Book of Changes - The Starting Point.
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The relative linguistic transparency of the Asian counting system has been used to explain Asian students’ relative superiority in cross-cultural comparisons of mathematics achievement. To test the validity and extent of linguistic transparency in accounting for mathematical abilities, this study tested Chinese and British primary school children. Children in Hong Kong can learn mathematics using languages with both regular (Chinese) and irregular (English) counting systems, depending on their schools’ medium of instruction. This makes it possible to compare groups with varying levels of exposure to the regular and irregular number systems within the same educational system, curriculum, and cultural environment. The study included three groups of first/second graders and third/fourth graders with varying degrees of experience to the Chinese language and counting systems: no experience (UK; n = 49); spoke Chinese at home and learnt to count in English at school (HK-E; n = 43); spoke Chinese at home and learnt to count in Chinese at school (HK-C; n = 47). They were compared on counting, numerical abilities and place value representation. The present study also measured nonverbal reasoning, attitude toward mathematics, involvement of parents, and extra-curricular mathematics lessons to explore alternative explanations of children’s numeric ability. Results indicated that students in HK-C were better at counting backward and on the numeric skills test than those in HK-E, who were in turn better than the UK students. However, there was no statistical difference in counting forward, place value understanding, and a measure of arithmetic. Our findings add to existent literature suggesting that linguistic transparency does not have an all-pervasive influence on cross-national differences in arithmetic performance.
Aspects that Affect Whole Number Learning: Cultural Artefacts and Mathematical Tasks
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The core of this chapter is the notion of artefact, starting from the discussion of the meaning of the word in the literature and offering a gallery of cultural artefacts from the participants’ reports and the literature. The idea of artefacts is considered in a broad sense, to include also language and texts. The use of cultural artefacts as teaching aids is addressed. A special section is devoted to the artefacts (teaching aids) from technologies (including virtual manipulatives). The issue of tasks is simply skimmed, but it is not possible to discuss about artefacts without considering the way of using artefacts with suitable tasks. Some examples of tasks are reported to elaborate about aspects that may foster learning whole number arithmetic (WNA). Artefacts and tasks appear as an inseparable pair, to be considered within a cultural and institutional context. Some future challenges are outlined concerning the issue of teacher education, in order to cope with this complex map.