國小數學教科書數學問題類型與呈現方式之比較分析－以臺灣、芬蘭、新加坡為例

A Comparison and Analysis of the Types and Representations of Mathematical Problems in the Elementary Mathematics Textbooks of Taiwan, Finland and Singapore

徐偉民(Wei-Min Hsu)

《科學教育學刊》 21卷3期 (2013/09) Pp. 263-289

https://doi.org/10.6173/CJSE.2013.2103.02

摘要

本研究以臺灣、芬蘭與新加坡國小數學教科書為對象，針對三國教科書中的數學問題進行分析。研究對象為三國使用最普及的數學教科書，採內容分析法，依數學問題的類型和呈現方式進行分析。結果發現，三國在問題的數量上有顯著的差異，以芬蘭的問題最多，臺灣的問題最少。各類型問題所佔的比例上，三國之間則有一致的現象，都明顯地偏重無連結程序的問題。臺灣數學問題的呈現以文字型態為主，芬蘭以數學型態為主，新加坡則兼顧不同型態的呈現。在例題上，臺灣多呈現不同的解題思考與歷程，芬蘭以定義和示範的方式來呈現，新加坡以示範和結構引導的方式來呈現。在練習題上，芬蘭和新加坡設計較多開放性、探索性、和腦力激盪的問題給學生。

關鍵字

內容分析 ； 問題表徵 ； 認知需求 ； 數學教科書 ； 數學問題

並列摘要

The focus of this study was to explore how mathematical problems are presented in the most popular elementary school mathematics textbook series of Taiwan, Finland and Singapore using content analysis. Mathematical problems were the unit of analysis and they were classified based on their cognitive demand and representational form. There was a significant difference in the number of problems presented in the textbooks of these three countries with more problems presented in Finland's textbooks than in those of Singapore and Taiwan. We found the ratio of different types of problems in the textbooks is similar across the three countries with most of the problems being classified as 'procedure without connection' in each country. When the representational form of problems was examined, we found that most problems were presented in a contextual form in Taiwan, but most frequently in a purely mathematical form in Finland. There was balanced arrangement among different representation forms in Singapore. Our analysis of example problems in the textbooks showed that Taiwan's textbooks usually presented different possible thinking processes and strategies for each example problem, while Finland's textbooks tended to present examples in a more definitive or demonstrative way. Singapore's textbooks used a combination of demonstration along with structural guides to present their examples. With regard to practice problems, there were more open, challenging, and explorative problems presented in the textbooks of Finland and Singapore than in those of Taiwan.

並列關鍵字

Content Analysis ； Problem Representation ； Cognitive Demand ； Elementary Mathematics Textbooks ； Mathematical Problems

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