臺灣與芬蘭國小數學教科書分數教材之內容分析比較

本研究旨在探討臺灣與芬蘭國小數學教科書分數教材內容呈現的情形。研究對象為臺灣N版、芬蘭W版數學教科書。本研究採用內容分析法，以「問題」為分析單位，探究兩國國小數學教科書分數教材的主題編排、內容比重與問題的呈現方式。研究發現，在分數主題類目「分數的構念」中，臺灣使用情境帶入教學，而芬蘭則是直接對分數的命名與符號的意義賦予定義；在「等值分數」中，臺灣先教擴分再教約分，芬蘭反之；在「分數的運算」中，兩國都是從「分數的整數倍」到「整數的分數倍」，而臺灣的分數除法是循序漸進地帶出除法成熟算則「倒數法」，而芬蘭則是直接呈現「倒數法」。在布題數中，芬蘭約是臺灣的3倍；在內容比重上，分數主題類目中，臺灣「等值分數」所占比例最高，芬蘭「分數定義」所占比例最高。在問題的呈現方式中，「問題的表徵型態」中臺灣以聯合型態為主，芬蘭以數學型態為主；「問題的解題認知負荷」中兩國皆以具連結程序型的題目為主；「問題的開放性」中兩國皆以封閉性的題目為主；「問題的情境真實程度」中臺灣以真實情境為主，芬蘭以無情境為主；「問題的解題步驟」中兩國皆以單步驟的題目類型為主。

關鍵字

國小數學教科書；分數教材；內容分析

並列摘要

The purpose of this research was to investigate the difference in the topic of fractions between mathematics textbooks in Taiwan and Finland. This study adopteds a content analysis method to explore: (1) how topics in fractions were introduced, (2) content sequences, and (3) problem types. Results of this study were as following: (1) In terms of “definition of fractions,” the Taiwanese textbooks provided a context problems before introducing the definition of fractions, while the Finnish textbooks gave the definition immediately in the unit. (2) In terms of “equivalent fractions”, the Taiwanese textbooks introduced expanding fractions and then reducing fractions, while the Finnish textbooks introduced them in reverse order. (3) In terms of “fraction operations,” both countries firstly introduced multiplication by integers and then introduced multiplication by fractions. Furthermore, the Taiwanese textbooks gave an explanation and a proof about dividing fractions before giving the rule, while the Finnish textbooks gave the rule of dividing fractions immediately. (4) The total number of the problems in the Finnish textbooks was three times more than the total number in the Taiwanese textbooks. (5) Regarding the problem distribution, the Taiwanese textbooks had the highest percentages in “equivalent fractions,” while the Finnish textbooks had highest percentages in “definition of fractions. (6) In the representation forms of problems, the Taiwanese textbooks were mainly based on the connection form while the Finnish textbooks focused mainly on mathematical form. (7) About the cognitive demand of problems, both countries focused mainly on proceduralproblems. (8) About the open-ended or closed-ended of the problmes, the two countries are mainly based on closed-ended question. (9) About the situational or non-situational problems, the Taiwanese textbooks focused mainly on situational problmes while the Finnish textbooks focused mainly on non-situational problems. (10) About the steps of problem solving, the two countries focus mainly on one-step problem types.