本研究主要目的是希望透過高中數學第一冊「數列級數」單元，去探討新版教科書對學生學習成效的影響，作為未來修訂教材者的參考。
研究對象自高雄市抽取三所高中（其中二所為公立高中，一所為私立高中），此三所高中於八十八年度開始使用三種不同版本的數學教科書，在各自選取一、二年級各一班，總共六班，共計237人來接受實驗。各校一、二年級的班級，皆被同一位數學老師教授過要研究的單元，其中三所學校甲校（高級中學87、88學年度錄取新生聯考分數580分以上）、乙校（高級中學87、88學年度錄取新生聯考分數530∼580分）、丙校（高級中學87、88學年度錄取新生聯考分數530分以下）；其中三種不同版本（舊版為國立編譯館出版，新版在本研究中採取南一書局、大同資訊企業股份有限公司、翰林出版社三種版本），經過教育部審定合格的高中數學課本（不包括教師手冊、數學講義、數學刊物、參考書等）。

利用研究者自邊的「數學測驗」來施測，結果採t-test法，又因為其中一所學校所蒐集的檔案資料其變異數相差太大，且樣本空間不相等，故在進行單因子變異數分析，顯示各班級的學生在學習成就上有無明顯差異；利用「數學意見調查表」所得之結果以‘5’、‘4’、‘3’、‘2’、‘1’計算其得分並進行變異係數（ANOVA），藉此探討學生學習態度的差異，結合本研究之分析結果，提出下面幾項結論：
一、 以t-test及變異數分析知：甲校一、二年級在學習成效上有顯著的差異；乙校一、二年級在學習成效上沒有顯著的差異；丙校一、二年級在學習成效上沒有顯著的差異。
二、 由學生作答的逐題得分率與錯誤類型，將試題分類為概念題、計算題、綜合應用題（包括理解、分析、應用之整合題目），針對三種試題分類結果知：
（1） 教科書對基礎較好的學生（指甲班）與基礎較弱的學生（指丙班）之概念題學習成效是沒有影響，新、舊版毫無差別。但對基礎一般的學生（指乙校）而言，新版教科書對學習成效有顯著影響。
（2） 教科書對基礎較好的學生（指甲班）與基礎較弱的學生（指丙班）之計算題之學習成效有影響，且新版教科書對一年級計算題的學習成效優於二年級。但對基礎一般的學生（指乙校）而言，新版教科書對其計算題之學習成效，除循環小數化為分數的計算有顯著影響外，其他計算題之影響是不顯著的。
（3） 教科書對基礎較好的學生（指甲班）與基礎一般的學生（指乙 班）之綜合應用題的學習成效有影響，且新版教科書對一年級的綜合應用題學習成效低於二年級。但對基礎較弱的同學（指丙校）而言，新版教科書對其綜合應用題之學習成效，有顯著影響，尤其以遞迴定理之綜合應用題的學習成效有顯著影響。
三、 以各校各班數學學習態度與學習成效的差異來探討，結果知：
甲校一、二年級在學習成效與學習態度上，有顯著差異。
乙校一年級在學習成效與學習態度上，無顯著差異。
乙校二年級在學習成效與學習態度上，有顯著差異。
丙校一、二年級在學習成效與學習態度上，無顯著差異。
四、 以三所學校一、二年級之數學學習態度（分成五個分量：學習習慣、學習過程、學習慾望、學習方法、準備考試）與學習成效的相關情形，結果知：
（1） 甲校一年級的學習成效與學習慾望及學習方法的相關性，與二年級在此兩分量的相關性有顯著差異，而學習慾望及學習方法與教科書有相關性，故新版教科書對甲校一年級的學習成效有顯著的影響。
（2） 大體上甲、乙、丙三所學校的二年級學生，其學習成效與學習態度的五項分量（學習習慣、學習過程、學習慾望、學習方法、準備考試）有顯著的相關性。而此學習態度的五項分量之表現，多少與使用的教科書有關，故新版教科書與學習態度的五項分量有顯著的相關性。
（3） 就學習方法而言，甲、丙二校一年級的學習成效與此分量（學習方法）之相關較二年級顯著（尤其甲校一年級）。
（4） 就準備考試而言，甲、乙、丙三校一年級的學習成效與此分量（準備考試）之相關性較二年級顯著。

Abstract

The main purpose of this study is to investigate, through the “Series” unit in the first volume of high school mathematics, the impact of the updated-version textbooks on the learning effectiveness of students so as to provide references to be used by future revisers of teaching materials.

The research subjects were drawn from Kaohsiung City high schools. Three schools were selected (two public and one private). These three high schools, from the 1999 academic year, began to use mathematics textbooks of three different versions, one to each school. A first-year class and a second-year class were drawn from each school, and there were six classes in total. In total there were 237 students receiving the experimentation. The students from the same school, no matter they were first-year or second-year, had been taught by the same teacher in respect of the unit that was included in the study. Among the three schools, School 甲校 admitted for the 1998 and 1999 school years new students with scores higher than 580 on the joint entrance examination, School 乙校admitted for the 1998 and 1999 school years new students with scores from 530 to 580 on the joint entrance examination, and School 丙校admitted for the 1998 and 1999 school years new students with scores lower than 530 on the joint entrance examination. The three new versions used in the study were published by Nan-I Book Store, Ta Tung Information Enterprise, Co., Ltd., and Han Lin Publisher respectively. They are high school mathematics textbooks examined and approved by the Ministry of Education (excluding Teacher’s Manual, supplementary materials, journals, reference books, etc). The outdated version was published by National Bureau of Editing and Translation.

Mathematics Test written by the researcher was used as the testing tool, and the t-test method was adopted. Moreover, because the variances of the file data collected from a school fluctuated tremendously and the sample space was unequal, a single-factor ANOVA analysis was conducted to indicate whether there existed a significant difference between classes in terms of their learning achievement. The “Questionnaire on Mathematics Opinions” was administered and the results were represented by ‘5’, ‘4’, ‘3’, ‘2’, ‘1’, which indicated their scores. An ANOVA analysis was conducted to investigate the differences in students’ learning attitude. After synthesizing the analytical results of this study, the author has come up with the following conclusions:

一、It is known from t-test and ANOVA analysis: in School 甲校, there existed a significant difference between the first-year and the second-year students in respect of their learning effectiveness; in School 乙校, there existed no significant difference between the first-year and the second-year students in respect of their learning effectiveness; in School 丙校, there existed no significant difference between the first-year and the second-year students in respect of their learning effectiveness.
二、According to the correct percentage of each question made by students and the error pattern, the test questions were classified into three types: concept, calculation, and comprehensive application (including questions that integrated comprehension, analysis, and application abilities). It was found from the classification of questions that:
(1) Textbooks have no impact on both the well-established (School 甲校) and the weak (School 丙校) students in respect of the effectiveness of learning concept questions. There is no difference between the outdated and the updated-version textbooks. However, as far as the students with ordinary achievement (School 乙校) are concerned, the updated-version textbooks have a significant impact on learning effectiveness.

(2) Textbooks have an impact on both the well-established (School 甲校) and the weak (School丙校) students in respect of the effectiveness of learning calculation questions, and the first-year students have benefited more from the updated-version textbooks than have their second-year counterparts in terms of the effectiveness in learning calculation questions. However, as far as the students with ordinary achievement (School 乙校) are concerned, the updated-version textbooks have a significant impact on the effectiveness of their learning to reduce cycle fractions, but have no significant impact on their learning other calculation questions.
(3) Textbooks have an impact on the effectiveness of learning comprehensive application questions, as far as both the well-established (School甲校 ) and the students with ordinary achievement (School乙校) are concerned. Moreover, the first-year students have benefited less from the updated-version textbooks than have their second-year counterparts in terms of the effectiveness in learning comprehensive application questions. However, as far as the weak students (School丙校) are concerned, the updated-version textbooks have a significant impact on the effectiveness of their learning comprehensive application questions. In particular, the updated-version textbooks have an especially significant impact on the effectiveness in learning the comprehensive application questions of regression principle.
三、From investigating the difference between attitude toward and effectiveness in learning mathematics as far as different groups are concerned, it has been found:

There existed a significant difference between learning attitude and learning effectiveness as far as the first-year and the second-year students of School 甲校 are concerned.

There existed no significant difference between learning attitude and learning effectiveness as far as the first-year students of School 乙校are concerned.

There existed a significant difference between learning attitude and learning effectiveness as far as the second-year students of School 丙校 are concerned.

There existed no significant difference between learning attitude and learning effectiveness as far as the first-year and the second-year students of School 丙校 are concerned.
四、From the correlation between the learning attitude (consisting of five sub- categories: learning habit, learning process, learning desire, learning method, and test preparation) and the learning effectiveness of the first-year and second-year students of the three schools, it has been found:

（1） As far as the correlations between their learning effectiveness and their learning desire and between their learning effectiveness and their learning method are concerned, there existed a significant difference between the first-year and the second-year students. Because both learning desire and learning method are related to textbooks, the updated-version textbooks had a significant impact on the learning effectiveness of the first-year students of School 甲校.

（2） On the average, there existed a significant correlation between the learning effectiveness of the second-year students of School甲校 , School 乙校, and School 丙校 and each of the five sub-categories of learning attitude (learning habit, learning process, learning desire, learning method, test preparation). Their performance on each sub-category of learning attitude is more or less related to textbooks. Therefore, there existed a significant correlation between the updated-version textbooks and each of the five sub-categories of learning attitude.

（1） The correlation between learning effectiveness and learning method presented by the first-year students of School 甲校 and School 丙校 (especially School 甲校) is more significant than that presented by their second-year counterparts.

（4） The correlation between learning effectiveness and test preparation presented by the first-year students of School 甲校, School 乙校and School 丙校 is more significant than that presented by their second-year counterparts.

第一章 緒論……………………………………………… 1
1.1 研究動機……………………………………………1
1.2 研究目的……………………………………………1
1.3 待答問題……………………………………………2
1.4 名詞解釋……………………………………………3
第二章 文獻探討………………………………………… 5
2.1 教科書的重要性、選擇與設計……………………5
2.2 解題歷程的探討……………………………………8
2.3 錯誤類型之研究………………………………… 9
第三章 研究設計與實施程序 …………………………12
3.1 研究方法……………………………………………12
3.2 研究樣本……………………………………………12
3.3 研究工具……………………………………………13
3.4 實施步驟……………………………………………17
3.5 資料分析……………………………………………18
3.6 研究限制……………………………………………20
第四章 結果與討論 ………………………………………21
4.1 「數學測驗」之學習成效的結果與討論……………21
4.2 「數學測驗」逐題得分率與錯誤類型的結果與討論……………27
4.3 「數學意見調查測驗」的結果與討論………………39
4.4 綜合討論………………………………………………51
第五章 結果與討論
5.1 結論…………………………………………………54
5.2 建議…………………………………………………55
參考書目……………………………………………………58
附錄次
附錄A：「數學測驗」之試題……………………………63
附錄B：「數學意見調查測驗」之試題…………………65
附錄C：「數學測驗」之難度及鑑別度…………………66
附錄D：甲、乙、丙三校各項分析之原始分數表 ……67
附錄E：原始分數次數分配表 ……………………………79
附錄F：原始分數累積次數分配表 ………………………79
附錄G：調整後分數的次數及累積次數分配表 …………80
圖錄次
圖 A：……………………………………………………81
圖 B：………………………………………………………82
圖 C：………………………………………………………83

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二、英文部分
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