國中數學教科書內容分析與內在評鑑之研究

Content Analysis and Intrinsic Evaluation of Mathematics Textbooks in Junior High Schools

羅瑞珍(Rey-Jen Lo) ； 郭重吉(Chorng-Jee Guo)

《科學教育》 3期 (1992/04) Pp. 199-240

https://doi.org/10.6767/JSE.199204.0199

摘要

本研究旨在以Q技術進行文獻分析，整理出「數學能力類目」及「數學素養學習經驗型式」，並依據這兩個分析架構，採用「內容分析技術」對現行國中數學教科書在此兩方面的內在特質進行分析與評鑑。
本研究所整理出的數學能力可分為四大類別：知識、篡本技能、心智方法、非認知與形上認知；而在數學素養學習經驗方面則可分為五大類型：價值、信心、解題、溝通、推理。
對於現行國中數學教科書在數學能力方面的內容分析，係利用分層抽樣方法，自每章中隨機抽取20%的頁數，以段為單位進行分析，向所得結果顯示其各類別所佔的比例及主要內涵如下：
1．「知識」佔27.43%；以數學體系內的知識為主，對於數學的本質、數學與其他學門的關係等介紹得很少。
2．「基本技能」佔49.25%；以抽象符號的運作及基本計算能力佔最大部份，較為欠缺的內涵包括：與科學過程技能相關的基本技能、計算機的使用、電腦素養等。
3．「心智方法」佔21.83%；以空問概念推理為主，對於較具統整性、靈活性的思考方式呈現得不多。
4．「非認知與形上認知」佔1.49%；主要為啟發策略。
至於現行國中數學教科書在數學素養學習經驗方面的內容分析，係以每節為單位，以複選的方式檢視其是否涉及各項數學素養學習經驗。分析結果顯示在所有91節課文中提供該類型學習經驗的百分率及主要方式可示之如下：
1．價值－24.2%；以介紹數學在日常實際生活的運用為主要方式。較為缺乏的內涵是：讓學生瞭解數學亦是一種思考的方法，及數學理論發展與數學實際應用兩者間的互動關係。
2．信心－58.2%；以鼓勵學生發現、猜測，及以實際經驗中的問題為教例為主要方式。可再加號的內涵包括：介紹人類在建立數學上的奮鬥過程，將形式化的方法與學生的自然策略相結合，及讓學生瞭解個人生活中的一些活動即是數學活動等。
3．解題－100%；以數學知識體系內的解題為主導，其他方式所佔的比例都不高。
4．溝通－12.1%；提供此類型學習經驗的方式以文字敘述為主，缺乏討論性及演示性的活動。
5 ．推理－69.2%；提供此類型學習經驗的方式較為多元化，主要方式為分析情境、利用歸納的方式認識型態、及利用推理的方式發展對數學敘述的合理論證。可再加強的內涵是讓學生瞭解到優美的推理過程比找到正確的答案更令人激賞。

並列摘要

The main purpose of this study was to construct two analysis schemes, called “Categories of Mathematical Abilities” & “Types of Learing Experience for Mathematical Literacy” from a review of literature with the use of “Q-Technique”, in order to investigate the intrinsic features of mathematics textbooks used iii Junior High Schools through an “Intrinsic Evaluation” using the “Content Analysis Technique”.
Results obtained in this study indicated that there are four categories of mathematical abilities including: (1) Knowledge, (2) Basic Skill, (3) Mental Method, and (4) Non-cognition & Metacognition.
There are also five types of learning experience for mathematical literacy including (1) Value, (2) Confidence, (3) Problem-solving, (4) Communication, and (5) Reasoning.
The intrinsic features of the mathematics textbooks regarding the mathematical abilities were found to be:
(1) knowledge 27.43%, with emphasis on the knowledge of the mathematics system.
(2) basic skill 49.25%, manipulation of abstract symbols and basic computional skills received the most strong emphasis.
(3) mental method 21.83%, stressing mainly on the reasoning of spatial concept.
(4) non-cognition & metacognition 1.49%, mainly on heuristic strategies.
The percentages of all the 91 sections in the mathematics textbooks which included a given type of ‘earning experience for mathematical literacy were found to be:
(1) value-24.2%, the emphasis was on introducing the uses of mathematics in our daily life.
(2) confidence-58.2%, the emphases were on stimulating students to explore and to conjecture, and using the examples of problems in daily experience.
(3) problem-solving-100%, solving the problems in mathematics knowledge system was the main focus.
(4) cominunication-12.1%, emphasizing verbal statements, while discussion and demonstraction were lacking.
(5) reasoning-69.2%, there were various ways supporting this type, with greater emphasis on analyzing situation, using inductive reasoning to recognize patterns, and using reasoning to develop plausible arguments for mathematical statements.