以心智習性為主之數學教科書內容比較研究

COMPARISON OF ELEMENTARY SCHOOL MATHEMATICS TEXTBOOKS BASED ON HABITS OF MIND

研究目的：本研究旨在透過分析教科書內容，瞭解國小高年級階段教科書設計的幾何圖形主題包含的心智習性類型和比例為何？並比較幾何圖形主題之特色，提供教學實務應用。研究設計／方法／取徑：資料蒐集與分析採質、量併陳方式，針對國內南一、翰林與康軒三版本教科書有關幾何圖形內容進行分析，以「題」為記錄單位，將課本的佈題依據分析類目進行分類計數。依次計算三套教科書中幾何圖形主題之單元數，在心智習性類型：一般化、關係的推理與探索不變性之題數與百分比；並針對心智習性類型之佈題作質性描述與分析。研究發現或結論：一、三版本之幾何圖形主題心智習性的內容，以關係的推理和探索不變性兩項數學心智習性為主，兩心智習性合計比例約在89至94%，三版本教科書彼此之間比例相差不大。二、N版教科書在提供命名、單位換算、物件形體變化和轉換等內容，比例較其他版本多；H版在辨識與分類、描述特徵關係和利用公式運算解題等內容比例最高；K版在進行物件組合與分解操作、繪圖等心智習性的內容比例最高。三、K版教科書特色為：透過鏡射理解線對稱圖形定義，操作與觀察實物理解等周長不等面積之圖形變化，應用圓概念之生活工具實測距離，提供示例建立平行四邊形與三角形面積關係；H版特色為：利用全等三角形各角組成平角瞭解三角形內角的和，利用圓圖形部分與整體關係介紹圓心角，提供繪圖步驟指導放大與縮小圖之實作；N版特色為：利用幾何圖形折疊實作，探討線對稱現象，運用釘板教導線對稱圖形的繪製，利用顏色的扣條彰顯圖形特徵，工具測量探索圓周率、圓周和直徑的關係，圓規檢視與驗證扇形特徵。研究原創性／價值：擴展先前研究集中在教科書之單元數、題數、表徵比較分析的主題和範圍，將重點轉移至對教科書內容有關認知成分的探討，提供不同的研究領域和觀點；研究者並對日後研究與教學實務提出建議，作為精進教科書比較分析之參考。

Purpose The purpose of this study was to analyze the contents of textbooks regarding the topic of plane figures. The mainly focus was to explore the habit of mind subject and further to compare the characteristics of several textbooks from different publishers for reference in teaching practice. Design/methodology/approach Quantitative statistics and qualitative descriptions were used to analyze the contents of the three textbooks. Findings The research found the main two focus of three textbooks were the reasoning with relationships and investigating invariants, and the proportions of these two habits of mind in the contents were ranging from 89% to 94% in three textbooks. Furthermore, Textbook N offers the most content regarding nomenclature, unit conversion, and the variations and conversions of plane figures more than the other two textbooks. Textbook H provides explanations regarding recognition and classification, describes relationships among characteristics, and uses formulas to solve problems. Textbook K contains the most content regarding drawing and composition and decomposition of figures. Additionally, Textbook K uses mirror reflections to explain symmetric figures, manipulates and observes figures to explain that perimeter does not equal area, practices circle concepts to measure distance, and provides examples to establish the relationship between the areas of parallelograms and triangles. Textbook H applies congruent triangles to explain that the angles within a triangle form a straight angle, uses the relationships between parts and wholes in circles to explain central angles, and explains the enlarging and reducing of figures via drawing procedures. On the other hand, Textbook N practices the folding of figures to explore symmetry, uses pegboards to teach how symmetric shapes are drawn, uses colors and buckles to accentuate figure characteristics, applies instruments to measure and explain the relationship among PI, circumference, and diameter, and examines and verifies the characteristics of sectors using a compass. Originality/value The research extend the findings of previous studies on investigating the number of units and the theme and scope of characterization, shift focus to explore the cognitive components in textbooks, and provide research in different fields and perspectives. Suggestions are provided for future research, educational practices, and the improvement of textbook comparison and analysis.