圖像式情境脈絡數學教材對國小資優生學習成效與基模影響之實驗研究

Effect of Situated Context Instruction in Mathematics Incorporating Pictures for Gifted Elementary School Students

本研究採準實驗研究設計，檢驗以情境脈絡布題的「圖像式情境脈絡數學教材」對國小資優生「立即學習成效」、「學習保留成效」及「基模表現」之影響。研究對象為臺北市11所國小高年級資優生，包含實驗組與對照組各30名，實驗組接受圖像式情境脈絡數學教材教學、對照組接受純文字奧林匹亞數學教材教學，兩組課程均為18堂課。本研究以自編工具檢驗實驗效果，採單因子共變數分析進行實驗效果之統計分析，研究結果發現：一、在學習成就表現的影響上：圖像式情境脈絡數學教材明顯有助於提升實驗組學生在「牛吃草」（速率與工程問題之跨概念整合單元）及「排列組合」單元之立即學習成效表現，且在學習保留成效上亦有相同效果；然於「速率」單元則無顯著效果。二、在基模表現部分：圖像式情境脈絡數學教材明顯有助於提升實驗組學生「牛吃草」單元的「陳述性知識」，在「排列組合」及「速率」單元則無顯著效果；在「程序性知識」部分，圖像式情境脈絡數學教材在「牛吃草」及「排列組合」單元明顯有助於提升實驗組學生的基模，在「速率」單元則呈現部分效果。整體而言，本研究結果顯示使用圖像式情境脈絡數學教材的布題與教學，能支持學生在「初始概念」學習時，建立有效的陳述性知識及程序性知識。相關脈絡知識的完整性可能有助於學生在記憶時形成具有線索指引的內在表徵，進而提升知識的習得與保留。最後，本研究提出後續研究與教育實務議題的建議。

Situated learning theory suggests that knowledge learning is embedded within a context. According to this theory, this quasi-experimental study explored the effect of situated context instruction in mathematics incorporating pictures (SCIMIP) on gifted elementary school students. Method: Sixty gifted students from 11 elementary schools in Taipei City participated in the study and were evenly divided into an experimental group and a control group. The participants in both groups attended 18 sessions during a 3- month extracurricular intervention. The mathematics materials used for both groups were adapted from the materials used in the Mathematical Olympiad, a challenging competition for students with high levels of mathematics ability. The experimental group received SCIMIP; the mathematics problems used for this group were embedded within pictures and story contexts. The control group was guided through traditional problemsolving materials used to prepare for Mathematical Olympiad. The materials were divided into 3 units: Velocity, Cow and Grass, and Permutation and Combination. SCIMIP emphasizes concept integration during the mathematics learning process. A pretest, posttest, and follow-up test were implemented before and after the teaching intervention. Three test instruments were developed for examining the learning effects, which included the effects on the immediate learning achievement performance, the learning retention performance, and the quantity of schema performance. Several oneway ANCOVA were conducted to examine learning effects in the experimental and control groups. Results/Findings: The major findings are outlined as follows: 1. SCIMIP benefited students in the experimental group, enabling enhanced immediate learning achievements and learning retention in the Cow and Grass and Permutation and Combination units. 2. SCIMIP aided the experimental group students in increasing declarative knowledge and procedural knowledge in the Cow and Grass unit and in the Cow and Grass and Permutation and Combination units, respectively. However, SCIMIP demonstrated a partial effect in the Velocity unit. In general, the experimental group significantly outperformed the control group in learning achievement and knowledge retention. The results suggested that the contextual clues might guide students in accumulating complete declarative knowledge of mathematics concepts and effective procedural knowledge of mathematics problem-solving strategies. Conclusions/Implications: SCIMIP helps students in establishing informative and integrated knowledge representation, particularly when students are learning initial concepts. Firmly established knowledge representation enhances performance in mathematics learning and retention. According to the study results, the researchers provide the following suggestions: In designing situated contexts for mathematics learning, teachers can effectively use pictures and stories. However, for some gifted students, mathematics problems embedded within picture and story contexts are only beneficial at the initial learning stages.