八年級生使用敘事說明學習數學概念之研究——屏東縣某國中為例

A study on learning mathematics concept by the narrative explanation for 8th graders at Pingtung county

本研究對屏東縣某國中254名八年級學生進行「0.9...=1」與「負負得正」二種數學概念測驗，探索學生分別閱讀敘事說明後，學習數學概念的認知與效果，並檢驗是否可以應用抽象學習五類型（「自明」、「衝突自清」、「衝突它清」、「衝突未清」、「未明未清」）分類。結論如下:「負負得正」數學概念測驗工具是有效的、有意義的，雖然受測學生「負負得正」口訣琅琅上口，但是大部分不懂負數乘法原始關係，學生學習時並不理解教科書說明意義，純粹會計算算式，受測時無法直接連結教科書敘事說明與最簡負數乘法算式（-2）X（-3）=6。「0.9...=1」數學概念測驗工具是有效的、有意義的，三成受測學生經過閱讀敘事說明可以學會這概念，結果類似其他研究。這二個數學概念測驗結果支持抽象數學學習理論，檢驗單一數學抽象概念，所有受測學生都可以被歸類到抽象學習五類型的某一類型，沒有類型不能描述的學生。榮格心理學基本理論模式可以清楚描述敘事說明與學習關係，它視閱讀敘事說明為一種體驗，若是進入意識則為「懂」，若非則進入潛意識，以後再遇到相關議題，可能啟動，可能不啟動心理功能，由不同心理功能啟動，可能成功解題，也可能失敗。另外，研究結果佐證可以利用心理學測驗的信效度分析在「數學敘事說明」上，專家效度幾乎可以推理與應用，信度分析的基本架構可以移植至分析數學敘事說明，這是初探，細節當然還需要更深入與嚴謹的探討。

In this study, 262 8th graders at a junior high school in Pingtung County were tested using text narrative explanation questionnaire of mathematical concepts on ''two negatives multiple makes a positive'' and ''0.9... = 1'' to explore students' perception on learning mathematics concept. And test whether classification for 5 patterns of learning abstract mathematics concept (''self-evidence'', ''conflicted self-clearing'', ''conflicted clearing by others'', ''Conflicted non-clearing'', ''Unknown ever'') was applied to junior high school students. There are the following conclusions: The mathematical concept test of ''Multiplying Negatives Makes A Positive'' is effective and meaningful. Although the tested students known the formula, most of them do not understand the primitive relationship of negative multiplication, and students do not understand the textbook explanations when they studied. They can calculate multiplication of negatives, but cannot be successfully connected the relationship between textbook narrative explanations and mathematical formulas when tested. The ''0.9... =1'' mathematical concept test tool is effective and meaningful. 30% of the tested students can learn this concept after reading the narrative. The results are similar to other studies. These two math concept tests support abstract mathematics learning theory. Under any single mathematical concept, all students can be classified into 5 patterns of learning abstract concept and there is no student who 5 patterns cannot describe. The basic theoretical model of Jungian psychology can clearly describe the relationship between narrative explanation and learning. It regards reading narrative explanation as an experience, and if it enters consciousness, it means ''understanding.'' If not, then the experience enters the subconscious. If the person encounters related issues later, the one may activate or not the psychological functions. If activated one of the psychological functions, one may succeed in solving the problem, or fail. In additional, the research results can be used to support the reliability and validity analysis of psychological tests. In the ''Mathematical Narrative Explanation'', expert validity can almost be reasoned and applied. The basic framework of reliability analysis can be transplanted to the analysis of mathematical narrative explanation, of course, this is first study the detail needs more in-depth analysis and rigorous discussion.