從數量推理能力與認知風格探討傳統教材與多媒體輔助教材對學習成就之分析-以國中二年級之等差數列與等差級數為例

Abstract

隨著科技的日新月異，以及電腦科技的發達，不管是在硬體的更新速度上，或者軟體的研發技術上，都漸漸的帶動電腦多媒體的教學及學習方式。在自己的教學歷程中發現有一些教學觀念不容易用傳統上課方式表達，以國中二年級數學課程「等差數列及等差級數」單元為例，國二學生剛接觸以符號代表數，對於多個文字符號的使用，以及代數式中將數代換成算數式的運算，這些概念的理解對國中二年級學生是抽象而且是難理解的，尤其連結到一些規律出現的圖形上時，學生在推理及認知上難以觀察到結果，並且推論到一般化的結論。 本研究主要探討多媒體教材教學與傳統教材教學對學習成就的影響。除此，學生在學習數學的過程中會受到許多因素的影響，例如學習興趣、接受訊息後的處理模式、個人的認知、類化後表徵符號的運用等，且數學的學習尤重推理能力，而學生的思考模式、接受訊息後的處理模式由大腦控制，左腦訊息處理方式重文字、語言等，右腦重圖象、想像等，可見學生認知風格的差異，處理數學問題的方式也會有所不同[8][9]。 本研究以國中二年級數學「等差數列與等差級數」單元，設計多媒體教材，以準實驗設計的方式，實驗對象係新竹市某國中二年級兩班級的學生。ㄧ班為實驗組，一班為控制組，實驗所得結果僅能推論國中二年級數學單元「等差數列與等差級數」之教學參考。認知風格量表採用吳武典教授修訂之「認知風格測驗」（CSI）作為學生認知風格的分類依據[8][9]；數量推理能力，以中國行為科學社所出版的新生入學智力測驗的「數量推理測驗」做為分類依據。 本研究實驗後，依統計分析的主要結果如下： 1.不同的教學方法，在「等差數列與級數」單元上，對於學生學習成就上有顯著差異。 2.在學習多媒體教材「等差數列與級數」單元下的不同認知風格學習者，對於學生學習成就沒有顯著差異。 3.在學習多媒體教材「等差數列與級數」單元下的不同數量推理能力學習者，對於學生學習成就整體上沒有顯著差異，但是高分組與低分組有顯著性的差異。 4.在學習多媒體教材「等差數列與級數」單元下，其不同認知風格的學習者與不同數量推理能力的學習者，對於學生學習成就沒有交互作用。 本研究的成果，可提供國中數學科教師在二年級單元「等差數列與等差級數」教學時，利用多媒體教學給予較合適的學習引導，在教材的設計上可再增加圖像、數量間的關係，更進一步的分析不同認知風格學習者的認知模式，也能提升低成就數量推理能力學習者的學習成效。

With the advance in technology and the improvement in computer, not only the upgrade of hardware but the development of software technology has gradually driven teaching in computer multimedia and computer learning. From my past teaching experience, there are more or less teaching courses and concepts that cannot be contented in a traditional classroom. Take the "arithmetic sequence and arithmetic series" in mathematics curriculum in grade eight for example, when the students just learned algebra, especially when it links to some regular graphics, the concept would be too abstract for students in the eighth grade to understand and to infer to a general conclusion in reasoning or cognition.

The study mainly discussed the different effects of multimedia based materials presentation and traditional text based materials on learning achievements. Students may be influenced by many factors in the process of learning mathematics, such as the motivation, processing mode after receiving messages, personal knowledge and the application of categorized symbols, etc. Furthermore, mathematic learning especially emphasizes on the reasoning ability. It can then be referred that different students may have different cognitive styles in learning. Human brain, at the right or left, respectively controls different aspects of message taking. The left side of the brain deals mainly with literary and language, while the right focuses on graphics and imagination [8][9]. Thus students’ cognitive styles and the ways they think about the mathematic questions will be different.

The unit "arithmetic sequence and arithmetic series" was taken as the teaching material in this study. A quasi-experiment was undertaken in two classes in one junior high school in Hsinchu. The subjects consisted of 66 students, of which 33 as experimental group, and 33 as control group. The Cognitive Style Scale was adapted from the “Cognitive Style Index (CSI) which was revised by Professor Wu, Wu-Dian [8][9]to categorize students’ cognitive styles. Quantitative reasoning ability was based on the quantitative reasoning test of intelligence test for school entrance, Chinese Behavioral Science Corporation, to classify. The results of the study can only be the reference of teaching “arithmetic sequence and arithmetic series” in grade eight. Major results were found statistically as followings: (1) There was significant difference in learning achievements among different teachings in the unit of "arithmetic sequence and arithmetic series".

(2) When learning the unit of "arithmetic sequence and arithmetic series" with multimedia material, learners with different cognitive styles showed no significant difference in learning achievements.

(3) Different learners with different quantitative reasoning ability have significant difference only in high-acquirement group and low-acquirement group when learning the unit of “arithmetic sequence and arithmetic series” with multimedia materials.

(4) There were no interactions among students’ learning achievements in the experimental unit when learning the unit of “arithmetic sequence and arithmetic series” with multimedia materials.

The results of this study would be useful to provide a reference to math teachers when teaching the unit of "arithmetic sequence and arithmetic series" in the eighth grade. Teachers can use multimedia materials presentation to provide students appropriate study guides. It suggests that the teachers can increase graphics, quantity, etc. to analyze the cognitive modes of learners with different cognitive styles and to promote the learning achievements of low-achievement learners with less quantitative reasoning ability.