小六學生空間與形狀心智習性表現之探究

A Study of the Sixth Grade Student Performances of Habits of Mind on Space and Shape

本研究旨在探索國小六年級學生面對幾何任務時，其心智習性的表現與解題的思考路徑，進而提供未來幾何有效教學的參考。受試者來自於台灣中部地區5所公立小學六年級的學生總計105名。根據提供的線索要求學生進行繪圖和運算的表現，配合訪談方式蒐集學生資料，以質性分析和量化方式描述研究結果。參與研究的六年級學生對於提供的空間與形狀任務，大多數學生的幾何心智表現不佳，無法對扇形、等腰梯形與長方體探索幾何元素的關係與對這些關係的推理、一般化幾何的概念、探究這些關係裡的變數和不變性，運用這些元素評估與繪製幾何的圖像，並利用其特徵進行運算解題。學生對於幾何任務的解題大致可分成以整體圖像和元素分析兩種思考類型，利用前者進行解題者其正確率高於後者；正確者能對構成幾何形體相關之間元素的關係有清楚之理解，並能利用他們進一步推理並連結而繪製正確的幾何形體並利用其一般化的公式解題；解題錯誤者則思考利用公式解題，並未對幾何元素之間關係加以思辨和推理。本研究採用線索閱讀引導理解的方式，激發學生幾何解題思考、推理和心智習性的表現，研究結果可協助國小實務教師進行有效的幾何教學與課程設計。

The purpose of this study is to explore the performance of the habits of mind of the sixth graders in the tasks of geometry, and to provide a reference for the future effective teaching of geometry. This study designed three graphical and spatial tasks to explore the students' geometrical habits of mind and concepts. The subjects were from 105 students in the sixth grade of five public primary schools in central region of Taiwan. According to the clues provided, students are required to perform the performance of drawing and calculation, collect student data in accordance with the interview method, and describe the research results in qualitative analysis and quantitative way. The sixth-grade students who participated in the research provided poor geometrical habits of mind. They could not explore the relationship between the geometric elements of the sector, isosceles trapezoid and the cuboid and the reasoning and generalization of these relationships. Concepts, explore the variables and invariances in these relationships, use these elements to evaluate and draw geometric images, and use their features to solve problems. Students' problem solving for geometry tasks could roughly divided into two types of thinking: the overall image and the elemental analysis. The accuracy of using the former to solve the problem is higher than that of the latter. The correctness of the problem of geometry tasks is different from that of the wrong person. The design of this research task uses clues to read and guide the understanding, to stimulate students to carry out geometric problem solving, reasoning and performance of habits of mind. The research results can assist the elementary school practical teachers to carry out effective geometric teaching and curriculum design.