以 van Hiele 理論探討圖形樣式思考層次之研究

A Study of the Thinking Levels of Pictorial Patterns from the Viewpoint of van Hiele's Theory

本文旨在將van Hiele思考層次應用到數學的圖形樣式解題上。研究者修正了Fuys、Geddes與Tischler（1988）針對van Hiele幾何層次所提出的部分行為描述，建立國小高年級學童解決圖形樣式題之思考層次行為，並依21個有關學生實際解決圖形樣式題表現之原案，嘗試擴展van Hiele理論之應用範疇至van Hiele圖形樣式思考層次。研究發現，高年級生對圖形樣式規律的思考層次行為符合van Hiele之理論，學生圖形樣式之思考仍可分派至某一個層次；其中因思考深度不同，層次二及三再細分為二A、二B及三A、三B。學童之樣式思考層次亦具有次序性、內因性與外因性，以及語言性之特性。學生若能用幾何圖形結構之間的關係來辨認樣式，則有助於圖形樣式思考層次的提升及代數知識的建造。此探索性研究之結果將提供給未來有嚴謹設計之後續研究者進行大樣本之檢測。

The purpose of this paper is to discuss the application of van Hiele’s thinking lev-els to problem-solving of pictorial patterns. The researcher modified some of the van Hiele level descriptors described by Fuys， Geddes， & Tischler (1988) and established the van Hiele level descriptors regarding 21 upper graders solving pictorial-pattern problems.The conclusions drawn from this study are as follows. (1) The students’ thinking on pictorial patterns fitted in with van Hiele’s theorem and could be classified into certain levels. (2) According to the different thinking degrees of the students， level 2 and 3 were divided into 2A， 2B and 3A， 3B， respectively. (3) Four properties were shown in the thinking levels: sequential， intrinsic and/or extrinsic， and linguistic. (4) If students could use the relations between the structures of figures to identify patterns， they were able to advance their thinking levels of pictorial patterns and to construct algebraic knowledge. It is hoped that the results of this explorary research will contribute to a more rigid study design with a larger sample in the future.