發展二階段診斷工具探討學生之統計迷思概念：以「相關」為例

Developing two-tierdiagnostic instrument for exploring students'statisticalmisconceptions: take correlation as the example

統計素養是當代公民的必備能力，然而學生在學習統計時，常會產生迷思概念。相較於其他科學領域已經發展二階段診斷工具來探究學生的迷思概念，在統計教育領域中罕有類似的工具。據此，本研究針對基礎統計學中重要的概念，「相關」，編製二階段診斷工具，Two-tier Diagnostic Instrument about Correlation Misconceptions（TDICM），並利用該工具對982 名已修畢「相關」課程的高三學生之作答反應進行分析，以探討其「相關」理解情形，「相關」迷思概念的類型、普遍性與可能成因。研究結果顯示：（1）TDICM 的試題難度分配平均，內部一致性信度與鑑別度均佳；（2）受測學生的相關概念理解情形不佳，部分受測學生雖然能答對TDICM 的第一階段試題，卻因為缺乏對相關概念的完全理解，而無法答對TDICM 的第二階段試題；（3）根據受測學生的兩階段答案組型，顯示TDICM 所診斷的14 個相關迷思概念皆被學生所普遍擁有；（4）上述14 個相關迷思概念中有7 個是過去研究曾探討過，有7 個是本研究於診斷工具發展過程中發現學生常具備的迷思概念。此外，本研究亦在研究結果與討論中探討這14 個迷思概念的可能成因與教育意涵。最後，本研究針對「二階段診斷工具」與「相關」迷思概念在統計教育研究之應用提出建議。

Therefore， the main purpose of the current study was to develop a two tier diagnostic instrument: Two-tier Diagnostic Instrument about Correlation Misconceptions (TDICM). This instrument was adopted to analyze the responses of 982 12th-graders who had taken statistics courses to “correlation”， and to explore the types， universality， and possible causes of such misconceptions in correlation. The research results showed that: (a) TDICM has satisfactory levels of difficulty， internal consistency reliability， and discrimination; (b) most participants do not have good comprehension of “correlation” concepts. Although some were able to answer the questions correctly in the first tier of TDICM， they failed to do so in the second tier due to lack of comprehensive understanding of correlation; (c) students' responses in the two-tier model indicated that there are 14 correlation misconceptions universally held by the participants; (d) seven of the 14 misconceptions has been discussed in the literature， and others were identified in this study. Furthermore， the possible causes of these misconceptions and the implications in education were discussed. Finally， this study provided some suggestions to the application of two-tier diagnostic instrument and the correlation misconceptions in statistics education.