國中學生在絕對值相關問題之概念錯誤研究

Abstract

本研究的目的主要為探討學生在解決絕對值相關題目時所遇到的困難，進而瞭解學生在解此類問題時出現錯誤之原因，希望研究的結果能夠提供教師作為補救教學或改進教學策略的依據，增進教學成效，並作為未來教學及研究的參考。\n\n 本研究採調查法，並輔之以訪談蒐集資料。第一階段為問卷調查，經由對絕對值相關概念作文獻探討，以及與多位數學教師討論之後，研究者以自編之絕對值相關概念試題本進行施測，藉此瞭解學生在各向度的答題情況，並且作為選擇訪談對象的依據。第二階段為無結構開放式訪談，主要訪談學生作答時之想法與解題策略，所有訪談皆全程錄音，並轉錄成文字檔後進行內容分析，進一步瞭解學生在概念上錯誤的內涵，以及探討解題困難產生的原因。\n\n 研究結果發現，學生在絕對值相關概念之錯誤可歸納出五大原因：過度簡化絕對值定義之口訣、無法進行絕對值概念中「幾何概念」與「算術概念」之間的轉化、不瞭解絕對值概念中各同義詞之間的關係、以偏概全絕對值之定義以及文字符號概念之理解困難。文後尚有提供絕對值相關教學改善的建議。

This study aims to explore the kinds of difficulties encountered by junior high school students in solving problems related to absolute value as well as analyzing and identifying the probable causes of such difficulties. It is hoped that the results from this attempt can provide teachers with useful information regarding how to improve their instructional practices and plan remedial instruction, thereby enhancing their teaching effectiveness. \n\n The main methodology for this study is survey design supplemented with clinical interviews that allowed for in-depth information collection regarding problem solving strategies and difficulties from selected respondents. During the first stage, a literature review was conducted on research studies that focused on absolute values. This was followed by discussions with several junior high school mathematics teachers relating to learning difficulties they observed. Subsequently, a paper and pencil test instrument on absolute values with three main dimensions was compiled by the author to test the learning status of the participating students. Their performances would form the basis for selecting them to participate in the second stage of the study, namely, the interview phase. All clinical interviews were unstructured and they were recorded and transcribed into verbal records. Analyses were then performed to identify the presence of conceptual misunderstandings and explored the causes of such difficulties. \n\nIt was found that students’ conceptual errors on absolute values can be classified into five different types, namely, oversimplifying the definition of absolute value into mnemonic phrases, inability to perform inscriptional transformation between geometric properties and arithmetical concepts of absolute values, incomprehension of the relationships among the synonyms related to the concept of absolute value, over-generalizing the definition of absolute values and difficulties in understanding the connotation behind letter symbols. Several suggestions regarding instructional practices as well as future direction of research based on the present findings were provided at the end of this study.