初任教師建立數學臆測規範之行動研究：以高年級為例

本研究的目的是探討初任教師建立數學臆測教學規範的歷程中，可能發生的問題以及因應方式，進而在不同的數學臆測教學階段發展出相關的社會規範以及數學臆測規範。本研究方法為行動研究法，以研究者任教的五年級新班級為研究場域，分別在七個單元中執行數學臆測教學。研究期間透過教材分析資料，以及教學現場錄影錄音、學生工作單、和諍友的對話等資料蒐集與分析，進行教學反省與改進。本研究在各階段建立的數學臆測教學規範包括社會規範和數學臆測規範。社會規範有階段一的「勇於嘗試，有自信的作答」、「說清楚、講明白」、「傾聽別人說話」、「各單手拿報告單」;階段二的「小組工作單放在小組桌的上方」、「檢驗放置」、「用紅筆批閱」、「用紅筆修改」、「去明星化」、「用不到的資料放班櫃上」，數學臆測規範有階段一的「排序資料」;階段二的「依數據提猜想」、「個人猜想要報告討論」、「依數據說話、對照」、「合併個人猜想，形成小組猜想」、「猜想單上要以文字說明，不以舉例說明」、「分類好的每一類個人猜想都要提出一個小組猜想」;階段三的「合併小組猜想，形成全班猜想」、「前提不當猜想提出」;階段四的「全班猜想前，加上前提」;階段五的「以合理的數學知識來解釋數學猜想」。在不同的數學臆測教學階段建立不同的社會規範以及數學臆測規範。研究結果發現：數學臆測教學規範支撐著整個數學臆測教學，在不同的數學臆測教學階段，會產生不同的規範，有些規範是屬於社會規範，有些規範是屬於數學臆測規範。而隨著不同的數學臆測教學階段發展會發現數學臆測規範的比重會比社會規範來的越來越重。最後，本研究對初次實施數學臆測教學之教學者和對建立數學臆測教學規範之教學者給予建議並提出未來研究方向。

關鍵字

臆測教學；規範；社會規範

並列摘要

The purpose of this study is to discuss the problems and the solutions that may occur when establishing the norms of mathematics conjecturing teaching as a first-year teacher, thereby, developing related social norms and mathematics conjecturing norms in different mathematics conjecturing teaching stages. This study uses action research, with the fifth-grade class taught by the researcher as the research field, doing mathematics conjecturing teaching in seven units respectively. With analyzing data and teaching materials, recording the videos and conversations, student worksheets and dialogues with friends, the researcher reflects on self-teaching and improves. The norms of mathematics conjecturing teaching which built in different stages in this research include social norms and mathematics conjecturing norms. Social norms consist of stage one “Willing to try. Answer confidently.”, “Speak clearly.”, “Listen to others.” and “Two students hold the worksheet with one hand each.”; stage two “Put group worksheet in the middle of the table.”, “Examine worksheet position.”, “Mark with red pens.”, “Revise with red pens.” , “Data speaks louder than star students.” and “Put the materials which are not in use on the cabinet.” Mathematics conjecturing norms consists of stage one “Sort the data.”; stage two “Conjecture boldly. Come up with ideas according to the data”, “Personal opinion should be presented and discussed”, “Speak according to the data and compare the conjectures with the data.”, “Combine personal opinions into a group opinion.”, “Conjecturing worksheets should be written down in words instead of giving examples.” and “Each classified personal conjecture of different category should bring up a group conjecture.”; stage three “Combine group opinions into a class opinion.” and “Premise shouldn’t be regarded as conjecture.”, stage four “Add premise before class conjecture.” and stage five “Explain math conjecture with reasonable math knowledge.” Establish different social norms and mathematics conjecturing norms in different mathematics conjecturing teaching stages. The research results find out that mathematics conjecturing teaching norms support the whole mathematics conjecturing teaching. There will be different norms in different mathematics conjecturing teaching stages. Some of them are social norms, and some of them are mathematics conjecturing norms. It comes out that the proportion of mathematics conjecturing norms increases more than social norms when developing different stages of mathematics conjecturing teaching. Finally, this research provides suggestions to the first-time mathematics conjecturing teaching instructors and establishing mathematics conjecturing norms instructors and gives directions to future research.