一位體制外教師實施臆測教學在造例階段的任務設計之行動研究

本研究旨在探討一位體制外教師初次設計臆測任務，在造例階段的任務設計及實踐的行動歷程中，透過教學實踐來修正造例設計。研究者使用行動研究，以任教的補習班為研究場域，一共設計二個任務，每個任務執行二個梯次，行動參與者為體制外補習班的國小三年級和四年級學生。任務設計以「任務與結構要完備」與「建立適切的教學目標」為目標，透過「造例設計及數據考量的面向」與「工作單的呈現方式要能發現與教學目標相關的數學關係」，來達成在造例階段的任務設計，教學實踐後，觀察學生造例階段的課堂表現及分析學生猜想，調整設計再進行第二梯次教學行動。在臆測第一階段以達成「學生能夠獨立造例」、「掌控造例數據的正確性」、「要能整合、分類個人造例的數據，聚焦數據間的關係」為目標，第二階段是讓學生「提出符合教學目標的猜想」為目標。本研究將學生猜想分成「符合教學目標」、「新目標」「非目標」、「其他」四類，研究結果發現，影響學生提出猜想之因素有四種情況：第一種是造例數據的類型不夠豐富或是不夠多，第二種是彙整單編排位置不恰當，第三種是彙整單未出現符合教學目標相關的數據；第四種是造例數據出現錯誤或不相關的概念或關係，前三種會造成預期教學目標沒有出現，第四種學生會提出非相關或是其他的錯誤猜想，設計時透過實際演練來避開干擾數據，當猜想出現和意圖目標有相關價值，可以增加教學目標，保留成為全班猜想。最後，本研究對數學臆測造例設計、教學實踐後的修正及未來研究提出建議。

關鍵字

造例階段；數學臆測；體制外補習班

並列摘要

The research is discoursed the teacher beyond the system designed the conjecturing task in the cram school for the first time. In the stage of designing and Implementing of constructing cases, revised constructing cases by teaching. The researcher’s target is「both of task and construction needed complete」,「construct suitable teaching target」. The researcher is through strategy of data analysis and worksheet design to complete the task design of constructing cases stage. After teaching, observed the students’ performance of constructing cases stage and analyzed the students’ conjecture. Adjected the design, and then proceed on the teaching for second time. In the conjecture the target of first stage is 「student can constructing cases by himself」,「student can write down the correct data of constructing cases and can classify that」, the target of second stage is 「make students propose the conjecture conformed with the teaching target」. The research made the student’s conjecture divide into the four kinds, including 「conformed with the teaching target」,「new target」,「non-target」,「others」.the research found there are four situations which can influence student‘ s conjecture. The first kind, data of constructing cases is not enough. The second kind, the layout of worksheet is not suitable. The third kind, worksheet doesn’t appear the data relative to the teaching target. The fourth kind, data of constructing cases appear the false or non-relative concept. The first three kinds will cause the expectative teaching target can’t be appeared. The fourth kind will make students propose non-relative or false concept. When designing, through implementing teaching, can skip interferential data. When appearing the conjecture relative to the intention target, and it can increase the teaching target, retained as the class conjecture. Finally, proposed the suggestion to this research about mathematics conjecture task design, revised the conjecture task after teaching and the research in the future.