數學新手與資深教師對學生學習困難的預測與教學策略之比對與分析：以一元一次方程式為例
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2016
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本研究為質性研究，針對新北市某偏鄉國中的新手與資深教師，七年級上學期「第三單元、一元一次方程式」的課程教學中，進行長期的課堂觀察記錄。欲探討新手與資深教師在針對學生學習困難上的預測，以及教學策略使用上的差異為何；同時，也進行該校學生學習困難的蒐集與整理。
兩位受測教師在知曉研究目的之狀況下進行教學，本研究的流程會先讓教師進行課前預測，再進行課堂的觀察與記錄，課程結束後的一兩天內再進行學生學習狀況測驗，並彙整告知受測教師，並繼續再後續課程觀察教師的因應教學策略會作何改變。
研究針對兩位教師在課前的預測進行統整與比對，並與後續學生學習困難整理對照，試圖描繪教師們容易忽略的細節；以及利用觀課筆記與教學影帶編碼分析，比較兩位教師在教學策略使用上的差異。
本研究的新手與資深教師在學生學習困難的預測上，僅有些微的差異，在與學生實際課後反應的學習困難對照，發現兩位受試教師皆有小部分的誤差，但也各有預測準確的部分。在教學策略上，新手教師使用的方式較為開放，多數的課堂時間皆以問答互動的方式進行，並時常利用一般化的例子或類比的方式進行引導，再類推至代數符號上；資深教師則以課本課程脈絡作為教學的主軸，並不時的針對其預測的學生學習困難處進行舉例、澄清，在課程進入中後段則採用大量的學生練習與上台演示來進行教學，如此一來可藉由學生於黑板上的反應，再針對其問題進行講解。而學生的學習困難部分，許多誠如多數文獻所提及；與兩位教師的預測進行比對後，建議教師須針對代數相關的重要專有名詞說明清楚，以及容易混淆的相關概念進行澄清，例如：化簡、列式、式子與方程式等，以及強化學生對等號意義上的認知。
This research focuse on teachers’ prediction and subsequent teaching strategies－using first degree equation in one variable as an example. The researcher spend about 4 months to follow a novice and an expert mathematics teacher, who predict their students’ learning diffculties before they start teaching to record their subsequent teaching stratieies by field notes or vedio records. We want to know the difference of predictions and subsequent teaching strategies between a novice and an expert mathematics teacher. And we also want to know what are the learning diffculties that students have at the end of the teaching session. After that the data about the problems students have are collected immediately to let the teacher know, and the changes of their subsequent teaching strategies are also recorded at their surplus classes This research indicates that a slight difference in prediction between novice and expert teacher. Comparing with students’ real learning diffculties, the prediction show the relative accuracy with some errors. Nevertheless, the diffience of subsequent teaching strategies are more worthy of our attention. The novice teacher tends to use the stratigy of questioning students at class, such as giving students general examples or using analogy for the mathematics conception to guide her students thinking and learning. The expert teacher’s subsequent teaching strategies are on the basis of the textbook, but he usually give the example or clarify some concepts at the point where he predicts the students may have learning diffcultes. Sometimes, he will give students times to practice some exercises by themselves, and ask some students to write down their calculation process on the board. As a result, he can explain for the problem. In addition, there is a difference between the teachers’ predictions and students’ real learning difficulties. Therefore, based on this discrepancies, it is advisable that teachers plainly explain and simplify mathematics concepts and terms, such as “Simplification”. Confusing concepts, such as formula and equation, should be illustrated clearly. Furthermore, the notion of equal mark should be strengthened, which may benefit students when learning algebra.
This research focuse on teachers’ prediction and subsequent teaching strategies－using first degree equation in one variable as an example. The researcher spend about 4 months to follow a novice and an expert mathematics teacher, who predict their students’ learning diffculties before they start teaching to record their subsequent teaching stratieies by field notes or vedio records. We want to know the difference of predictions and subsequent teaching strategies between a novice and an expert mathematics teacher. And we also want to know what are the learning diffculties that students have at the end of the teaching session. After that the data about the problems students have are collected immediately to let the teacher know, and the changes of their subsequent teaching strategies are also recorded at their surplus classes This research indicates that a slight difference in prediction between novice and expert teacher. Comparing with students’ real learning diffculties, the prediction show the relative accuracy with some errors. Nevertheless, the diffience of subsequent teaching strategies are more worthy of our attention. The novice teacher tends to use the stratigy of questioning students at class, such as giving students general examples or using analogy for the mathematics conception to guide her students thinking and learning. The expert teacher’s subsequent teaching strategies are on the basis of the textbook, but he usually give the example or clarify some concepts at the point where he predicts the students may have learning diffcultes. Sometimes, he will give students times to practice some exercises by themselves, and ask some students to write down their calculation process on the board. As a result, he can explain for the problem. In addition, there is a difference between the teachers’ predictions and students’ real learning difficulties. Therefore, based on this discrepancies, it is advisable that teachers plainly explain and simplify mathematics concepts and terms, such as “Simplification”. Confusing concepts, such as formula and equation, should be illustrated clearly. Furthermore, the notion of equal mark should be strengthened, which may benefit students when learning algebra.
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新手教師, 資深教師, 一元一次方程式, 學生學習困難預測, 教學策略, Novice teacher, Expert teacher, First degree equation in one variable, The prediction of students’ learning diffculties, Teaching strategies