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題名：國小三年級數學多階段動態評量之研究
作者：許家驊 引用關係
作者(外文)：Jia-Hwa Shew
校院名稱：國立高雄師範大學
系所名稱：教育學系
指導教授：邱上真
張新仁
學位類別：博士
出版日期：2001
主題關鍵詞：數學問題解決；數學文字題；二步驟四則問題；評量；動態評量；教學中介；可能發展區間；mathematics problem solving；mathematics word problem；two-step operator compound word problem；assessment；dynamic assessment；instructional intervention；Zone of Proximal Development (ZPD)
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本研究旨在整合動態評量取向來建構一評量與教學結合的「多階段動態評量」模式，對國小三年級學生在數學「二步驟四則問題」單元教學上的學習表現，作系列性的評估及促進。
依據上述主旨，本研究可歸結出三項研究目的：（1）建構多階段動態評量模式。（2）探討多階段動態評量對個體學習的描述、診斷及促進功能。（3）評估多階段動態評量所發揮的功能實效。
為達成這三個研究目的，首先研究者藉由對教學流程、動態評量流程的分析及搭配來建構所需模式，其次根據此一模式發展所需各項工具、設計實施程序，最後依照實施程序、運用工具來收集研究資料並加以分析。
以研究的樣本來說，共有41位三年級學生參與研究，但隨著研究階段的需要，樣本人數漸次篩減，第一次單步驟數學文字題解題測試及二步驟四則問題作業前測共有41位個體參加，其中27位未精熟者接著接受標準化中介學習，之後12位需讀題協助以上的個體繼續接受非標準化中介學習。之後的二步驟四則問題作業後測、三步驟遷移測試、第二次單步驟數學文字題解題測試則有27位個體參與。
以研究的模式來說，係結合二步驟四則問題教學的進行將評量的流程分為輸入、處理、輸出三個階段來實施。輸入階段主要在設計評量工具及蒐集個體先備數學能力資料。處理階段主要在於整合使用評量工具及先備能力資料來進行動態評量的各項程序（前測、標準化中介、非標準化中介、後測及遷移測試），並蒐集個體在協助後單步驟數學解題能力的改變，而輸出階段則主要在將處理階段所得之資料作整體及個別式的分析。
以研究的實施程序來說，在前置檢核階段，共有4位學術專家及12位實務專家參與多階段動態評量模式建構的評定。在準備階段，進行各項評量工具的分析設計及建立單步驟數學解題起始能力。在執行階段，則以各項二步驟數學解題作業及中介系統來進行動態評量的流程，並蒐集個體第二次的單步驟數學解題表現。在分析階段，則分別以團體及個案為基本分析單位，來分析個體的各項學習表現。最後在後效評估的階段，則有12位實務專家參與教學回饋性及評量功能實效的評定。
研究的結果發現：（1）模式的建構相當良好。（2）能夠清楚細緻地描述個體於接受中介協助前後在單步驟、二步驟、三步驟各項作業上的表現狀況，並且提供足夠的訊息量。（3）能夠清楚地區辨及診斷個體於接受中介協助在二步驟作業上的表現狀況及相關學習問題，並且提供足夠的訊息量。（4）所提供的中介協助能夠明顯有效地提昇個體在單步驟、二步驟、三步驟各項作業上的表現狀況。（5）其所提供的訊息比起靜態評量更能夠提供評量上的相關訊息，且這些訊息對教師的教學反省及教學行為調整具有相當的功能。（6）標準化中介協助量數能夠相當程度地預測個體於接受中介協助後在二步驟及三步驟作業上的表現狀況。（7）發現個體各項作業的協助前表現與協助後表現都有顯著的正向相關，也就是先備能力與能力成長及新能力的開展都是有著正向的關聯。（8）二步驟解題起始能力中等者，各項能力成長較多，能力高及低者，各項能力成長較少。（9）大部份個體只有在定期考查時才會認真檢查，其比率亦與本研究各項作業表現較有關聯，且是在全部題目都寫完後，才以先將題目及算式重看一遍再重算答案的形式作檢查。（10）雖然個體各項表現的描述、診斷及補救結果均有一定的趨勢，但仍會因題型結構的不同、個體各項能力（解題先備能力等）而有局部的變異。（11）大部份的個體僅接受標準化中介協助即有所助益，但有的個體卻需再接受非標準化中介的協助才成長得較好，甚至有個體必須接受個別化的策略引導才能有所助益。
根據以上的發現，研究者歸納出幾點結論：（1）多階段動態評量所使用的評量配合教學的共生模式是可行的。（2）多階段動態評量具有描述力。（3）多階段動態評量具有診斷及區辨力。（4）多階段動態評量具有助益力。（5）多階段動態評量對能力的開展具有預測力。（6）多階段動態評量的結果具有教學回饋性。（7）多階段動態評量比起靜態評量更具有功能實效。（8）題目性質與個體的能力是造成個體表現的變異來源。（9）中介協助的安排應視個體個別差異而定。（10）個體能力的成長及發展空間與其基本先備能力有關。
最後根據這些結論，研究者再分別提出教學與評量、未來研究上及行政上的建議。
The investigator constructed a Multi-Stage Dynamic Assessment (MSDA) model that integrated some Dynamic Assessment (DA) approaches. The aim of this model is to assess and facilitate the performance of two-step mathematics word problems for third graders. The purposes of this research were three: (1) to construct a MSDA model; (2) to explore the functions of describing, diagnosing, and facilitating subject’s learning performance when MSDA model was operated; and, (3) to evaluate the overall effects after MSDA model be implemented.
First, the investigator constructed the model through analyzing and reassembling the process of instruction and DA. Second, there was design of instruments and the development of procedures according to MSDA model. Third, the administration of the instruments to collect and analyze data accordingly.
The subjects of this research were 41 elementary school children in third grade. All 41 children took single-step mathematics word problem pretest and two-step mathematics word problem pretest. These subjects could be divided into two groups. In group one, there were 14 subjects completely mastered and in group two there were 27 who did not. The 27 continued to receive two-step mathematics word problems with standardized prompting. This group was further divided into another two groups: 12 children needed more prompts and 15 did not. Finally, the 27 subjects receiving one or each prompt continued to take posttest on two-step mathematics word problem, three-step, and, single-step.
The model of this research combined three assessment stages to the instruction of two-step mathematics word problems. The input stage was to design instruments to collect mathematics prerequisite data. The process stage was to implement the procedures of DA (Pretest, standardized prompting, non-standardized prompting, posttest, transfer test), by integrating instruments and data designed and collected before. The output stage was to analyze the data obtained in the process stage on overall and individually.
At preliminary stage, four academic specialists and 12 practical specialists contributing to rate each dimension of MSDA model. Then, at planning stage, the researcher designed each instrument and collected first time subjects’ performance of single-step mathematics word problems. At execution stage, came the practice of the procedures of DA, and the second time collection of subjects’ performance of single-step mathematics word problem solving. During analytical stage, the researcher begun to analyze subjects’ each performance on overall and individually. Finally, at contingency stage, there were 12 practical specialists rating the state of instructional feedback and assessment functions of MSDA model.
The findings of this research were as following. First, the construction of MSDA model was feasible. Second, the MSDA model could provide enough information to describe, discriminate, and diagnosis subjects’ performance briefly. Third, the prompting which MSDA model provided could promote subjects’ performance efficiently.
Fourth, the MSDA model could provide more information to reflect and adjust the instructional actions for teachers than the static assessment could. Fifth, the standardized prompting quantity of MSDA model provided could predict the subjects’ performance in two-step and three-step mathematics word problems effectively after they had received the prompting. Sixth, the correlation was significant between the performance of subjects with prompting and without prompting. Seventh,
the pretest performance of two-step mathematics word problems would determine the zone of ability growth, the higher and the lower grew less, the middle group grew more. Eighth, the majority of subjects checked their solving processes and results seriously just in formal examination, this tendency correlated with each performance appearing in research procedure more. These subjects checked the text and operation first, then they recalculated the answer. Ninth, there were still partial variations in tendency of subjects’ performance, although results of description, diagnosis, and facilitation had existed some general pattern. Tenth, the majority of subjects with standardized prompting could perform better than before, but minority of subjects had to continue to receive non-standardized prompting, even individualized strategic guidance in order to facilitate the performance efficiently.
Based on the above findings, the conclusions of this research were proposed as following. First, it was feasible that the procedure of assessment integrated teaching be used in MSDA model. Mean while, it was beneficial for assessment and teaching each other, too. Second, the MSDA model could provide descriptive, diagnosis, discrimination, predictive and facilitation information for the performance of third graders. Third, the MSDA model could provide more instructional feedbacks and assessment functions for teachers than the static assessment could. Fourth, the variations between subjects’ performance originated from problem difficulty and individual ability. Fifth, the providing of prompts had to be determined by individual variations. Sixth, the zone of ability growth had correlation with individual prerequisite ability.
Finally, the researcher provided some suggestions for teaching, assessment, future study, and administration according to the conclusions just mentioned.
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