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題名:試算表融入數學素養動態評量的發展與應用
作者:蕭嘉偉
作者(外文):Chia-wei Hsiao
校院名稱:國立臺南大學
系所名稱:教育學系測驗統計博士班
指導教授:洪碧霞
學位類別:博士
出版日期:2012
主題關鍵詞:試算表數學素養動態評量階層線性模式方程式應用mathematical literacydynamic assessmenthierarchical linear modelingspreadsheetformula application
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本研究目的在探討國中數學素養落後學生的表現特徵與介入需求,研究中發展電腦化基礎數學素養評量及試算表融入數學素養的介入設計,統整稱為動態評量系統。首先藉由電腦化基礎數學素養評量描述落後學生的特徵,再針對學生的方程式應用解題表現,運用試算表環境建構數學解題活動的引導與支持,讓數學落後學生以小組合作的方式進行學習,鷹架建構的邏輯是循序增加未知數個數及情境複雜度。本研究討論的議題包含電腦化基礎數學素養評量的信效度、動態評量的介入效益、以及落後學生歷程作業的成長量。電腦化基礎數學素養測驗的施測樣本為臺南市870位8年級學生。測驗內涵同時包含PISA所釋出的數學素養試題及本研究所研發的Flash操作型試題,目的在盡量與PISA未來的電腦化測驗接近。動態評量介入的實驗樣本共有29位,介入時距共十週,主要發現如下:
一、電腦化基礎數學素養評量的平均IRT難度b參數為0.41,鑑別度D值為0.43,較一般數學成就測驗困難。在信度方面,四式的內部一致性信度α係數介於0.71 ~0.85之間,評分者一致性信度介於0.94~1之間。在效度方面,數學素養與在校數學成就之相關為0.582,與在校國語成績為0.576,顯示數學素養與在校數學和國文成就相關的差距不大。此關聯組型與PISA 2009及基本學力測驗國文與數學得分的相關情形類似。
二、臺南市8年級學生的數學素養與國際OECD平均15歲學生的數學素養表現相近,但有較高比例未達數學素養水準1。在性別差異上,男、女學生數學素養未達顯著差異,男學生的標準差略大於女生。數學素養未達水準2的男學生比例較女學生多4.5%;數學素養水準4以上,男學生所占的比均略高於女學生,此結果與臺灣男女學生於PISA 2009不同表現水準分配情形一致。
三、數學素養落後學生能理解熟悉情境或例行的數學問題描述、能運用題目所提供公式解題、也能報讀基本的統計圖表資訊;但他們尚未能有效辨識圖形與數字的規律、也無法有效應用已知方程式解題、將文字轉譯成數學方程式也還有些障礙。
四、動態評量實驗組與控制組學生數學素養成長斜率呈現顯著差異,實驗組每隔一次評量,數學素養增加約35.6分,控制組則未能呈現成長。實驗處理可解釋約6%的成長斜率的變異。數學素養成長明顯的學生,在動態評量試算表應用解題作業表現較佳,多能依據提示修正自己的錯誤。而數學素養成長較不明顯或退步的學生試算表應用解題的表現較不理想。
綜合以上資訊,本研究對動態評量設計和實施提出未來研究和應用的建議。
The purpose of this study was to investigate the characteristics of students below level 2 on mathematical literacy assessment. The computerized basic mathematical literacy assessment and the spreadsheet integrated mathematical literacy intervention tasks were composed as a dynamic assessment system. Students worked on the tasks collaboratively. The number of relevant variables and the degree of complexity for problem situations were increased sequent to scaffold students’ learning progress. The issues included were the validity of the computerized basic mathematical literacy assessment (CBMLA), the intervention effect, and the correlation of growth slopes between formative and objective assessments. Eight hundred and seventy 8th graders of Tainan were selected as the norm sample for CBMLA. The PISA released items were converted and the flash interactive items were developed to form CBMLA. Fifty-eight 8th graders of Tainan were included as the experiment and control sample of this study. Half of them were assigned to the experiment group,
and the other half were in the control group. The intervention period lasted for ten weeks.
The main findings were summarized as followings:
1. The average of IRT difficulty parameter b is .41 of the CBMLA. The average discrimination D is .43. The internal consistency indices α of four form were between .71 to .85. The index of inter-rater consistency were between .96 to 1. The Pearson correlation coefficients of the assessment and school mathematics and language grades were .582 and .576, respectively. The correlation coefficient pattern was similar to the PISA 2009 and the basic competence test (Bctest)
in Taiwan.
2. The mathematical literacy of 8th graders of Tainan were similar to OECD 15-year-old students. The boys’ mathematical literacy average was slightly lower than girls’, but there was not significant differences. The standard deviation of boys’ mathematical literacy was larger than the girls’. The pattern of gender difference in Tainan was similar to the results of Taiwan PISA 2009.
3. The students below level 2 on CBMLA can read familiar situations or routine mathematical description of the problem. They were able to apply the formula provided by the item, and they could also use the basic statistics information from charts to solve the problem. But they could not identify the pattern of graph and numbers. They had some barriers to convert the text into
mathematical equations.
4. The slope of mathematical literacy of experimental group was significantly higher than the slop of control group. Experiment group students Increased 35 points between two assessments.
The treatment group can explain about 6% growth variance.
Based upon the results, some suggestions for further development and application of dynamic assessment on mathematical literacy were provided.
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