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題名:以階層式試題反應理論為基礎之電腦化全數數感多元評量開發與應用研究
作者:李淑娟
作者(外文):LEE, SHU-JUAN
校院名稱:國立臺中教育大學
系所名稱:教育資訊與測驗統計研究所
指導教授:施淑娟
郭伯臣
學位類別:博士
出版日期:2018
主題關鍵詞:數感多元評量系統數感解題策略縱貫研究潛在成長模式number sensemultiple assessment systemproblem-solving strategies with number senselongitudinal researchlatent growth modeling
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本研究目的是以數感多向度為評量架構,建置一套電腦化全數數感多元評量系統,用以探討中年級學生的數感能力發展並獲得更完整正確的數感評量回饋資訊,進而提昇中年級學生的數感學習成效。研究方法是先評估三種試題反應理論與施測資料的適配度以獲得數感最佳測量模式。再以此評量系統蒐集縱貫研究資料,據以分析中年級學生的數感解題策略並以潛在成長模式了解學生在數感總體能力與四個領域能力的成長變化,此外,性別、家庭收入、國語學業成績等預測變項亦加入潛在成長模式中共同分析對數學學習成就的影響。
本研究主要發現如下:
一、 本研究的全數數感評量架構以二階四向度模式最為適配,最佳測量模式為HO-IRT模式。
二、 中年級的數感解題成功策略以一次就估中或使用有方向性的漸進調整策略為主,數感解題失敗者所使用之策略對於題型所暗示的調整方向較無法察覺,三個年級與不同性別的學生皆有類似情況。
三、 在數感總體能力與四個領域能力的潛在成長模式中,中年級學生的起始點與成長率有顯著的個別差異,成長變化軌跡並非人人相同。學生在數感總體、向度1與向度3能力的成長軌跡上出現天花板效應(ceiling effect),向度4能力則有馬太效應(Matthew effect)存在。
四、 在數感總體、向度1與向度3能力的條件式潛在成長模式中,中年級學生的國語學業成績愈佳,起始點就愈高,數學學業成績表現就越好;男生的起始點比女生高,但成長率卻是女生明顯增加較多。在向度2能力的條件式潛在成長模式中,中年級學生的國語學業成績愈佳,起始點和成長率就愈高,數學學業成績表現就越好;男生的起始點和數學學業成績都比女生高。在向度4能力的條件式潛在成長模式中,中年級學生的國語學業成績愈佳,起始點和成長率就愈高,數學學業成績表現就越好;男生在數學學業成績的表現明顯優於女生。家庭收入對五個條件式潛在成長模式的起始點和成長率沒有影響。
綜合上述,本研究所開發之數感評量系統有助於瞭解中年級學生之數感總體能力與各領域能力,並且能同步記錄與分析學生的數感解題策略,評量分析結果將可提供改進國內數學教育之參考。
The goal of the study is to construct a computerized whole-number number sense multiple assessment system with multilevel factor number sense models as the framework for investigating the development of number sense of the third and fourth grades of elementary school, for collecting complete information on assessment of number sense and for enhancing learning efficiency. In study, the best measurement model of number sense was first determined from three item response theories by assessing model fit indices. Then the longitudinal research data were gathered by this assessment system to analyze the problem-solving strategies with number sense used by the third and fourth graders in elementary schools. Latent growth modeling (LGM) was used to understand the developmental trajectories of students’ overall number sense ability and four domain abilities (L1 to L4). Furthermore, the effect of background predictors including gender, income status and Chinese achievement on mathematics achievement were evaluated.
The major findings in this study are shown as follows:
1. Second-order four factors model is the most appropriate for the computerized whole-number number sense multiple assessment system established in this study and HO-IRT model is the best assessment model.
2. The strategies 「No adjustment and hitting at the first time」or directional adjusted strategies used majorly by the successful problem solvers in 3th and 4th grades. The strategies used by the unsuccessful problem solvers in 3th and 4th grades for the reorientations implied from assessments are relatively undetectable. Strategies used by genders are similarity between the successful and unsuccessful problem solvers in 3th and 4th grades.
3. In latent growth model of overall number sense ability and the four domain abilities, there is a significant difference between initial level and rate of growth change of the third and fourth grades of elementary school. Growth trajectories of students are not the same. Ceiling effect is observed in the growth trajectories of overall number sense ability and abilities of L1 and L3. Matthew effect exists in L4 ability.
4. In conditional latent growth model of overall number sense ability and the abilities of L1 and L3, students with better grades in Chinese language have higher initial level and better achievement in mathematics. The initial level of males is higher than that of females, however the rate of growth change of females increases significantly compared to that of males. In conditional latent growth model of L2 ability, students with better grades in Chinese language have higher initial level and rate of growth and better achievement in mathematics. The initial level and mathematics achievement of males are higher than that of females. In conditional latent growth model of L4 ability, students with better grades in Chinese language have higher initial level and better achievement in mathematics. Mathematics achievement of males is better than that of females. In conditional latent growth model of 5 abilities, income status has no effect on initial level and rate of growth.
To sum up, the computerized whole-number number sense multiple assessment system constructed in this study may contribute to clarification of the assessment of number sense ability and development of assessment tool and mathematics education in Taiwan.
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