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Item 108課綱高一數學素養試題開發(2022) 陳宗聖; Chen, Tsung-Sheng針對新實行的「108課綱」所做的改變，素養導向的評量試題也隨之興起。本研究旨在開發以素養為導向的評量試題，並作為發展教師在素養試題之命題上的參考範例。為了達到研究目的，研究者以「大學入學考試素養導向命題簡介」為依據，並從生活情境及科普書籍取材，以高中數學第一二冊內容為範圍，同時考量試題需符合高中生的數學能力，進而產出以素養為導向的評量試題。研究方法採用半結構式訪談與量表問卷，以研究者任職學校的教師及學生為施測及訪談對象，以期達到良好的信效度，以作為未來高中數學教師在素養導向的命題上的參考及依據。Item 108課綱高中素養試題開發(2023) 張紜愷; Chang, Yun-Kai隨著新課綱的頒布，教學現場出現眾多素養試題，一道素養試題的優劣該如何判斷是一大難題。本研究的目的在於開發符合108課綱的數學素養試題，並探討優良的素養試題需要具備的條件及元素。研究者以大學入學考試中心公告的「大考命題方向說明」及「108新課綱素養導向命題精進方向」作為優良數學素養試題的參考原則，並以龍騰版高一、二數學教科書內容作為命題依據，開發出符合優良定義的數學素養試題。本研究以現職教師作為審題及訪談對象，提高研究的信度與效度。Item Item A Dynamical Systems Approach to Complementarity Problems(2020) JAN HAROLD MERCADO ALCANTARA; JAN HAROLD MERCADO ALCANTARAnoneItem Item A note on gradient estimate for the equation associated to the p-Laplace operator(2014) 藍格維In this paper, we study p-Laplace operators on complete noncompact manifolds. Ac- cording to Kotschwar-Ni gradient estimat for positive p-harmonic functions, we extend their result to more general equation associated to the p-Laplace operator whenever the sectional curvature of M has lower bound.Item Item A Scalable and Ultrafast Eigensolver for Three Dimensional Photonic Crystals on GPU(2017) 蔡欣翰; Tsai, Hsin-Han無中文摘要Item An Experimental Performance Study of Polynomial Preconditioner in PCG(2022) 張耀文; Chang, Yao-WennoneItem An ordinary differential equation approach for nonlinear programming and nonlinear complementarity problem(2019) 伊爾凡; Irfan NurhidayatnoneItem AN OVERVIEW OF ZETA FUNCTIONS ON HYPERSURFACES OVER FINITE FIELDS AND DWORK'S THEOREM(2014) 連城We study the Hasse Weil zeta function associated to a hypersurface of dimension n over finite field. The main goal is to give an overview of the proof of Dwork's Theorem. The main ingredients are p-adic analysis, linear algebra, and Weierstrass Preparation TheoremItem APOS教學對七年級學生學習線型函數概念之影響(2013) 張 耀文本研究主要目的是以「線型函數」單元為主題，探討「APOS教學方式」與「傳統教學方式」兩種教學，對學生學習線型函數概念的影響。研究設計是採準實驗研究法。研究對象為台北市某國中七年級學生，分兩組為實驗組與對照組。實驗組進行APOS教學課程，對照組則進行傳統教學課程。 兩組的教學教材，皆為翰林版國民中學數學課本第二冊與習作為主。但APOS教學活動是以Asiala等人(1996)所建立的「概念層次」為架構，將課本與習作重新依概念層次編排而成；傳統教學是依照翰林版國民中學數學課本第二冊所呈現的內容順序進行。 研究依據Dubinsky(1991)所提出的概念發展層次：「動作」、「過程」、「物件」及「基模」，進行上述重組教材實驗教學，並設計線型函數測驗卷（後測及延後測），來安置學生在教學後與經過一段時間後（約莫一個月）的線型函數概念層次，以分析學生概念改變及保留情形。 本研究主要發現如下： 1．經過教學後，實驗組與對照組學生在後測的概念層次上以「百分比同質性檢定」未達顯著水準，但兩組在延後測時則得到 p^(**)＝.041<.05，達到顯著水準。顯示接受APOS教學方式的學生概念保留的程度較傳統教學方式的學生高。 2．實驗組在三次測驗中，學生進階至「物件」層次且維持的人數較對照組多，而退階至「動作」的人數亦較對照組少，顯示APOS教學方式對學生概念提升與理解有所助益。 3．在三次測驗中，兩組在代數表徵與圖像表徵的延後測上，以「百分比同質性檢定」皆達到顯著水準；而表列表徵則在三次測驗中無顯著差異。顯示APOS 教學在函數的「代數表徵」與「圖像表徵」的概念保留上，有明顯助益。Item Applications of Smoothing Functions for Solving Optimization Problems Involving Second-Order Cone(2019) 阮成昭; Nguyen Thanh Chieu無中文摘要Item Bayesian evaluation of inequality constrained hypotheses of means for ordered categorical data(2016) 陳冠宏; Chen, Kuan-Hung本研究利用了多群組離散型驗證性因素分析模型來分析多群組的有序分類數據，主要目的在於利用貝氏估計在最小限制式的條件下，來估計模型中的閾值、潛在因子的平均與變異數等參數，我們利用了資料擴張與Gibbs抽樣的方式來估計這些參數的聯合分配。並利用貝氏因子來檢驗潛在因子的平均是否滿足不等限制的假說。而藉由模擬與實徵資料的分析，貝氏因子已被驗證在檢驗不等限制的假說上是可行的。Item Bayesian evaluation of response styles in polytomous data with multiple group factor analysis model(2016) 賴驥緯; Lai, Chi-Wei本研究之主要目的在於檢定態度量表中，作答者是否受到作答風格而影響問卷之作答，即兩群人是否有作答風格之差異。所謂作答風格乃是當潛在態度相同的兩位作答者可能會因為作答風格的差異，而做出不同的回答。本研究利用了多群組離散型驗證性因素分析模型來分析多群組的有序分類數據，其中利用貝氏估計在最小限制式的條件下，來估計模型中的閾值、潛在因子的平均與變異數以及因素負荷量等結構參數，並且使用Gibbs sampling來估計這些參數的聯合分配。再利用貝氏因子來檢驗李克氏五點量表在兩群組間是否存在作答風格差異。於本研究中，透過模擬所得之結果顯示，貝氏因子可用來檢定極端、默認肯定及默認否定等作答風格。本研究中分析「1998 年國際資訊科技教育應用研究 (SITES 1998)」之跨國五點量表問卷，選取其中來自法國及義大利的作答者，分析對於資訊融入教學的學習成效認同程度。其中，義大利的作答者相對於法國之作答者具有默認肯定之作答風格。Item Clustering analysis of trajectory data: Comparison of mixture of regression models and hierarchical clustering with dynamic time warping(2019) 蕭詠文; Hsiao, Yung-Wen路徑資料為對應著時間的曲線資料，常見於許多領域如氣候、時間序列等。而路徑資料的分群為統計分析中重要的一環，透過分群我們將相似的資料分為一群，藉此我們可以分析各群的性質甚至預測下一個資料屬於的集群。這篇論文中我們使用了兩種分群方法，混合回歸模型（mixture of regression models）和應用動態時間扭曲法的階層分群法（hierarchical clustering with dynamic time warping），透過模擬以及實際資料的分析將之做比較。 在模擬中我們以分群的正確率來比較兩個方法在不同情況下的表現，以及討論了混合回歸模型在不同情況下參數估計的結果。根據模擬結果，兩個方法並沒有絕對的優劣，而是在不同情況下擁有各自的優勢。最後則是將這兩個方法分別應用在實際資料的分析上。Item A Comparison of Three Polytomous DIF Detection Methods(2004) 吳冠瑩The performance of the three procedures -- the Logistic Regression procedure (Logi; French& Miller, 1996), the Likelihood Ratio test (LR; Thissen, Steinberg, & Gerard, 1986), and the Differential Functioning of Items and Tests procedure (DFIT; Flowers, Oshima, & Raju, 1999) in detecting differential item functioning (DIF) under the graded response model (GRM) were compared in a simulation study. Factors manipulated included sample size, differences in the ability distributions between the focal and the reference groups, and four different percentages of DIF items contained in a test.For each of the sixteen combinations, 100 replications of DIF detection were simulated. All three DIF procedures adhered to nominal Type I error rates under most conditions. LR was the most powerful among the three under all situations. DFIT was less powerful than LR, but also useful for DIF detection especially with groups of different ability distributions and relatively large percentage of DIF items. Logi, with mean Powers lower than 0.4 in all conditions, appeared to be sensitive only to items with large DIF size. In addition, the three procedures were used to assess DIF of the Cognitive Ability Screening Instrument (CASI) and the results of the DIF analysis were compared to previous studies.Item Computations on the Deuring Correspondence of Supersingular Elliptic Curves(2007) 李忠穎此篇論文是以實際例子 p=41 之情形, 驗證 Deuring Theorem 的對應性.Item Computerized Adaptive Testing for Cognitive Diagnosis in Classroom: A Nonparametric Approach(2017) 張沅培; Chang, Yuan-PeiThe Cognitive Diagnostic Computerized Adaptive Testing (CD-CAT) has been suggested by researchers as a diagnostic tool for assessment and evaluation. While model-based CD-CAT is relatively well-researched in the context of large-scale assessments, this type of system has not received the same degree of development in small-scale settings, where it would be most useful. The main challenge is that the statistical estimation techniques successfully applied to the parametric CD-CAT require large samples to guarantee the reliable calibration of item parameters and accurate assignments of examinees. In response to the challenge, a nonparametric approach that does not require any parameter calibration, and thus can be used in small educational programs, is proposed. Unlike other CD-CAT algorithms, the proposed nonparametric CD-CAT uses the nonparametric classification (NPC) method to assess and update the student's ability state while the test proceeds. Based on a student's responses, possible proficiency classes are identified, and items which can discriminate them are chosen next. The simulation results show that the proposed nonparametric item selection (NPS) method outperformed the compared parametric CD-CAT algorithms and the differences were more significant when the item parameter calibration was not optimal.