Hsu Hui-Yu

• Doctor of Education
• Professor (Full) at National Tsing Hua University

This paper presents systematic survey of empirical studies that implement neurocognitive tools to study mathematical processing, learning and problem solving. The survey comprised three stages: identification, screening, and analysis. The search was restricted to English-language papers published in research journals. Of a total of 35,692 records t...

本文以臺灣資賦優異高中生與一般生為對象，探究其在函數圖形與方程式表徵轉換解題行為和腦波表現。以瑞文氏空間智力測驗篩選出33位資賦優異生及38位一般生，檢測兩組學生的行為表現和腦波反應。就解題行為分析顯示資優生答題正確性顯著高於一般生；兩組學生在答題的反應時間則無顯著差異。就腦波分析顯示，所有學生在函數圖形與方程式轉換階段（S2）的腦區反應顯著高於函數圖形閱讀階段（S1），顯示函數圖形和方程式表徵轉換需要較高的認知資源。另從P300分析顯示，函數圖形和方程式表徵轉換會造成側腦化現象。就兩組學生比較，其在閱讀函數圖形階段，事件相關電位（event-related potential）成分均無顯著差異，顯示兩組學生在函數圖形閱讀階段腦區反應並無顯著差別。但在函數圖形與方程式表徵轉換階段，資賦優異學...

Leikin 所發展的測驗 工具瞭解臺灣學生創造力的表現，並以數學成就測驗 SAT-M 將學生區分為高、中、低三群，探 究數學成就是否影響數學創造力表現，最後，探究數學創造力與一般創造力是否存在關聯性。 研究樣本為新竹地區三所國中共 313 位八年級學生。研究結果包括： (1)八年級學生在四題數 學創造力問題流暢性、靈活性、獨創性、和創造力面向的表現均呈現顯著差異。其中，距離問題 在流暢性、靈活性、獨創性和創造力表現最佳。而果醬問題則在流暢性、靈活性、獨創性和創造 力表現最差。進一步將四題數學創造力問題區分為幾何和代數，分析顯示學生在流暢性、靈活 性、獨創性、創造力，幾何均顯著高於代數。 (2)不同數學成就的學生在流暢性、靈活性、獨創 性、創造力等部分皆達顯著性差異，此現象顯示學生的數學成就...

In mathematics education research, visualization is generally referred to as the product and the process of creating, using, interpreting, and reflecting on visual information. It plays an important role in mathematical thinking and in most branches of mathematics: there is general consensus in the mathematics education community that visualization...

Over the past few decades, the impact of mathematical instructional tasks on student learning has been recognized and studied. Mary Kay Stein and a group of colleagues, including Edward Silver, proposed an analytical scheme known as the Mathematical Tasks Framework (MTF). They also identified the levels of cognitive demand specific to mathematical...

Thius document includes a collection of the position documents presented at the International Workshop of Israel Science foundation. https://curiosity-isf.edu.haifa.ac.il/

The study adopted an ERP methodology to examine two psychological constructs-field-dependence-independence (FDI) and symmetry (SYM)-on geometry problem solving. Based on a newly developed instrument, analyses of Taiwanese high school students showed that both FDI and SYM significantly influenced students' response accuracy (Acc). The FDI also deter...

Solving geometry problems is challenging for students of all ages. The complexity of geometry problems is multidimensional and is linked to visualization, auxiliary constructions required for solutions, computational and proof skills, and deep and robust knowledge of geometry concepts and their properties (definitions, axioms, and theorems). In thi...

This chapter reports an investigation on Taiwan middle school teachers’ collection of mathematical instructional tasks. Specifically, the analysis focuses on geometry tasks from a cognitive-complexity perspective. Six Taiwanese middle school teachers teaching at schools with different levels of mathematics performance participated in this study. Th...

In this study, we aim to investigate the types of questions that Taiwanese mathematics teachers pose and in which instructional situations they do so during mathematics lessons at the secondary school level. The classroom teaching of six experienced mathematics teachers was analyzed. Quantitative analysis showed that the mathematics teachers tend t...

In this paper we report the results of a study in which we investigated how formal education and shadow education in Taiwan provide students opportunities to learn mathematics. Based on the conceptual framework of Opportunity to Learn (OTL), aspects specific to formal education, including mathematics curriculum, mathematics textbooks, and teachers’...

本研究旨在探討動態幾何環境之拖曳行為如何影響學生理解不同四邊形間的包含關係。從三位五年級學生個案資料分析得知：第一，即使學生能在紙筆測驗正確回答四邊形定義，動態幾何環境圖形的呈現方式仍會改變他們對於定義的想法。第二，從分析學生在動態幾何環境拖曳，區別出六種不同認知行為和思維類別：（1）認為拖曳無法窮盡各種圖形；（2）關注圖形外觀；（3）微幅調度；（4）以特定性質為目標；（5）結合表格分析策略；（6）從一般例到特例。不同拖曳行會影響學生後續是否成功建構四邊形的包含關係。第三，研究提出學生不同判定四邊形關係的思維模式，包括分類思維、交集思維和包含思維。依據研究結果，本文進一步提出動態幾何環境拖曳和包含關係的研究和教學相關建議。 This study investigated how draggi...

We used mathematics-pedagogy tasks (MPTs) to design content and methods (pedagogy) courses to facilitate the professional growth of pre-service elementary teachers, especially those who did not study in mathematics-related areas. MPTs, together with the use of relevant theories, enable pre-service elementary teachers to coordinate the learning of m...

This study explored the perspectives of mathematics teacher educator-researchers (MTE-Rs) on the use of theory in facilitating teacher growth. We adopted the framework of the theory-centered scholarship triangle (Silver & Herbst, 2007) to probe the underlying meanings of perspectives on theory use expressed by MTE-Rs. Qualitative analysis revealed...

The chapter begins with the present challenges that mathematics educators in Taiwan are facing. It outlines the hierarchical structure of in-service teacher development and highlights how the top-down approach often adopted may not address the needs of classroom teachers. The authors of the chapter next describe an innovative school-based program,...

本研究探討國中生如何在動態幾何環境下臆測幾何性質。研究以程序性反駁模式為中介理論架構設計幾何臆測學習單，目的是瞭解國中生如何在動態幾何環境中建構圖形案例，並依據案例來臆測正確的幾何性質。其中，本研究特別強調將動態幾何軟體定位為「例子產生器」，結合幾何圖形案例測量值的紀錄表格，鷹架學生進行臆測活動。研究樣本為15位七年級國中生，以質性分析方法為主、量化資料輔助說明下，研究發現（1）動態幾何環境下，幾何性質本身涉及測量值關係的複雜程度及幾何性質是否容易在圖形上視覺觀察，影響學生造例與臆測表現。同時這兩個因素影響學生在動態幾何環境下的認知行為和學習困難；（2）具備良好的幾何物件分類系統是在動態幾何環境中成功臆測的重要關鍵；（3）學生對圖形進行分解與重組操作有助於在動態幾何環境中察覺圖形中蘊含的特徵...

本研究旨在探討分類活動對提昇國中生判斷四邊形包含關係的成效。幾何的包含關係是由幾何性質之間的上下關聯性所形成的集合概念，分類活動提供學生在給定的幾何圖形分類時，觀察圖形隱含的性質，且在命名時掌握圖形的定義，逐漸理解及判斷包含關係。本研究以前實驗設計法（pre-experimental design）之架構，採單組前後測量設計（one-group pretest-posttest design），研究結果發現（1）八年級學生在教學前對四邊形包含關係的迷思概念有以下三種：第一、學生習慣注意矩形和正方形邊長的屬性，不易知覺其角度的屬性。第二、學生的典型（prototype）心像容易導致無法接納非典型圖形。第三、學生對梯形與平行四邊形的互斥關係理解上有困難。（2）學生經過圖卡分類教學介入後在正方形與...

This paper aims to explore the educative power of an experienced mathematics teacher educator-researcher (MTE-R) who displayed his insights and strategies in teacher professional development (TPD) programs. To this end, we propose a framework by first conceptualizing educative power based on three constructs—communication, reasoning, and connection...

We examined geometric calculation with number tasks used within a unit of geometry instruction in a Taiwanese classroom, identifying the source of each task used in classroom instruction and analyzing the cognitive complexity of each task with respect to distinct features: diagram complexity and problem-solving complexity. We found that instruction...

This paper presents three investigations related to algebra problems; (1) Taiwanese sixth graders' problem-solving performance on story problems, word-equation problems, and equation problems; (2) Taiwanese mathematics teachers" posing sequences towards these problems and their hidden teaching beliefs; and (3) the relationship between student's per...

In this paper, we report on a comparison of the treatment of addition and subtraction of fractions in primary mathematics textbooks used in Cyprus, Ireland, and Taiwan. To this end, we use a framework specifically developed to investigate the learning opportunities afforded by the textbooks, particularly with respect to the presentation of the cont...

In Taiwan, students have considerable experience with tasks requiring geometric calculations with number (GCN) prior to their study of geometric proof (GP). This dissertation examined closely the opportunities provided to Taiwanese students??? experiences with GCN and their performance on GCN and GP. Three sequential studies were conducted, corresp...

In this paper, we report on an analysis of the treatment of addition and subtraction of fractions in elementary mathematics textbooks used in Cyprus, Ireland, and Taiwan. For this purpose we developed and applied a framework to investigate the learning opportunities afforded by the textbooks. We found key similarities and differences among the text...