Ying-Hao Cheng

• University of Taipei

This study explored mathematics teachers’ reasoning regarding their instructional design for technology use in teaching mathematics. Various types of qualitative data were obtained and analysed from a sample of 19 secondary and 28 primary preservice teachers. The findings showed that the purposes of technology use, teachers’ conceptions of mathemat...

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...

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...

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...

Geometry theorem proving involves skills that are difficult to learn. Instead of working with abstract and complicated representations, students might start with concrete, graphical representations. A proof tree is a graphical representation of a formal proof, with each node representing a proposition or given conditions. A computer-assisted learni...

This chapter traces the long-term cognitive development of mathematical proof from the young child to the frontiers of research. It uses a framework building from perception and action, through proof by embodied actions and classifications, geometric proof and operational proof in arithmetic and algebra, to the formal set-theoretic definition and f...

In this article, we discuss the complexity of geometric proofs with respect to a theoretical analysis and empirical results from studies in Taiwan and Germany. Based on these findings in both countries, specific teachings experiments with junior high school students were developed, conducted, and evaluated. According to the different classroom and...

Domain-general inductive skills are important in science, math, and other disciplines but are difficult to teach directly. We have designed a computer-assisted learning environment called InduLab for learners to perform inductive tasks with self-directed experiments. In the experiment, 50% of 66 fourth grade students could find exterior angle prope...

In different international studies on mathematical achievement East Asian students outperformed the students from Western countries. A deeper analysis shows that this is not restricted to routine tasks but also affects students’ performance for complex mathematical problem solving and proof tasks. This fact seems to be surprising since the mathemat...

The reading and coloring (RC) strategy has been verified that it can enhanced incomplete provers' performance to Taiwan junior high students while they had learnt the multi-steps formal geometry proof. In this study, we transfer the RC strategy into whole class regular teaching and explore its effectiveness and limitation. The results show that the...