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( Leung K C Issic ),( Lin Ding ),( Allen Yuk Lun Leung ),( Ngai Ying Wong ) 한국수학교육학회 2014 수학교육연구 Vol.18 No.3
Mathematically deductive reasoning skill is one of the major learning objectives stated in senior secondary curriculum (CDC & HKEAA, 2007, page 15). Ironically, student performance during routine assessments on geometric reasoning, such as proving geometric propositions and justifying geometric properties, is far below teacher expectations. One might argue that this is caused by teachers` lack of relevant subject content knowledge. However, recent research findings have revealed that teachers` knowledge of teaching (e.g., Ball et al., 2009) and their deductive reasoning skills also play a crucial role in student learning. Prior to a comprehensive investigation on teacher competency, we use a case study to investigate teachers` knowledge competency on how to teach their students to mathematically argue that, for example, two triangles are congruent. Deductive rea-soning skill is essential to geometry. The initial findings indicate that both subject and pedagogical content knowledge are essential for effectively teaching this challenging topic. We conclude our study by suggesting a method that teachers can use to further improve their teaching effectiveness.
( Leung K C Issic ) 한국수학교육학회 2014 수학교육연구 Vol.18 No.1
When taught the precise definition of π, students may be simply asked to memorize its approximate value without developing a rigorous understanding of the underlying reason of why it is a constant. Measuring the circumferences and diameters of various circles and calculating their ratios might just represent an attempt to verify that π has an approximate value of 3.14, and will not necessarily result in an adequate understanding about the constant or formally proves that it is a constant. In this study, we aim to investigate prospective teachers` conceptual understanding of π, and as a constant and whether they can provide a proof of its constant property. The findings show that prospective teachers lack a holistic understanding of the constant nature of π, and reveal how they teach students about this property in an inappropriate approach through a proving activity. We conclude our findings with a suggestion on how to improve the situation
( Issic Kui Chiu Leung ),( Lin Ding ) 한국수학교육학회 2014 수학교육 학술지 Vol.2014 No.2
This study is a part of a larger scale of study in investigating the Hong Kong pre-service teachers` knowledge of teaching and beliefs. In this article, the eight pre-service teachers` knowledge of teaching on one topic named systems of linear equation in two unknowns is presented. The knowledge of teaching was examined by the framework of “Knowledge Quartet” (Rowland, Huckstep & Thwaites, 2005a; 2005b). The results reveal that the majority of participated Hong Kong pre-service teachers possess knowledge at the level of procedural boundedness and insufficient understanding of algebraic operations of this topic, which leads to inefficient explanations and representations. In addition, they demonstrate to have developed a good master of routine skills such as classroom management and homework check, yet lack the knowledge and experience in preparing for students` unexpected questions and explaining the underlined rationale behind steps in solving equations. This paper discusses the implications for teacher education at the end..
( Leung K C Issic ),( Ding Lin ),( Leung Allen Yuk Lun ),( Wong Ngai Ying ) 한국수학교육학회 2014 수학교육 학술지 Vol.2014 No.1
Mathematically deductive reasoning skill is one of the major learning objectives stated in senior secondary curriculum (Curriculum and Assessment Guide S4-6, 2007, page 15). Ironically, students` performance in their routine assessment on geometric reasoning, such as proving geometric propositions, and justifying geometric properties, is far below teachers` expectation. One might argue that it is due to teachers` lack of relevant subject content knowledge. However, recent research findings reveal that teachers` knowledge for teaching (e.g. Ball et al 2009) in deductive reasoning skills also plays a crucial role on students` learning. Prior to a comprehensive investigation on teachers` competency, in an analogue approach of case study, we aim at investigating teachers` knowledge competencyon how to teach their students to argue mathematically that, as an example, two given triangles are congruent. In which skilful reasoning of deduction is essential. Initial findings show that both subject and pedagogical content knowledge are essential for an effective teaching on this challenge topic. We conclude our study by suggesting a way that teachers can further improve their teaching effectiveness.
( Leung Issic Kui Chiu ) 한국수학교육학회 2014 뉴스레터 Vol.30 No.5
This study is a part of a larger scale of study in investigating the Hong Kong pre-service teachers`` knowledge of teaching and beliefs. In this article, the eight pre-service teachers`` knowledge of teaching on one topic named systems of linear equation in two unknowns is presented. The knowledge of teaching was examined by the framework of "Knowledge Quartet" (Rowland. 2005). The results reveal that the m~jority of participated Hong Kong pre-service teachers possess knowledge at the level of procedural boundedness and insufficient understanding of algebraic operations of this topic, which leads to inefficient explanations and representations. In addition, they demonstrate to have developed a good master of routine skills such as classroom management and homework check, yet lack the knowledge and experience in preparing for students`` unexpected questions and explaining the underlined rationale behind steps in solving equations. This paper discusses the implications for teacher education at the end.
( K C Issic Leung ) 한국수학교육학회 2013 수학교육 학술지 Vol.2013 No.2
When taught the precise definition of π, students may be simply asked to memorize its approximate value without developing a rigorous understanding of the underlying reason of why it is a constant. Measuring the circumferences and diameters of various circles and calculating their ratios might just represent an attempt to verify that π has an approximate value of 3.14, and will not necessarily result in an adequate understanding about the constant or formally proves that it is a constant. In this study, we aim to investigate prospective teachers` conceptual understanding of π, and as a constant and whether they can provide a proof of its constant property. The findings show that prospective teachers lack a holistic understanding of the constant nature of π, and reveal how they teach students about this property in an inappropriate approach through a proving activity. We conclude our findings with a suggestion on how to improve the situation.