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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 ),( 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.