Leung K C Issic , Lin Ding , Allen Yuk Lun Leung , Ngai Ying Wong

DOI: Vol.18(No.3) 171-185, 2014

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.

mathematics teachers` competency, pedagogical content knowledge, congruent triangles

Levenberg Ilana

DOI: Vol.18(No.3) 187-208, 2014

This study engages in the features of interaction in elementary school mathematics lessons as reflected in the class discourse. 28 pre-service teachers documented the discourse during observation of their tutor-teachers` lessons. Mapping the interaction patterns was performed by a unique graphic model developed for that purpose and enabled providing a spatial picture of the discourse conducted in the lesson. The research findings present the known discourse pattern “initiation?response?evaluation / feedback”(IRE/F) which is recurrent in all the lessons and the teacher`s exclusive control over the class discourse patterns. Hence, the remaining time of the lesson for the pupils` discourse is short and meaningless.

classroom interaction, mathematics discourse, discourse pattern

Qiao Ping Zhang

DOI: Vol.18(No.3) 209-221, 2014

In the last few decades there has been much interest in how mathematics can be effectively taught and learnt. The Third Wave is a unique ongoing international collaborative mathematics education research project, which aims to explore the relevant values of effective school mathematics teaching from both the teacher and student perspectives. As part of this project, this study investigates the related findings from students on the Chinese mainland. Multiple data were collected through classroom observations, focus group interviews, and written, open-ended questions. Twenty-four students from junior and senior secondary schools were invited to write down their views on an effective lesson, a good mathematics teacher, and how to do well in mathematics learning. Results showed that among the eight values determined in the study, the values of involvement, explanation, and examples were embraced by students across all grades. Students preferred teacher-led mathematics teaching. Junior secondary students placed more value on teachers` personalities, whereas senior students placed more value on teachers` teaching manners.

the Third Wave, effective mathematics lessons, effective mathematics teacher, values

Hee Jeong Kim

DOI: Vol.18(No.3) 223-234, 2014

Research shows that formative assessment has a more powerful effect on student learning than summative assessment. This case study of an 8th grade algebra classroom focuses on how the implementation of Formative Assessment Lessons (FALs) and the participation in teacher learning communities related to FALs changed in the teacher`s instructional practices, over the course of a year, to promote students` mathematical reasoning and justification. Two classroom observations are analyzed to identify how the teacher elicited and built on students` mathematical reasoning, and how the teacher prompted students to respond to and develop one another`s mathematical ideas. Findings show that the teacher solicited students` reasoning more often as the academic year progressed, and students also began developing mathematical reasoning in meaningful ways, such as articulating their mathematical thinking, responding to other students` reasoning, and building on those ideasleading by the teacher. However, findings also show that teacher change in teaching practices is complicated and intertwined with various dimensions of teacher development. This study contributes to the understanding of changes in teaching practices, which has significant implications for teacher professional development and frameworks for investigating teacher learning.

mathematical reasoning, formative assessment, classroom practice, accountable discussions