SYMPOSIUM: PEDAGOGIES ADOPTED BY COMPETENT SECONDARY SCHOOL MATHEMATICS TEACHERS

This Symposium consists of three papers revolving around the issues on pedagogies adopted by competent secondary school mathematics teachers.  These papers arose out of Study 1 of the AG Programmatic Research on “A Study of the Enacted School Mathematics Curriculum (Secondary)” (OER 31/15 Bk).
 
Paper 1 – Pedagogies adopted by competent secondary school mathematics teachers in relation to the intended curriculum
Authors: Lee, N.H., Ng, K.E.D, Yeo, B.W.J., Yeo, K.K.J., Kaur, B., Toh, T.L., Leong, Y.H., & Tay, E.G.
This paper examined 21 lessons enacted by four competent secondary school mathematics teachers from 2 different schools, with 2 teachers from each schools.  The 21 lessons were coded to examined for patterns in the pedagogies adopted by these competent mathematics teachers from the perspective of the intended curriculum.  These lessons were coded according to types and phases from the perspective of teaching and match against those on learning that were detailed in the mathematics curriculum document.  In addition, these enacted lessons were also examined from the perspective of the Singapore School Mathematics Curriculum Framework.
 
Paper 2 – A Constructivist Approach to the Teaching of Arc Lengths, Sector Areas and Radian Measures
Author: Ng Kit Ee Dawn (Mathematics and Mathematics Education Academic Group, National Institute of Education, Singapore)
Trigonometry is an important topic in school mathematics. Weaker students often find the learning of arc lengths, sector areas, and radian measures challenging, particularly the transition from degree to radian measures. According to Moore (2012), quantitative reasoning plays a central role in students’ trigonometric understandings. This paper presents a case study of a teacher who adopts a constructivist approach in facilitating quantitative reasoning to develop students’ understanding of arc lengths, sector areas, and radian measures with a Secondary Four (Normal Academic) class in a Singapore government school. Instead of developing the new concepts through a didactic approach, the teacher used a variety of activities, teaching materials, and questioning techniques to elicit students’ mathematical reasoning and prompt for relational understanding of concepts (Skemp, 1976). Implications from the teacher’s pedagogical approach will be drawn.
 
Paper 3 – Mathematical Practices Enacted in the Lessons: A Case Study of Teaching Quadratic Equations
Author: YEO Kai Kow Joseph (Mathematics and Mathematics Education Academic Group, National Institute of Education, Singapore)
As teaching is a multifaceted process that involves many elements, it is imperative that teachers think attentively about what they do and the way they do it, that is, about the fine-grain decisions they make when teaching.  It is not only the structures apparent in teaching that are essential, but it is how they are enacted that is important.  Teaching quadratic equations are closely tied to the Singapore School Mathematics Curriculum Framework, in particular, conceptual understanding, skill fluency, and strategic competence. Ideally, these strands are interdependent and are to be developed simultaneously in balanced ways.  This paper reported the sequence of mathematical practices that a competent teacher designed and enacted during her mathematics lessons when teaching solving quadratic equations in a Secondary 3 classroom. Specifically, it attempted to answer the following questions: What mathematical practices are entailed in a mathematics teacher’s instructional design and enactment when the teacher is teaching solving quadratic equations?  From the findings, the instructional design and enactment of the various mathematical practices had created a positive learning environment that had potentials in facilitating conceptual understanding, skill fluency, and strategic competence.