Mathematics Education Abstracts of Presentations

Proving without proofs

Leong Yew Hoong

Most mathematicians cannot conceive of mathematics without proofs; proofs are the essential contents – perhaps even the ostensible defining trait – of mathematics. However, proofs in its rigorous forms are often considered not easily accessible for many students who have weak foundations in mathematics. What does a maths teacher do when caught in this situation of conflicting instructional goals: keep true to the disciplinarity of mathematics in proving while not presenting proofs in a formal way? We present a way to cope with this dilemma as used in the project schools.

Professional development for teachers of mathematical modelling in Singapore

Tan Liang Soon

A school-based professional development programme (SBPD) aimed at developing secondary school mathematics teachers’ competencies to teach mathematical modelling in Singapore is presented and evaluated in this thesis. The SBPD is characterized by three key dimensions of learning–content dimension to develop teachers’ knowledge and skills, process dimension where teachers are engaged in transformative learning cycles to elicit, enact, and reorganize their orientations in a mathematical modelling classroom, and context dimension to adjust the SBPD programme implementation based on school contextual factors. A multiple-case study approach was adopted to examine teachers’ developmental trajectories in their practice of teaching mathematical modelling. Goal-based decision making analysis of teachers’ practice suggests that this SBPD positively influences teachers’ knowledge and resources, goals and orientations in planning, designing and enacting modelling learning experiences. Implications for the SBPD programme in terms of its contributions to educational theory and practice are also discussed.

Using activity theory to study the development of an (aspiring) professional learning community

Romina Yap Ann Soon

Professional learning communities (PLCs) have been endorsed as social infrastructures that can effectively support teachers’ collective and individual learning. However, fostering effective PLCs can be a challenging task because it needs to consider personal, interpersonal, and institutional orientations, relations, and capacities. Studying PLC building initiatives can provide insight into how these social infrastructures can proceed with more success. In this presentation, I will present how the lens of activity theory can be useful for studying the development of PLC initiatives while taking into consideration their multifaceted nature. To demonstrate, I use the case of a group of secondary mathematics teachers in the Philippines who were collaborating for mathematical problem solving instruction.

Informing mathematics pedagogy: Singapore practices and US reform

Katie Bueker-Sibbit

This session will report the findings of one Fulbright teacher’s research in mathematics teaching practices and beliefs. The study compared Singapore teachers’ practices to recommendations by US reform movements through the United States’ Common Core State Standards. In addition, both US and Singapore teachers and students’ beliefs about math teaching and learning were studied in comparison to the National Council of Teachers of Mathematics (NCTM) recommendations about productive and unproductive beliefs. Through a series of student and teacher interviews and observations, comparisons were made with the hope of informing US reform through Singapore’s success. The researcher will share pragmatic insight into student and teacher beliefs about math teaching and learning, as well as strategies and resources for international best practice in all contexts in the field of mathematics.

Teaching for Metacognition – Teachers working and learning collaboratively in two-tiered communities of practice

Berinderjeet Kaur & Wong Lai Fong

Kaur developed a hybrid model of professional development for teachers in Singapore. The model draws on significant findings of effective professional development programmes. During the presentation she will discuss the enhancement of the model that has led to the development of two-tiered communities of practice in a cluster of schools that were developing their classroom practices to teach for metacognition.