Abstracts of Presentations

Secondary school teachers' perceptions of diagrams in mathematics

Manju Manoharan

The revised secondary school mathematics curriculum places emphasis on Big Ideas in Mathematics, which includes Diagrams. To support the use of diagrams by teachers as a Big Idea it is pertinent to explore their perceptions. This will allow for appropriate developments in support of enhancing their pedagogies for mathematics. This study examined secondary school teachers’ perceptions of diagrams in mathematics. It focused on two aspects: i) teachers’ perceptions on the utility value of diagrams and how they incorporate them in their instructional practice and ii) teachers’ perceptions about their students’ use of diagrams in mathematics. An open-ended survey was administered to 20 secondary school teachers, with at least three years of mathematics teaching experience, seeking their perceptions. Findings of the study will be shared during the presentation.

Constructivist Learning Design for Singapore Secondary Mathematics Curriculum: a tripartite synergy of research, practice and policy

Lee Ngan Hoe, Gayatri Balakrishnan, Cynthia Seto, Pang Yen Ping & Chew Chong Kiat

A key enabler in realizing and translating pedagogical innovations require the synergy among research, practice and policy. The importance of this tripartite relationship has been pointed out in past research, with local examples across a range of curriculum range areas highlighted (Tan et. al., 2015). In Mathematics and Mathematics Education Academic Group, a key project that exemplified the synergistic collaboration among researchers, practitioners, and policy makers was the “Constructivist Learning Design for Singapore Secondary Mathematics Curriculum” (project code DEV 04/17 LNH). To support and sustain the use of a constructivist learning design (CLD) that might be better aligned to the learning experiences encouraged in the enhanced secondary mathematics curriculum (Ministry of Education, 2012, 2020), the research involved strong collaboration from NIE researchers, a Curriculum Specialist from Curriculum Planning Development Division (CPDD, Ministry of Education), and Master Teachers from Academy of Singapore Teachers (AST). In the three-year project, the team developed and validated the CLD, and established a Networked Learning Community (NLC) that helps to champion the CLD after the research.

In this presentation, members from the research team will provide insights into this collaborative tripartite relationship in promoting and sustaining the CLD approach in the Singapore secondary mathematics classroom. Associate Professor Lee Ngan Hoe, the Principal Investigator (PI) of the project will elucidate the research component, sharing the CLD from its conceptualisation to its execution and achievements. Commenting from the policy perspective, Ms Gayatri Balakrishnan, Lead Specialist from CPDD and a co-PI of the project, will describe how the CLD project provided a vehicle for her to communicate and translate the aims of the revised curriculum through task design, and to work with teachers in co-creating knowledge that impacted their practice. Shedding light on the CLD project from the practice lens will be Dr Cynthia Seto, Principal Master Teacher and a co-PI of the project. Joining her in her commentary are Ms Pang Yen Ping and Mr Chew Chong Kiat, both Master Teachers and collaborators of the project. They will reflect on their journey in building a community of practitioners, addressing gaps in practice, translating and scaling research across schools, and shaping the inquiry framework for the mathematics classroom. The presentation will conclude to highlight the nature of this tripartite relationship and reflect on the potential of such models in fulfilling the research-practice nexus in future mathematics research projects.
Four solutions of a Geometry Problem about Angles on Lattices

Toh Pee Choon

Helen is a primary school student who was stuck on a geometry problem. She asked Ivan, a mathematics expert from her coin-collectors club, to help her with the problem. Ivan proposed four different approaches to the problem, ranging from elementary to advanced, using techniques in trigonometry, vectors and even number theory. The different approaches will be discussed in this talk.

Arc reversals of cycles in orientations of G vertex-multiplications

Willie Wong Han Wah

One of the early problems concerning arc reversals is: Given two tournaments of the same order, is it possible to obtain one from the other by a sequence of a prescribed type of arc reversals? Let Ck denote a directed cycle of length k. In 1964, Ryser gave an affirmative answer of using C3 for any two tournaments with the same score sequence. Later, Waldrop gave an independent proof and further established two results in which “C3” is replaced by “C4” and by “C5”. Beineke and Moon proved the C4-equivalence for any two bipartite tournaments with the same score lists. In this talk, we discuss some extensions of these results to multipartite tournaments and more broadly, orientations of G vertex-multiplications.

Sparse fused group lasso models for spectroscopic data

Soh Chin Gi

High-dimensional spectroscopic data has applications in many fields such as food science, forensic science and biomedical science due to the information it provides about the chemical compositions of the samples. The fitting of classification and regression models to such data is a challenging task due to the high-dimensional setting, as well as the issue of high correlation between spectral variables. This talk presents a regularized model for spectroscopic data that incorporates sparsity, smoothness and group structure. The results from some simulation studies on the use of the regularized model will be discussed. An application of the model to Fourier-transform infrared spectroscopic data adulteration studies in olive oil will also be presented. The results suggest that the sparse fused group lasso is able to achieve good prediction performance, while improving on the interpretability of the resulting models.

Similarities in geometry

Zhao Dongsheng

The notion of similar triangles plays a very important role in geometry. There are several different conditions for similarity. In this talk, we shall
(1) examine the relationships among such conditions,
(2) show some applications of similar triangles both in mathematics theory and the solution of practical problems, and
(3) explore the possibility of extending this notion to other classes of objects.