Abstracts of Presentations

From Problem Solving to Practice: Designing a Coherent Mathematics Teacher Preparation Sequence at Roger Williams University

Professor Jenny Tsankova, Roger Williams University

In this colloquium, I will present an overview of the mathematics education teacher preparation sequence at Roger Williams University and how it intentionally connects problem solving, methods coursework (elementary and secondary), and field experiences into a coherent developmental arc. I will share examples of instructional routines and assignments that build candidates’ capacity to elicit and use student thinking, support mathematical discussion, and make informed instructional decisions across grade bands. I will also highlight several current research and improvement projects examining candidate growth in pedagogical content knowledge, the role of formative assessment in methods courses, and how near-peer and school-based partnerships can strengthen both candidate learning and local classroom practice.

A Teacher’s Interpretation of Concrete-Pictorial-Abstract and his design and enactment of a lesson on solving Word Problem

A/P Toh Tin Lam, MME/NIE

The Concrete-Pictorial-Abstract (CPA) approach is one that has been adapted from Bruner’s multimodal representation and an approach to teach secondary mathematics. This talk presents an interpretation of CPA approach used by one mathematics teacher in designing and enacting his lesson on Sec Two Word Problems (resulting in linear equations).

Exploring Secondary Mathematics Teachers’ Support of Student Metacognitive Experiences in the Mathematics Classroom

Lee Mei Ling Sharon, MME/NIE (PhD Student)

This proposed study explores how secondary mathematics teachers in Singapore understand and support students’ metacognitive experiences, particularly Judgements of Learning (JOL) expressed through feelings of confidence, feelings of difficulty, perceived fluency, and perceived effort. While metacognition is widely recognised as critical for mathematical problem solving, existing research has largely emphasised metacognitive knowledge and metacognitive regulation, with comparatively less attention to metacognitive experiences. The study aims to generate insights into how teachers interpret and act on students’ JOLs, informing the development of pedagogical approaches that support more accurate and productive student judgements of understanding in mathematics.

What did CHATGPT “notice” about prime numbers? Insights from an AI-generated Lesson Play

A/P Choy Ban Heng, MME/NIE

In this presentation, I examine ChatGPT's capacity to generate lesson plays, which are scripted, imagined conversations used to develop and analyse mathematical teaching expertise. By prompting ChatGPT to address a student's misconception about prime numbers, I analysed its responses in terms of mathematics, student confusion, and instructional responses. While the AI successfully anticipated certain difficulties and employed collaborative discourse patterns, the findings reveal significant limitations.

Recent Results on Hamiltonian Properties of Graphs

A/P Tian Tao, Fujian Normal University (NIE visiting scholar)

Research on Hamiltonian properties is a central topic in graph theory, with wide applications in combinatorics, optimization, and network design. In this talk, we present several recent results on Hamiltonicity, traceability, Hamilton-connectedness, and the existence of 2-factors.

The Bin Packing Problem

RAYNER TAN CHEK KHAI, MME/NIE (degree student)

The Bin Packing Problem (BPP) is a classical NP-complete optimization problem in which items must be packed into the minimum number of bins subject to capacity constraints. This project investigates several approaches for solving BPP instances through computational experiments. We first examine simple upper and lower bounds derived from greedy heuristics and volumetric arguments. Although these bounds efficiently solve many small instances, they are often insufficient to determine optimality for larger instances. To address this limitation, exact algorithms are employed, in particular the Martello–Toth branch-and-bound algorithm and Korf’s bin completion method. These algorithms approach the problem from two complementary perspectives: Martello–Toth adopts an item-oriented branching strategy, while Korf’s algorithm focuses on constructing feasible bin completions. Using these two methods, we analyze the effectiveness of exact algorithms on different classes of BPP instances and investigate how structural properties of item size distributions influence problem difficulty.

Heteroscedastic General Linear Hypothesis Testing Problem for HDLSS: a Normal Reference F-type test

WANG PENGFEI, MME/NIE (Ph.D. student)

In recent years, advances in data acquisition and storage have led to the widespread emergence of high-dimensional datasets, where the number of variables may greatly exceed the available sample size. Although many tests exist for mean vectors under homoscedasticity, few address general linear hypothesis testing in the presence of heteroscedasticity and singular covariance structures. To fill this gap, we introduce a novel centralized L2–norm–based F-type statistic that replaces the usual inverse covariance matrix with its trace, ensuring well-posedness in HDLSS settings. Under mild moment and regularity conditions, we show that its null distribution converges to a chi-square–type mixture and derive a three-cumulant matched chi-square approximation with consistently estimated parameters. This leads to a practical Welch–Satterthwaite adjustment for the degrees of freedom. We establish the test’s asymptotic power under local alternatives and demonstrate its robustness to non-normality. Extensive simulation studies illustrate that our normal-reference F-type test maintains accurate size control across various correlation regimes and achieves substantially higher power than some existing competitors.
Lattices of Scott-closed Sets

BRIAN CHEW (ZHOU YIKAI), MME/NIE(degree student)

This presentation gives an overview of the main ideas on the order-theoretic structure of lattices of Scott-closed sets. After briefly reviewing key notions from domain theory, such as directed complete partial orders and continuity, the talk focuses on properties of the lattice of Scott-closed subsets of a poset . In particular, we discuss the beneath relation and the notion of C-continuity, which provides an order-theoretic framework analogous to continuity. The presentation highlights how these concepts help describe structural properties of Scott-closed set lattices and offers an accessible overview of several results and ideas explored in the project.

Two-sample tests for equality of covariance matrices

LIM HWEE MIN VIVIAN, MME/NIE(degree student)

Test for the equality of covariance matrices of multivariate data has various uses. In this report, we study four different two-sample tests for the equality of covariance matrices. Three of the tests are existing tests and the last test is a new test that we suggest by constructing a test statistic with reference to a test for equality of means of high-dimensional data. We will present the results from simulation studies conducted on the four tests with respect to empirical size and empirical power.