Abstracts of Presentations

Learnings from a multidisciplinary programmatic research project - Exploring and fostering metacognition for learning and transfer to pave the way for towards lifelong and lifewide learning

Lee Ngan Hoe, Imelda Santos Caleon, Melvin Chan Chee Yeen, Dawn Ng Kit Ee, Tay Lee Yong, Teo Wei Peng & Lee Peh Chye June (National Institute of Education, Singapore)

Recognising the strong link between metacognitive ability and the acquisition of new skills and competencies that are crucial for lifewide and lifelong learning necessary for learning in the 21st Century, a team of NIE researchers conceptualised this programmatic research project to advance the understanding and enhancing Singapore secondary students’ metacognition. Supported by officers and Master Teachers from the Ministry of Education and international researchers, this multidisciplinary research programmatic research project builds a database on students’ metacognitive processes and teachers’ metacognitive practice and put forth intervention programmes through five sub-studies. Quantitative and qualitative insights into students’ metacognition and teachers’ metacognitive practices in Mathematics and English contexts were examined in the first two studies, while the third study offers an alternative, objective examination of students’ metacognition via neural imaging techniques. Insights drawn from the first three studies are utilized in the fourth and fifth studies, with the former developing a metacognition intervention programme for students, and the latter, a metacognition professional development programme for teachers to foster students’ metacognition. Research is still ongoing, but preliminary results reveal positive relationships between student metacognition and achievement, metacognition’s influence on transfer and the the potential influence of teacher’s metacognition on students’ metacognition, particularly in the English context. This presentation, by the Core Team of this programmatic research project, shares both the conceptualization of the project as well as some preliminary findings.

A study of out-of-school mathematics practice books for the PSLE in Singapore

Teo Pei Pei & Berinderjeet Kaur (National Institute of Education, Singapore)

This exploratory and small-scale study was guided by two research questions. Drawing on a convenient sample of 76 PSLE Mathematics practice books it attempted to document the features of the books and examine how the books supported test-taking preparation and test-taking skills for the PSLE Mathematics? During the presentation we will share our findings and also propose further studies that would help us glean insights on how such books facilitate or hinder preparation for the PSLE Mathematics. It would also be helpful to explore how these book support examination preparation from the perspectives of students and parents.

Metacognition and flowcharting experience in the learning of trigonometry: case studies of two low attainers

Cheryl Lee Mei Chen (Peirce Secondary School, Singapore)

In recent years, there is a call to place greater emphasis on developing students’ metacognition and computational thinking skills. This proposed research aims to explore how flowcharts, which is commonly used to represent an algorithm in the of computational thinking, might impact the development of students’ (low attainers in particular) metacognitive strategies in the learning of trigonometry.

Elementary school students’ motivations in learning mathematics

Elaine Cai Yu Ling & Gregory Arief D. Liem (National Institute of Education, Singapore)

The study examines the tole of task-, self- and other-based goals in mediating the links between autonomous and controlled motivation and student engagement towards mathematics learning among elementary school students in Singapore. 491 students from Grades 4 to 6 were administered questionnaires assessing their motivations, achievement goals and level of student engagement. Path analysis and Mplus syntax for multiple mediation were used to analyse the data. The study found that achievement goals significantly linked motivation to student engagement. Students who endorsed autonomous motivation and found mathematics interesting and meaningful would think more elaborately. Self-based goals were the only achievement goal which significantly mediated motivation to elaboration. It also strengthened the benefits of autonomous motivation for elaboration and channelled the adaptive role of controlled motivation on elaboration.

Weighted Generalized Crank Moments for k-colored Partitions

Toh Pee Choon (National Institute of Education, Singapore)

In this talk, we will briefly introduce the concept of k-colored partitions and the associated generalized crank moments. Thereafter, we will present some results obtained by the author and his collaborators.

A Glimpse of Graph Colorings

Meiqiao Zhang (National Institute of Education, Singapore)

Graph coloring is one of the most important and long-standing topics in graph theory. Not only does it tie many concepts in graph theory in surprising ways, but it also has a wide range of real-world applications. In this talk, I will briefly introduce a few different kinds of graph colorings, along with some simple but fascinating results of them.

NRAFHDLT: A R package for the high-dimensional location testing problems with the normal-reference approach

Wang Pengfei (National Institute of Education, Singapore)

In this talk, we give the most current of methods based on normal reference approach to test the equality of the mean vectors of high-dimensional samples with possibly different covariance matrices. We conveniently group the methods into two categories which are two-sample problem and general linear hypothesis testing problem based on the number of samples. We offer some perspectives on the connections and distinctions among the tests. An R package named NRAFHDLT is given to show the implementation of these tests and which also provides an easy and user-friendly access to the above tests. Simulated Type I error rates and powers of the sum-up tests are also shown. We illustrate the implemented procedures by two real examples from biology for different categories.

 

An Elementary Exploration of Knot Theory

Deng Qingying (Xiang Tan University, China)

Knot theory is a unique branch of mathematics dedicated to the study of the properties of closed curves or ropes. This elementary report provides an overview of the fundamental concepts of knot theory, including the definition and properties of knots. We briefly touch on its history and some practical applications to inspire an interest in this fascinating field of mathematics.

Polynomials of graphs

Fengming Dong (National Institute of Education, Singapore)

There are various polynomials of graphs, which reflect the structures and properties of graphs. In this talk, we will introduce some polynomials of graphs.