Abstracts of Presentations

Using Real-World Context to Teach Probability

Queenie Chiu

Like how Mathematics education has often been associated with just formulae and procedural steps, probability in Singapore’s Mathematics Education has often been reduced to a set of procedures or formulae. In this presentation, we discuss the use of real-world context to facilitate the development of secondary school students’ probabilistic reasoning ability, in order for them to truly grasp probability concepts well. Through an extensive literature review in the probability education, we present our TIDE framework for the teaching of probability.
Tackling students’ common misconceptions of chance.
Introducing probabilistic reasoning in order to move away from deterministic thinking.
Drawing links between students’ intuition and probability concepts.
Encouraging a problem-solving approach when it comes to solving questions.
This framework is to mainly serve as a guide for teachers to introduce the topic of probability. An activity plan, which uses the famous Monty Hall Problem, will also be presented to show how the TIDE framework is applied.

Developing Positive Attitudes in Students

Joseph Yeo Boon Wooi

Based on lesson observations of 30 experienced and competent secondary school mathematics teachers, I will present some research findings on what they did to develop positive attitudes in students and to make lessons interesting. In particular, I will examine in detail how one of the teachers made use of snippets of a funny Korean drama to engage the hearts of her class and to link the drama to the learning of mathematics. It will end with some implications for mathematics teaching.

The Neutralization on an Empty Number Line Model for Integer Additions and Subtractions

Puspita Sari

This study focuses on how the ‘Neutralization on an Empty Number Line’ (NNL) model can be used in a classroom to help students better understand the meaning of integer addition and subtraction. The design research methodology that was used in this study was conducted in three phases: first, a Hypothetical Learning Trajectory (HLT) was designed, second, the HLT was tried out in a classroom, and third, an analysis of how the learning process took place as well as how students developed during the lessons was carried out. Although there was little evidence on the development of students’ thinking in the classroom, a closer observation of a student helps us understand that with a thorough planning, the NNL model has the potential to help students in developing an understanding of integer addition and subtraction.

Factors that Influence Teachers' Selection and Modification of Mathematics Tasks for Instructions

Soon Apollonia

This study examined factors that influence teachers’ selection, modification and design of mathematics tasks for instruction. It comprised two phases, a qualitative survey and an interview using stimulus texts. The qualitative survey solicited the manner in which teachers select their tasks, the types of tasks they use in the classroom and the considerations behind this use. The interview using stimulus texts probed teachers thought process during task selection to teach the sub-topic, polygons. During the presentation findings of the study will be shared with participants.

Calculus in the Singapore School Mathematics Curriculum

Toh Tin Lam

In this talk, a discussion of the key features of the calculus strand in the Singapore School Mathematics Curriculum (from Secondary to Pre-University level) will be presented. Many of the features observed are aligned to the overall objective of the Singapore mathematics curriculum framework and some features of the calculus content knowledge have been discussed by researchers as early as the 1980s. The talk will also present a glimpse of the students’ attainment of various calculus thinking through the performance of a group of pre-university students in a calculus instrument.
Some open problems in Domain Theory

Ho Weng Kin

Domain theory, roughly speaking, is topology done on partially ordered sets, and is hence a meeting place of Topology and Order. Being a successful theory in explaining the phenomenon of approximation in many contexts ranging from Computer Science to even linguistics, Domain Theory is very rich in itself as a field of mathematical study. In this talk, we shall look at some open problems in Domain Theory which are both interesting in their own right and important in the mainstream theoretical development.

Independence polynomials and independence equivalence classes

Ng Boon Leong

The independence polynomial of a graph G is the polynomial where the coefficient of xk is the number of independent sets in G of cardinality k. Graphs with the same independence polynomial are called independence equivalent graphs. In this presentation, some properties of the independence polynomial will be discussed, with an emphasis on independence equivalence of trees and cyclic graphs.

Baire One Functions

Vera Lee Man Er

We are all familiar with the epsilon-delta definition of continuity at a point. Given an equivalent definition of continuity, we would like to study the type of functions that can be obtained when a simple modification to this definition is made.

l,+m systems for positive integer pairs

Janice Lim Hong Min

Given the numbers 1,1,2,2,3,3,4,4, how can we arrange them in a row such that there are exactly r-1 numbers between a pair of `r' where r=1,2,3,4? And is there always a way to arrange 2n numbers, 1,1,2,2,3,3,…,n,n in this way for different values of n where n∈N?

Thoralf Skolem explored this problem in his paper. My project involves rewriting his paper in a more detailed and comprehensive manner with additional theorems as extensions and addressing certain errors made in the paper. In this presentation, I will prove some of the main results and include a few computer programming codes created using Visual Basic for Applications (VBA) on Excel to demonstrate the l,+m systems for different values.

Combinatorial Identities

Dong Fengming

An interpretation to an identity is very helpful for understanding the identity. Finding an interpretation to an identity may be quite challenging for students. This talk will introduce some well-known combinatorial identities and their interpretations.