Abstracts of Presentations

The Microgenetic Method: Explained through my doctoral studies

Chang Suo Hui

During the process of learning, changes are constantly taking place. An understanding of the change itself, events that lead to the change and the subsequent impact of the change are important information to both researchers and teachers. In this presentation, I will introduce Siegler’s Microgenetic Method adopted in my doctoral studies. This method was used to understand the changes that took place among 44 low-progress students during the learning of Primary Three concept of equivalent fractions over the period of two to three weeks. The pertinent elements involved in the Microgenetic Method, issues surrounding its use, the formulation of the changes of learning for the particular concept of study as well as the complementary instruments to support the investigation of change will be covered.

Making sense of teachers’ design of instructional materials

Chin Sze Looi

Teacher’s use of curriculum resources is an important aspect of their practice. Although the large range of textbooks offer an abundance of content and suggestions for classroom instruction, some teachers still prefer to design their own materials prior to instruction, or at least transform these textbooks to better accommodate their students’ needs. But how exactly does this design process occur? How does the teacher select, rearrange or adapt the content from the textbook to design a new set of instructional materials? This presentation provides a review of literature on the possible lenses that can be used to zoom in on the intricacies of the process and to zoom out to observe the broader decisions teachers make in creating these materials. Based on this review, we consider the potential aspects at the core of the design process that are yet to be captured by existing research.

Journal writing in primary mathematics classroom: Its affordances in eliciting students' number sense

Karin Yeo Lei Teng

Number sense has been highlighted as a vital prerequisite to success in mathematics. As such, the development of number sense plays a key role in mathematics education. To develop students with good number sense, teachers not only need to equip themselves with strategies that can foster number sense, but also assessment methods that can obtain rich knowledge of students’ number sense abilities. Research has suggested the use of journal writing to access to students’ number sense but there seems to be a lack of studies exploring the use of journal writing as a tool to assess students’ number sense. Using a case study methodology, this study investigated the affordances of journal writing in eliciting students’ number sense. Four different journal tasks were given to 94 Primary 5 students who were studying in a typical Singapore government school. These tasks were designed with appropriate writing prompts and aligned to the different components of number sense to allow students to demonstrate their number sense abilities. Other than students’ journal entries, their Primary 4 year-end assessment results were also collected as part of the data for the study. Eventually, a total of 16 journal entries from four students were analysed in depth using thematic analysis to surface possible affordances of journal writing through their writings. Analysis of students’ journal entries revealed that journal writing offers a ‘window’ into understanding students’ number sense through three different lenses. Findings from the study suggested that these three affordances of journal writing are: (1) revealing students’ conceptions and misconceptions of numbers and operations, (2) making students’ thinking processes visible and (3) manifesting students’ flexibility with numbers and operations. Such information on students’ number sense may not have surfaced from a paper-and-pencil assessment. In fact, it was found that good performance in summative paper-and-pencil assessment does not necessarily equate to good number sense abilities and vice versa. Thus, teachers need to examine beyond answers to gain a better understanding of students’ understanding and thinking of numbers and operations. In this study, it is evident that journal writing can provide that avenue. Evidence from students’ journals also supported the use of different types of journal writing to elicit a variety of responses from students so as to have a better picture of the students’ number sense abilities. This study provided some designs of tasks that teachers and teacher educators could use as authentic examples. Other implications include contributing to the existing literature on journal writing and assessment of number sense, especially in local context, to trigger more conversations and create greater awareness among teachers.

Ideas of Proof in a Secondary School Textbook

Tay Han Dong

Studies have indicated that the demand for proofs is significantly different between secondary school and university mathematics. This study explored the ideas of proof in a secondary school textbook. Volume A and B of “Additional Maths 360” textbook published by Marshall Cavendish Education was used. The content, worked examples and extent questions in this textbook were analysed and proofs were categorized according to their adopted presentation. Use of examples emerged as the most common approach for illustrating proofs. The discussion centers on the pedagogical and learning implications for teachers and students, respectively.

Use of instructional materials in secondary school mathematics lessons

Cheng Lu Pien & Leong Yew Hoong

In this presentation, we will share our findings on how experienced Singapore secondary school mathematics teachers select and modify materials for instructional practice based on A Study of the Enacted School Mathematics Curriculum (Secondary), Study 2, research project. We analysed the survey responses of 677 participants across a wide range of secondary schools to determine the extent of modification among teachers before identifying which instructional materials were used as reference materials in their modification. We also analysed the instructional materials of 30 experienced teachers to examine teachers’ selection and modification moves for their instructional materials. Our findings reveal some characteristics of the instructional materials that help teachers enact worthy instructional goals of teaching mathematics.
Reflection on my research done at NIE

Teo Beng Chong

In this talk, I would like to share some of things I did for the various research projects undertaken over the years at NIE. Since I joined NIE in 1992, there have been many opportunities to participate in various projects and initiative programs such as the IT Master Plans (various phases), CITE, SMAPP, TDU, edulab, MDA Testbed, Maker Space and CRPP/OER with over a few millions of funding involved. I will be talking about some of these work, their outcomes and some lessons I have learned through them.

Proofs of Eta Quotients Identities and its Applications to Ramanujan’s Congruences

Chun Guan Yang

Abstract: The Jacobi Triple Product Identity and Quintuple Product Identity are two well-known identities, as we can represent an infinite product as an infinite sum of a closed form expression. By using the Triple and Quintuple Product Identity, we can derive other identities called the eta quotient identities, where we can express products or quotients of Dedekind eta functions as a single variate theta function. Oliver proved that there are only twenty eta quotient identities which can be expressed as a single variate theta function but did not prove these identities. We aim to cover the gap by including all twenty proofs of the eta quotient identities. Some of these eta quotient identities can be used to prove two of Ramanujan’s partition congruences for the partition function, which is considered as an uncommon approach. Other than proving Ramanujan’s partition congruence, we aim to introduce two other expressions conjectured by Lin which has some fascinating partition congruences and prove the partition congruences using the eta quotient identities.

Hamilton Decompositions of Graphs

Hang Hao Chuien

The talk will introduce and define relevant concepts, and survey the topic of Hamilton decompositions of graphs. Some new results that we have recently obtained in this area will then be presented.

Statistics on Ascent Sequences

Soh Chin Gi

High-dimensional spectroscopic data is informative, and has applications in many fields such as biomedical sciences and food science. The fitting of regression models for the purposes of prediction is known to be a challenging task due to the high-dimension of the datasets, as well as high correlation between wavenumbers in the data. One method that has gained interest in recent years is the use of regularization to overcome these challenges. In this talk, we present a regularized model for spectroscopic data. Depending on the penalty functions used in the regularized model, different computational challenges may arise. We will discuss some algorithms that are of interest in solving for such regularized model coefficients, as well as the advantages and disadvantages of these algorithms.

A Haskell Implementation of the Lyness-Moler's Numerical Differentiation Algorithm

Ho Weng Kin

This paper describes a computational problem encountered in numerical differentiation. By restricting the problem to a proper subclass of differentiable functions, a numerical solution first proposed by Lyness and Moler is considered and implemented in the functional programming language Haskell. The accuracy of the calculation of the numerical derivative using the Lyness-Moler's method crucially lies in our recursive algorithm for computing contour integrals.