Abstracts of Presentations

Factors Influencing the Use of Dialogic Teaching in a Secondary 2 Mathematics Classroom in Singapore

Martin Andrew Jonathan

In this presentation, I will discuss my EdD research on factors which may influence the use of dialogic teaching. Two mathematics classrooms in a local secondary school were observed across five lessons. Transcription of audio recordings were analysed using the Teacher Scheme of Educational Dialogue Analysis (Hennessy, 2006) and the Monologic-Dialogic Continuum framework. Results obtained from the quantitative and qualitative analysis via each framework revealed that there was a dominance of monologic interactions during the mathematics lessons. In addition, the preliminary analysis identified five factors which had an influence on the extent of dialogue observed in these two mathematics classrooms. These were: 1) the willingness of students to engage in dialogue, 2) discrepancy in the teacher’s own perception of dialogue, 3) teachers’ teaching habits of delivering a lesson as compared to facilitating one, 4) a greater emphasis on practice questions in the design of the prescribed textbook and 5) the proportion of practice question enacted in the mathematics classroom in comparison to concept development tasks. While the prescribed textbook was discussed to be largely on point in fostering an environment for co-construction of knowledge, it was argued that a main contributor to these influencing factors resided on the inadequate training received by the teachers with regard to: 1) the use of the mathematics textbook and 2) the questioning techniques, necessary for a classroom dialogue. This in turn had implications on the teachers’ belief towards engaging dialogic teaching in their mathematics classrooms.

Use of Assessment Tasks as Impetus for Primary Math Teachers’ Reform in their Instructional Practice

Berinderjeet Kaur, Jahangeer Bin Mohamad Jahabar, Tong Cherng Luen

As part of a larger study on Big Ideas in School Mathematics (BISM), mathematics teachers in two primary schools are involved in a two-year long professional development (PD) programme. Each year the PD of the mathematics teachers began with two introductory sessions. The first engaged them in working through assessment tasks that involved the big idea of equivalence, in the first year and the big idea of proportionality in the second year. During the second sessions they worked in their grade level groups exploring, for a topic they planned to teach in the coming weeks, episodes that would illuminate the big ideas they explored in their first sessions. Using assessment tasks to kick start teachers’ PD may lead one to speculate that the programme was preparing teachers to teach to the test. Focus group discussions were carried out with groups of teachers in both schools who had planned lessons to teach for the respective big ideas. In this presentation we share findings about how the experience of working with the assessment tasks impacted their classroom practice.

Pre-service Teachers' Views on Students' Attitudes Towards Mathematics

Shervonne Yeo Xin Ting

In this presentation, I will discuss my Educational Research study on pre-service teachers’ views on students’ attitudes towards mathematics, and some strategies they believe are helpful to develop students’ attitudes. Research literature views the affective domain as comprising of beliefs, attitudes, and emotions, while the Singapore Mathematics Curriculum framework considers beliefs, appreciation, confidence, motivation, interest, and perseverance as various aspects of attitudes. It is believed that positive attitudes towards mathematics help students to do well in the subject. The data for my study were collected using a survey. It was found that most pre-service teachers believed that confidence is the most important category, followed by perseverance. To build students’ confidence, teachers can strive to set questions at an increasing difficulty level and help students to believe in their potential in excelling in mathematics. The category with the most suggested strategies in the survey is interest, where pre-service teachers proposed the use of games or ICT tools during lessons to engage students and to make lessons more fun.

Grade Two Students’ Approach to Solving Problems

Leow Si Hoon

Most studies in problem solving target intervention strategies, measuring their impact on learners. Yet the learner is one important element in the didactic triangle. Young children often come with their set of ideas and opinions. Do these contribute to their mathematical problem solving abilities? After posing a non-routine mathematical problem to Grade Two students, their responses are analyzed for the role of informal thinking in formal Mathematical tasks. The methodology, results and findings are presented, along with possible future research areas.

Teacher Design of Instructional Materials

Leong Yew Hoong

“It is common – but uncommon in other parts of the world – for Singapore Secondary Mathematics teachers to design instructional materials (often colloquially termed as “Worksheets”) for use in classroom teaching. This practice opens up new opportunities to study the instructional work of teachers. In this talk, the focus will be on two affordances in these fields: research, and educational design”.
A Further Study on Chen--Qin's Test for Two-Sample Behrens--Fisher Problems for High-Dimensional Data

Tianming Zhu

A further study on Chen--Qin's test, namely CQ-test, for two-sample Behrens--Fisher problems for high-dimensional data is conducted, resulting in a new normal-reference test where the null distribution of the CQ-test statistic is approximated with that of a chi-square-type mixture, which is obtained from the CQ-test statistic when the null hypothesis holds and when the two samples are normally distributed. The distribution of the chi-square-type mixture can be well approximated by a three-cumulant matched chi-square-approximation with the approximation parameters consistently estimated from the data. The asymptotical power of the new normal-reference test under a local alternative is established. Two simulation studies demonstrate that in terms of size control, the new normal-reference test with the three-cumulant matched chi-square-approximation performs well regardless of whether the data are nearly uncorrelated, moderately correlated, or highly correlated and it performs substantially better than the CQ-test. A real data example illustrates the new normal-reference test.

Discrimination of Olive Oils by Geographical Origin Using a Regularized Logistic Regression Model

Soh Chin Gi

The identification of geographical origin of a given sample of olive oil is a challenging task that has implications in the field of food fraud detection. Spectroscopic techniques are able to capture chemical information that may be useful in identifying the geographical origin of an oil sample, but the resulting data is challenging to analyse due to issues with high-dimension and multicollinearity. Traditional approaches rely on projection-based methods such as principal components analysis combined with discriminant analysis. This talk presents an alternative method for modelling spectroscopic data to solve this classification problem via regularized logistic regression models, along with the relevant optimization algorithm. The regularization penalties enforce sparsity, smoothness and group structure in the model coefficients. Some interesting fitted models will also be presented, and comparisons to the results obtained using traditional approaches will be made.

On Henstock-Kurzweil Integration Theory: Moving Between Stochastic and Non-Stochastic Case

Toh Tin Lam

The classical Riemann integral is well-known. However, the Riemann integral is unable to handle functions which are highly oscillating, as it uses uniform meshes in its definition of the Riemann sums. However, a slight modification of the Riemann integral, by replacing the uniform mesh with one that varies from point to point, results in an integral that is much more general than the Riemann integral, and even the Lebesgue integral. This was independently discovered by Henstock and Kurzweil, hence the integral was termed Henstock-Kurzweil integral. The tag in the interval-pair point can be any point within the interval. In extending this notion of non-uniform mesh to stochastic integral, much restrictions on the tag occurs. Still, the modified Henstock-Kurzweil stochastic integral has been shown to encompass the classical stochastic integral, namely, the Ito integral and the Stratonovich integral. Through the work of the stochastic integral, a re-visit to the non-stochastic integral brings new light on the approach to the integral. This talk discovers the gist in the journey of the work described above.

Henstock Ito’s Approach to Non-Stochastic Integral

Clara Lim Ying Yi

We are all familiar with the Riemann integral. In this presentation, we explore the generalized Riemann approach using non-uniform mesh, which gives rise to integrals that are more general than the Riemann integral. We consider the special interval-point pair in defining the Riemann sum, where the point (or the tag) is the left-hand point of the interval. As a result, the integration-by-substitution and by-parts formulae become easy consequences of the definition.

Probabilistic Powerdomains

Mark Lim

In my Masters research, I aim to understand the domain-theoretic properties of the probabilistic powerdomains and their topological selves, the spaces of valuations. The probability theory we are all familiar with involves finite sets such as coins tosses, or the tossing of a dice and are deterministic. The event space is mapped to the interval [0, 1]. Valuations become important when dealing with non-deterministic events. One of the major results in Valuations is the Jone’s Lemma. In the course of my research I have studied this lemma and will now be the theories leading up to the lemma. While it is unlikely for my presentation to cover the entire lemma deeply, I hope that it will at least spark interest in this beautiful area of Mathematics.