Abstracts of Presentations

Teaching multiplications of decimals by 10, 100 and 1000

Jahangeer Bin Mohamed Jahabar

This presentation will show how a P5 math teacher attempted to facilitate the development of the Big idea of Equivalence whilst engaging students in working through the multiplication of decimals and numbers like 10, 100 and 1000. An interesting incidental finding surfaced when a student attempted to explain how a decimal point cannot shift during the multiplication process!

Impact of listening pedagogy on mathematics teacher thinking during lesson study

Aneesah Latife

Listening is involved in daily school activities, but its importance is often overlooked and underestimated. Good teaching practices evolve from telling to listening in order to understand the needs of the student. Listening to students’ thinking is vital for mathematics instruction to be effective. This presentation presents lesson study, a form of teacher professional development, as a contextual platform for developing the practice of listening pedagogy. In this study, it is proposed that listening pedagogy can serve as a critical enabler for effective teacher learning from lesson study. Learning from lesson study requires substantial efforts from teachers to adopt a listening stance such that it points to a dialogic relationship between lesson study and listening pedagogy. This dialogic relationship poses two interesting questions that were investigated: 1) What are the changes in a teacher’s thinking of listening pedagogy during lesson study? and 2) how do these changes in thinking impact a teacher’s classroom practices? The findings of the study suggest that lesson study allowed for rich teacher learning to take place which had an impact on teacher beliefs that contributed to the thinking of listening pedagogy.

The Considerations when Teaching Lower Progress Students Indices

Lee Ming Xuan Damien

In schools, Indices can sometimes be seen as a chapter consisting of many formulas that students have to memorise with little to understand. Lower progress students, especially, may have difficulty in making sense of the chapter. How can teachers, then, try to help lower progress students make sense of indices, while also focussing on helping them gain fluency in the use of these formulas? In University Mathematics, we always start with the definitions of mathematical objects before understanding the relationships between these objects. Similarly, in the case of Indices, the laws of indices can be derived from some basic definitions. However, when considering the teaching of indices in secondary settings for lower progress learners, starting with these definitions would result in a high cognitive load for students, and lower progress students may find it difficult to accept these laws or definitions without a meaningful context. Therefore, we want to find a way to balance the need to keep to the disciplinary process of mathematics while not cognitively overloading the students. This presentation will discuss i) the need for motivation leading to definitions of zero and negative indices, ii) the importance of structure in the instructional materials for teaching indices, iii) how to link the laws of Indices in order to reduce cognitive load for students and iv) how these considerations can be applied in other topics.

Teaching Percentages: How else can we do it?

Nyam Hsu Tse Sarah

The benefits of the Concrete-Pictorial-Abstract (CPA) approach are plenty, however little work has been done in Singapore to investigate the prevalence of CPA usage and how CPA has been or can be used in our context. Since the introduction of the Primary Mathematics Project (PMP), textbooks have been produced resembling the CPA approach – however, CPA is currently not used regularly in Singapore as teachers often face time pressure, resulting in the neglect of building sense-making processes in students (Leong, Ho, & Cheng, 2015). Percentage has been a topic which students have struggled with for a long time – one of the most common difficulties is seeing the relation between fractions, decimals and percentage (Parker & Leinhardt, 1995). Students have traditionally been taught rote procedures, which have resulted in instrumental understanding more than relational understanding (Glatzer, 1984). This results in students lacking the necessary structures or “back-up” that they can fall back on, should they be unable to solve a problem. This presentation will illuminate how the CPA approach may support the sense-making approach to the learning of percentages by students.

The CTD Lesson planning tool for mathematics teachers

Caron Ong Kai Loon

Lesson planning is a critical aspect of teachers’ planning for instruction. A mathematically robust lesson is one in which the mathematics is focused and coherent, the cognitive demand of work students engage with is appropriate, and students have agency, authority and identity for the learning of mathematics (Schoenfeld, 2014). In a mathematically robust lesson, classroom discourse is a lens through which the teacher can assess student learning (Smith & Stein, 2011). The revised secondary school mathematics curriculum places emphasis on Big Ideas in Mathematics, with the aim for students to develop mathematical knowledge as a body of connected knowledge rather that isolated bits of knowledge spread across the years of schooling (MOE, 2018). For teachers to teach towards Big Ideas, they need to make deliberate plans about how they would enact the core of their mathematics instruction, comprising content, task and discourse. To facilitate their planning the CTD lesson planning tool may be warranted is proposed. During the presentation aspects of the Tool and its efficacy will be discussed.

A mathematics education dissertation – what does it entails?

Berinderjeet Kaur

Postgraduate students pursuing the Master of Education (Mathematics) have an option to do a dissertation as part of their study at the National Institute of Education, Singapore. A dissertation is an academic piece of writing on a piece of research that is focussed and original. This presentation will share with participants the scope and expectations of such an academic endeavour.
Two ways to a fractal

Tay Eng Guan

A deterministic fractal may be defined to be a fixed point of a contractive transformation on a metric space comprised of the compact sets of R2 and a suitable metric. We are more familiar with the ‘definition’ of a fractal as “beautiful natural looking images with inherent self-similarity”. In this talk, we shall discuss the underlying theory of fractals and show how to generate fractals in two ways – deterministic and probabilistic. We will use simple VBA coding in the Excel environment to graph beautiful fractals such as the Sierpinski Triangle, the Koch curve and its fortuitous variant the Fire.
Ramsey number, anti-Ramsey number and Turán function

Zhang Meiqiao

Imagine that you are about to host a party. How many people do you need to invite to make sure that at least r people will know each other or at least s people will not know each other? One interpretation of this problem makes perfect use of graph theory and introduces the concept of the Ramsey number R(r, s), whose existence actually reveals that there is order in chaos. In this talk, some classical results of Ramsey numbers will be introduced, as well as some related contents of anti-Ramsey numbers.
An introduction to Jacobi's Triple Product Identity

Chan Heng Huat

In this talk, I will first derive an identity which generalizes the finite version of the binomial theorem. I will then introduce Jacobi's Triple Product Identity from this generalization of the binomial theorem. The talk will end with some remarks about other proofs of Jacobi's Triple Product Identity.

A study of Ou Yongbin’s “Intersecting and t-cross-intersecting Set Systems”

Queenie Chiu

There are many problems involving communication and passing on information, and we focus on two modified versions of such problems where two divisions of spies can successfully share intel only when there are at least a required number of common spies between the two divisions. Motivated to find the maximum number of possible divisions with the requirement that every spy knows all intel, we studied two chapters of Ou Yongbin’s thesis where he stated some common results as well as proved a few main results. In our report, we looked closely at the proofs provided by Ou as well as related theorems that were stated without proof and filled in the gaps wherever necessary.

Domain Theory

Emil Lua

An injective space is a topological space with a strong extension property for continuous maps whose evaluation takes place in it. This Final Year Project (Academic Exercise) is devoted to studying only one famous theorem that was first established by Dana Stewart Scott in 1972– the main idea of which is to give a purely topological characterization of continuous lattices in terms of T0 spaces as injective objects in the category of T0 spaces and continuous maps. We also studied some known facts about hypercontinuous lattices and have some new findings concerning these lattices. These new findings are a result of joint-work with my supervisor, A/P Ho Weng Kin.