Abstracts of Presentations

Computational thinking: Research areas and development – ideas from the Topic Study Group in the recent ICME 2024

A/P Tay Eng Guan , MME, NIE

According to Stephens and Kadijevich (2020), Computational Thinking (CT) consists of the four components, decomposition, abstraction, algorithmisation, and automation. Further, they stated that Algorithmic Thinking (AT) consists of decomposition, abstraction, and algorithmisation. AT is one form of mathematical reasoning, required whenever one has to comprehend, test, improve, or design an algorithm. Mathematicians have done this long before the electronic computer. Putting the two descriptions together, we have that CT is thus “AT with a computer”.

At the International Congress of Mathematics Education held in July in Sydney (ICME-15), I co-chaired the Topic Study Group 1.9: Teaching and Learning of Computational Thinking. The talks were divided into four areas: Theory, Curriculum, Teaching and Learning, and Teacher Education. In this talk, I will summarise the main areas of CT research and development that were presented and from these, recommend what I consider viable and fruitful directions for CT research and development in Singapore.

Reference:

Stephens, M., & Kadijevich, D. M. (2020). Computational/Algorithmic Thinking. In Lerman, S. (Ed.), Encyclopedia of Mathematics Education (pp. 117–123). Springer.

Promoting Metacognition and Engagement in Vocational Students

Jerry Wee, EdD graduate student supervised by A/P Lee Ngan Hoe , MME, NIE

This planned study explores the promotion of metacognition and engagement among vocational students enrolled in the Institute of Technical Education (ITE), specifically second-year students in the Higher Nitec in Business Information Systems programme, aged 17 to 19. This study proposed a mixed-method approach, and infuses an intervention programme into the practical labsheets of the "Networking Technology" course. The infused intervention will be applied to one of two intact classes, while the other class will serve as a comparison group. The primary aim of this study is to assess whether there is a significant difference in metacognition and engagement levels between the intervention and comparison classes following the infused intervention. Additionally, the study seeks to capture students’ perceived impact of the intervention on their learning process. Findings from this study could offer valuable insights into promoting metacognition and student engagement within vocational education.

An exemplification of the mathematics register Knowledge Quartet through three tasks

Dr Pauline Tiong, Teaching Fellow , MME, NIE

Language has increasingly been discussed in terms of its role as an important resource in mathematics education research. Similarly, teachers have often been encouraged to use proper mathematical language in their classrooms. However, not many researchers focus on understanding the specific knowledge teachers have in relation to language (in particular, the mathematics register) and how they attend to language in the mathematics classroom. In this presentation, I attempt to exemplify teachers’ knowledge in this aspect through the four dimensions of an adapted version of the Knowledge Quartet, which focuses on the mathematics register as the key aspect of knowledge being analyzed and discussed. Eleven experienced mathematics teachers were interviewed and asked to reflect upon what they noticed and how they would respond to three tasks, designed to illustrate situations which might lead to language-related dilemmas and challenges in using the mathematics register. Their responses were used to exemplify their knowledge (or lack of knowledge) of the mathematics register, in relation to the four dimensions of the Mathematics Register Knowledge Quartet, thus providing insights into how language might be attended to in the teaching and learning of related concepts.

A student’s interplay of cognitive and metacognitive processes when solving word problems: an exploratory study

Melissa Ng, EdD Graduate student supervised by A/P Choy Ban Heng, MME, NIE, and co-supervised by Dr David Huang, OER, NIE.

Studies on mathematical problem solving have suggested that both cognitive and metacognitive processes are crucial for problem solving. Newman (1983) had identified five cognitive processes, which come into play when students are solving word problems, namely reading, comprehending, transforming, processing, and encoding. Wilson and Clarke (2004) referred to metacognitive processes as the awareness of one’s own thinking, evaluation, and regulation of that thinking. Although it is clear that solving a problem involves a complex process, characterised by a continual alternation between cognitive and metacognitive processes, how these two processes work together remains unclear. In this presentation, I examined this interplay of cognitive and metacognitive processes of a high-achieving student as she attempted to solve a challenging word problem. The student was asked to think aloud as she solved an arithmetic word problem and introspective and retrospective interviews were conducted to capture as many thought processes as possible throughout the problem-solving process. The data collected and analysed consisted of the audio and video records of the student’s think-aloud problem-solving attempts, fieldnotes, and the student’s written work. The student’s verbalisations were transcribed and analysed in terms of the cognitive and metacognitive processes to understand how the two processes work together—the interplay of these two processes. I will report on my initial findings and highlight some possible insights and implications for future research and teaching practice.

Development of Items to Assess Big Ideas of Equivalence and Proportionality

Jahangeer Bin Mohamed Jahabar, Teaching Fellow, MME, NIE

Big Ideas can be seen as overarching concepts that occur in various mathematical topics and strands within a syllabus. Within our project on Big Ideas in School Mathematics, we developed instruments to measure two Big Ideas: Equivalence and Proportionality. The instruments we developed seek to assess students’ ability to see these Big Ideas as common ideas connecting within and across topics, and their ability to apply these Big Ideas in solving problems. In this sharing, I discuss how the items developed within each instrument assess the two Big Ideas highlighted.
SSA congruency test and some related results

A/P Zhao Dongsheng, MME, NIE

It is well known that Side-Side-Angle is not a triangle congruency test. We call a triangle ∆ABC an SSA-triangle if for any tringle ∆DEF, ∆ABC is congruent to ∆DEF whenever AB = DE, BC=EF and m∠C= m∠F. We first show a necessary and sufficient condition for SSA-triangles. Then we demonstrate some results in topology, real analysis and domain theory, which have arisen from similar types of problems in the respective areas.

Open-set maize seed variety classification using hyperspectral imaging and one-class classification based incremental learning

Zhang Liu, NGS student at MME, NIE

Rapid and non-destructive classification of seed varieties is one of the important goals pursued by modern seed industry. Due to the large number of maize varieties in practice, collecting training samples that exhaust all varieties to train a classifier is extremely difficult. Therefore, maize seed classification in the real world faces the challenge of variety renewal and rejection of unknown varieties. In this talk, an end-to-end trainable incremental learning (IL) framework based on hypercube data is presented. This method achieves class-IL via learning one-class classifier (OCC) incrementally, and directly uses raw data as input without additional data preprocessing and feature extraction. The OCC is a dual deep support vector data description, which makes full use of spectral and spatial information to establish an exclusive hypersphere for a specific variety to receive the variety and reject unknown varieties. To remove the interference of redundant bands, a band attention and sparse constraint module is added to automatically assign the weights of redundant bands to zero, thereby maximally improving the performance of the model. Moreover, a new loss function is defined to alleviate the difficulty of parameter updating after sparse constraint. Experimental results on our open set indicate that the accuracy of the proposed method for receiving known varieties and rejecting unknown varieties are both above 91 %, which has significant advantages over the other state-of-the-art IL methods. In the future, the corresponding OCCs can also be deleted from the whole framework according to the varieties eliminated by the government to reduce computational overhead and inter-class interference. Overall, the proposed method can perform both IL and open set recognition.

Exactly when is the open set lattice of a topology continuous?

Emil Lua Boon Tiong, Master student at MME, NIE

In learning domain theory, one will start with point set Topology and order theory. In the latter discipline, one will learn about a well-known relation known as the way below relation and the continuous lattice. The subset inclusion is a relation in itself and hence a topology endowed on a set X, Ο(X), is a poset, more precisely a complete lattice. As a poset, one may wonder when Ο(X) is continuous. In this presentation, we will look at the concept of core-compact spaces and the core-open topology. Furthermore, we will look at two very special mappings, Appₓ and Λₓ for function spaces and how these maps help us in understanding the way below relation in topological spaces. This, together with the concept of core compactness, brings out a beautiful result where the natural topology coincides with the core open topology.
Anti-Ramsey numbers for cycles in n-prisms

Li Yibo, NGS student at MME, NIE

An edge-colored graph is called rainbow if all the colors on its edges are distinct. A rainbow copy of a graph H in an edge-colored graph G is a subgraph of G isomorphic to H such that the edge-coloring restricted to H is rainbow. For any two graphs G and H, the anti-Ramsey number, denoted by Ar(G, H), is the maximum number of colors in an edge-coloring of G which has no rainbow copy of H. For n≥3, the n-prism is the cartesian product Cn  K2. In this talk, I will introduce a result determining the anti-Ramsey numbers for cycles in n-prisms.

Linear Vertex Arboricity: Desert or Oasis

Dr. Hang Kim Hoo, MME, NIE

In this talk, an introduction to vertex-arboricity (or point-arboricity) and linear vertex-arboricity of simple graphs will be given. The speaker will share some simple results on the linear vertex arboricity of simple graphs. In particular, results on the full characterization of maximally critical graphs and minimally critical graphs up to order 8 will be presented. Some results on both the vertex-arboricity and linear-vertex arboricity of planar graphs will be highlighted with a suggestion of an alternative pathway to the proof of the 4-colour problem.