Toh, Tin Lam

2024, Ng, Yu Xin, Toh, Tin Lam

In addressing the key role that problem solving has been playing in mathematics instruction for K-12, this paper aims to assist mathematics teachers and educators to consider a set of guiding principles for designing problem solving tasks for classroom instructions. The set of guiding principles was synthesized and proposed through the researchers’ systematic review of existing education literature on problem solving.

2022, Toh, Tin Lam

A case study of calculus instructional material (comprising of lecture notes and tutorial practice worksheets) designed by teachers from a Singapore pre-university is presented in this paper. As textbooks have not been available for mathematics at the pre-university levels, the instructional material was a product of the teachers’ collaborative work based on their interpretation of the school mathematics curriculum. Through a study of the instructional material, the teachers’ instructional goals and their alignment to the curriculum were examined. It was clear that the instructional material was more than a mere compilation of resources for the instruction; the teachers’ effort was also in building the close connection within and across the concepts and sub-topics. The discrete parts of the content were organized under a “big idea” in the lecture notes. Anchor questions were used in the tutorial practice worksheets to facilitate students to recognize the similarity of the underlying structures of seemingly different questions. In addition to the teachers’ articulated instructional goals such as covering all the key concepts, reducing students’ cognitive load, or developing their algorithmic mastery, the study revealed the unarticulated goal as to raise the students’ cognitive growth, which could be explained by the APOS cognitive growth model. In aligning to the school curriculum, it was observed that the teachers made judgement to tap on the advantage of the spiral curriculum to advance their students’ understanding of calculus from the secondary level using a higher perspective, and to better their students’ understanding of calculus concepts in addition to focusing on algorithmic mastery. The effort to engage their students in problem-solving and the use of technology to develop higher order thinking or enhance conceptual understanding remained implicit.

2021, Toh, Tin Lam

In this paper, the Singapore school calculus curriculum at the upper secondary and the pre-university levels is examined in the light of the Singapore mathematics curriculum framework. Three key features of the calculus content are discerned: (1) an intuitive approach to calculus supported by the use of technology; (2) an emphasis on techniques; and (3) an emphasis on procedural over conceptual knowledge. Following that analysis, a review of the performance of a group of pre-university students on selected calculus tasks in a calculus survey prior to and after their learning of pre-university calculus is discussed. The students’ performance in the survey shows that many students did not visually identify calculus concepts that were studied procedurally. They demonstrated a lack of conceptual understanding of the calculus procedures. This study suggests that the partial calculus knowledge acquired in the early upper secondary levels might not necessarily facilitate the acquisition of a more complete concept at the pre-university level. Furthermore, the students’ procedural knowledge of calculus did not seem to develop their procedural fluency or flexibility.

2023, Tay, Xiu Wen, Toh, Tin Lam, Cheng, Lu Pien

A research project on using comics for teaching mathematics was initiated in one Singapore primary school. One class of Grade 5 (students of age 11–12) students was exposed to comics for mathematics instruction. This paper reports a case study of seven students’ perception of the features of the comics instructional package and how these features impacted their learning of mathematics. The students’ responses in an interview with the researchers were analysed using Thematic Analysis and presented using the Singapore mathematics curriculum framework. Four main features of the comics instructional package: (1) humour; (2) story narrative; (3) scaffolding provided by the questions and (3) visuals and four main themes: Increase in (a) enjoyment; (b) understanding; (c) appreciation of real-world applications of mathematics and (d) participation during lessons; were uncovered. The use of comics could potentially impact positively on developing students’ Attitudes, Skills, Concepts and Processes of the Singapore mathematics curriculum framework in learning mathematics.

2023, Soh, Chin Gi, Zhu, Ying, Toh, Tin Lam

Geographical origin of extra virgin olive oil is a factor that consumers may take into account when making purchasing decisions. Oils that are labelled to be from regions famous for olive cultivation may be assumed to be of higher quality. However, difficulties in the authentication of the geographical origin of olive oils arise due to the similarity in chemical compositions of the oils involved. Fourier-transform infrared (FTIR) spectroscopy has been found to be a viable technology for the classification of oil samples by geographical origin. However, classical methods involving dimension reduction before model fitting usually yield models that are more challenging to interpret. Sparse fused group lasso logistic regression (SFGL-LR) is used with FTIR spectroscopic data to discriminate between Greek and non-Greek organic extra-virgin olive oils. The prediction performance is also compared with that obtained by partial least squares linear discriminant analysis (PLS-LDA). While both methods give comparable good prediction performance, with more than 90% accuracy in classification, the SFGL-LR model demonstrates improvements in the interpretability of the model coefficients.

2024, Muhammad Noor Kholid, Yoga Tegar Santosa, Toh, Tin Lam, Agung Putra Wijaya, Imam Sujadi, Heris Hendriana

Study on fragmentation and defragmentation of reflective thinking structures has never been conducted. Therefore, the purpose of this study was threefold: (1) to identify the types and forms of fragmentation of students’ reflective thinking structures in solving mathematical problems, (2) to describe attempts to defragment students’ reflective thinking structures in each type and form of fragmentation, and (3) to find out if such defragmentation attempts can work for reflective thinkers who experience fragmentation. This research was qualitative, exploratory, and descriptive. The subjects included in this study were students who thought reflectively and experienced fragmentation at each level of reflective thinking when solving mathematical problems. Data collection was conducted using tests, interviews, think-aloud protocols, and observation. Data analysis was conducted using constant comparative method. Data validity was established using method and source triangulation. The results showed: (1) Scanning Defragmentation work for Less-Strict Fragmentation, (2) Schema Emergence Defragmentation work for Pseudo-True Fragmentation, (3) Schema Activation work for Pseudo-False Fragmentation, (4) Connection Emergence Defragmentation work for Nonexistent-Connection Fragmentation, (5) Compare-Reflect Defragmentation work for Confidence-False Fragmentation. The results of this study can be reference for mathematics researchers and educators to develop learning models that can prevent the occurrence of fragmentation of reflective thinking structures.