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Toh, Tin Lam
- PublicationOpen AccessFrom the past to the future of technology in mathematics education in SingaporeThis paper discusses the changes in classroom instructions due to technology over the years in mathematics education, and how these changes have impacted mathematics learning and teaching. The impact on learning can be seen over a few phases in Singapore: The use of scientific and graphing calculators has allowed the focus on the developing of higher order thinking skills, while at the same time de-emphasizing the routine computation. With the introduction of various computer softwares such as spreadsheets, mathematics teaching and learning has moved towards the next level of emphasis on coding and computational thinking. Technology can and has been harnassed by teachers to enhance student learning. These will be discussed in details in the talk, with particular reference to the Singapore education context.
32 377 - PublicationOpen AccessUse of real-world contexts in instructional materials designed by pre-university mathematics teachersPre-university education in Singapore serves as a bridge between secondary and university education. Despite its importance in the Singapore education system, few studies have been conducted on Singapore pre-university mathematics. We also notice that problems in real-world contexts have been increasingly emphasized in the Singapore mathematics curriculum. In this paper, we study the infusion of real-world contexts in the design of instructional materials in a typical pre-university institution, with a focus on the topic of vectors. The real-world contexts used in the instructional materials are categorized into neutral contexts or real-life experiences, where each of these categories has their benefits. These include the potential to raise students’ awareness that mathematics can be used to solve real-world problems and explain real-world phenomena. Their alignment to the Singapore mathematics syllabus and 21st Century Competencies is also discussed.
83 93 - PublicationOpen AccessUse of dynamic geometry software in the teaching of matrix and transformation: An exemplar of a classroom enactmentPurpose and Research Question - In this paper, we propose a SCCG framework for using a dynamic geometry software (DGS) to enact a lesson on “Matrix and Transformation” based on intuitive-experimental approach. Methodology - A systematic literature review was conducted focusing on the impact of DGS on students’ learning, drawing on various learning theories, including Skemp’s relational understanding, social dimensional constructivism, and discovery learning. Findings - We demonstrate with an exemplar the use of SC2G framework in designing one lesson on “Matrix and Reflection” for senior high school students.
45 291 - PublicationOpen AccessComics for mathematics instruction for future-ready learners(Association of Mathematics Educators, 2023)
; ; ; In this paper we present the views that the roles of comics for mathematics instruction extend beyond the role of addressing the affective needs of students, in particular the lower achieving students. We argue that within the broader framework of contextualization, comics have the potential to reach out to the entire spectrum of students to develop their higher order thinking skills and even raise their cognizance to environmental issues. Two exemplars based on the research carried out by us are presented.76 120 - PublicationMetadata onlyThe evolution of mathematics education research in Singapore
Up until 1990, the Institute of Education in Singapore was primarily a teaching institute involved in training teachers for Singapore schools. Since the inception of the National Institute of Education (NIE) in 1990, as an institute of the Nanyang Technological University, the focus of the institute has been enlarged to include research in education. This chapter examines, through a documentary analysis, how a research culture specifically in mathematics education at the National Institute of Education was nurtured, developed and supported from 1990 onwards. Development of the culture for Mathematics Education Research (MER) has been in tandem with all other areas of research at the NIE. Both top-down and bottom-up approaches have been adopted to support research as part of an academic’s work at the institute. Policies related to recruitment and promotion of academics were developed to ensure that emphasis was on both teaching and research. Development of research, from individually led bite-sized grains to team-based project with coherent themes, was supported. The setting up of the Centre for Research in Pedagogy and Practice in 2004 and dedicated funding from the Ministry of Education Singapore for research of the Singapore education system heralded an era of MER that has made significant contributions both nationally and internationally. This chapter will also illuminate the four main areas of focus and sources on MER through examples of studies carried out in Singapore since 2000. In addition, it briefly outlines the contribution of MER in ASEAN countries.
17 - PublicationRestrictedEnhancing the pedagogy of mathematics teachers to facilitate the development of 21st century competencies in their classrooms (EPMT-21st CC)(Office of Education Research, National Institute of Education, Singapore, 2023)
; ; The results of both PISA (2009, 2012) and TIMSS (2011, 2007) for Singapore show us that majority of our students are very good in applying their knowledge in routine situations and this is definitely a consequence of what teachers do and use during their mathematics lessons. For our students to scale greater heights we need our teachers to nurture metacognitive learners who are active and confident in constructing mathematical knowledge.
A significant finding from the CORE 2 research at NIE led by Professor David Hogan is that amongst the secondary three and primary five mathematics lessons that were studied teachers appeared to engage students in doing performative tasks (77.3% for secondary 3 and 63.7% for primary 5) more often than knowledge building tasks (22.7% for secondary 3 and 36.3 % for primary 5) (Hogan et al, 2013). A performative task mainly entails the use of lower order thinking skills such as recall, comprehension and application of knowledge while a knowledge building task calls for higher order thinking skills such as synthesis, evaluation and creation of knowledge.
Hattie (2009), drawing on 50,000 research articles and related achievement of 240 million students, notes that the greatest source of variance in the learning equation comes from teachers. Therefore as we are desirous of improving student learning, in our mathematics classrooms, it is critical that we engage our teachers in specific and targeted professional development.
24 9 - PublicationOpen AccessHow formal should calculus in the school mathematics curriculum be: Reflections arising from an error in a calculus examination question(Association of Mathematics Educators, 2023)
; ; ; ; Lee, HenryThis paper examines the calculus curriculum in the current Singapore secondary and pre-university levels. Two concepts, (1) increasing and decreasing functions and their derivatives, and (2) the second derivative test for the nature of stationary points, are elaborated. An example of an incorrect calculus item in a national examination is brought up in relation to conditional reasoning involving calculus concepts. We reckon that the current emphasis on procedural knowledge in calculus is useful. However, we argue that formal conditional reasoning should not be introduced prematurely for school students.289 217 - PublicationOpen Access
27 56 - PublicationMetadata onlyA regularized logistic regression model with structured features for classification of geographical origin in olive oilsGeographical 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.
Scopus© Citations 2 46 - PublicationOpen AccessA model for scaffolding mathematical problem-solving: From theory to practiceDevising a plan is an important phase in the teaching and learning of mathematical problem-solving in a mathematics classroom. In this paper, we propose devise a plan (DP) model for scaffolding students in devising a plan to engage them in mathematical problem-solving for classroom instruction and beyond. Although mathematics educators have proposed problem-solving scaffold, mainly building on Polya’s (1945) and Schoenfeld’s (1985) problem-solving models, for authentic problem-solving in the classroom, the phase on devising a plan was generally brief. We expand on the scaffolding of the intermediate stages of devising the plan for teachers to teach problem-solving, with a more ambitious goal of enabling students to engage in independent problem-solving beyond the classrooms. Features that are used in the planning stage of problem-solving are identified through a systematic literature review. Our proposed DP model includes the use of both metacognitive strategies and problem-solving heuristics. The application of our proposed model was exemplified by the solution of three non-routine problem on proportionality.
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