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# Ng, Wee Leng

- PublicationOpen AccessThe delivery role and assessment role of computer-based technology in a flipped university mathematics course(2019)
; ; ;Wong, Khoon YoongKwan, Kang LingIn recent years, computer-based technology (CBT) has enabled university lecturers to teach their courses using non-traditional pedagogies. One such pedagogy is the flipped learning model. Under this model, students learn the basic content on their own using pre-class tasks and then come to class to engage in more challenging work such as solving difficult problems. CBT can play two important roles in flipped learning, namely to deliver learning materials efficiently and to assess student achievement effectively. This paper describes how these two roles were applied to a flipped Linear Algebra II course in the National Institute of Education (Singapore), taken by a group of student teachers (n = 15) over a 12-week period from January to April 2018. Their perceptions of flipped activities were gathered using weekly surveys, mid-semester survey, end-of-course survey, and end-of-course interviews. They generally agreed that flipped learning using CBT was helpful and enjoyable. As flipped learning becomes more common among university lecturers in Asian countries, it is beneficial to share experiences of utilising CBT to promote active learning of mathematics among university students.159 100 - PublicationOpen AccessUsing dynamic geometry software to enhance student understanding of the concept of speed(2016)
; Ho, Foo HimThe authors of this paper have conceptualized and constructed a tool, using dynamic geometry software, to simulate scenarios of word problems involving speed, and used it to help students acquire the concept of speed and solve speed problems involving two objects moving toward each other. This paper demonstrates how such a tool can be created using GeoGebra, and describes how the use of this tool had improved understanding of speed concept, and ability to solve speed problems for a class of sixth grade students in Singapore.78 91 - PublicationOpen AccessTeaching and learning calculus with the TI-Nspire: A design experiment(2009)
; ;Tan, Wee ChuenNg, Nancy Meow LengA design experiment was conducted to examine the role of the TI-Nspire, the latest graphing calculator from Texas Instruments, in teaching and learning calculus. This paper reports details on, and preliminary results of, the design experiment involving the design and conduct of a TI-Nspire Intervention Programme for an intact class of thirty-six secondary four students (15-16 years) from a secondary school in Singapore. Use of the TI-Nspire was integrated into teaching and learning Calculus concepts with the aid of the TI Navigator, a wireless classroom network system that enables instant and active interaction between students and teachers. Mathematics attitudes surveys and structured interviews were administered to assess the effects of the use of the TI-Nspire on students’ attitudes towards mathematics. It was found that appropriate use of graphical, numerical and algebraic representations of Calculus concepts using the TI-Nspire could enable the subjects to better visualize the concepts and make generalizations of relevant mathematical properties. Results of paired samples t-tests and interviews with students suggest that there the use of the TI-Nspire has a positive effect on students’ confidence in and perceived usefulness of mathematics.80 136 - PublicationOpen AccessA retrospective study on the effects of flipping a calculus course(2017)
; The purpose of this study was to examine the effects of a calculus course using the flipped classroom model on undergraduate students’ achievement in mathematics which was measured by their scores on three quizzes, a test, and a final written examination, as well as their overall scores. The scores of a total of 58 second year students, comprising 17 students in the experimental group and 41 students in the control group, enrolled in a university degree programme in Singapore were analysed retrospectively using analysis of covariance (ANCOVA) so as to control for initial differences. The experimental group comprised students who took the flipped calculus course in the August 2016 semester while the control group comprised students who took the same calculus course taught using a lecture-tutorial approach in the August 2013 semester. Results of ANCOVA show that after controlling for initial differences the experimental group scored statistically significantly higher in the test but lower in the final examination than the control group.282 77 - PublicationRestrictedTheory of nonabsolute integration(1997)The main objective of this thesis is to define a nonabsolute integral measure theoretically. More precisely we define an integral of the Henstock type, called the H-integral, on measure spaces with a locally compact Hausdorff topology that is compatible with the measure. Relevant results pertaining to the H-integral are established.

In Chapter 1, we define the H-integral and derive the properties that are fundamental to an integral. We describe in Section 1.1 how certain objects in the space are chosen to be generalised intervals and relate the definition to some concrete examples. The H-integral is defined in Section 1.2 and we prove that it includes the well-known Kurzweil-Henstock integral [18] on the real line. The basic properties that hold true for the H-integral, in particular, the Henstock's lemma and the monotone convergence theorem, are derived in Section 1.3.

Chapter 2 aims to relate the H-integral to known integrals. In Section 2.1, we define the M-integral, which is a McShane-type integral, and prove that a function is M-integrable if and only if it is absolutely H-integrable. The domains of H-integration and M-integration are also extended to measurable sets. Subsequently in Section 2.2 we establish the equivalence between the M-integral and the Lebesgue integral. we also show that a function H-integrable on an elementary set is Lebesgue integrable on a portion of the elementary set. In Section 2.3 we establish the fact that the H-integral includes the Davies as well as the Davies-McShane integral defined by Henstock in [13]. This is done by establishing the equivalence between the Lebesgue integral and the Davies as well as the Davies-McShane integral. The conclusion here is that if a function is measurable then the absolute H-integral, the M-integral, the Lebesgue integral, the Davies integral and the Davies-McShane integral and the Davies-McShane integral are all equivalent.

Further results of the H-integral are given in Chapter 3. We begin by proving in section 3.1 that H-integrable functions are measurable and proceed to give a necessary and sufficient condition for a function to be H-integrable. We also prove that the H-integral is genuinely a nonabsolute one by constructing an example which is H-integrable but not absolutely H-integrable. Two concepts very relevant to the H-integrability, namely the generalised absolute continuity and equi-integrability, are introduced in Section 3.2 and some results involving these concepts are proved. Section 3.3 is devoted to proving the convergence theorems of the H-integral. We start with the proofs of the equi-integrability theorem and the basic convergence theorem and illustrate how the mean convergence theorem can be proved with the aid of the two former theorems. The controlled convergence theorem is proved in s few lemmas and by applying the basic convergence theorem.

Chapter 4 is the most important part of this thesis. We generalise our work in [23] for the H-integral in this chapter. The main theorem, namely the Radon -Nikodym theorem for the H-integral, is proved in Section 4.1 with which we give a descriptive definition of the H-integral in Section 4.2. By imposing a different condition, a second version of the main theorem and subsequently a second descriptive definition of the H-integral are also given. The purpose of Section 4.3 is to report on our findings in [23]. some results corresponding to those we prove in Section 4.1 are given for the Euclidean space setting. We also show how some known results on the real line, for example, the fundamental theorem of calculus for the Kurzweil-Henstock integral, can be deduced.362 12 - PublicationRestrictedFlipped linear algebra and calculus for pre-service teachers (FLACPT)
In recent years, university instructors in many countries have implemented “flipped” learning as one form of “blended learning” to bring about more active learning of undergraduate courses, in particular Mathematics, Science, Engineering, Computer Science, and Information Technology. Under this model, the traditional pedagogy of using class time to lecture on new academic content followed by completing assignments outside class is “flipped” so that students learn some of the new content on their own and then come to class to resolve their confusions and to engage in extended problem solving. The details of flipped learning vary considerably, but the main claim, based on learning theories and research findings, is that under this learning model, supported by digital resources, students will enjoy this type of learning, master the academic contents, and develop intellectual skills, such as independent learning using technology and print materials, critical thinking, and collaboration (Bishop & Verleger, 2013; Brewley, Boindala & Sinclair, 2017; Fulton, 2014; Hamdan, McKnight, McKnight & Arfstrom, 2013; Herreid & Schiller, 2013; Love, Hodge, Grandgenett & Swift, 2014; O’Flaherty & Phillips, 2015).

In Singapore, DPM Heng Swee Keat, then Minister for Education, in his keynote address at Work Plan Seminar 2013, recommended developing flipped classroom as an initiative to enrich student learning in schools. At the university level, Nanyang Technological University (NTU), through the NTU Education 2013 initiative, has begun to trial flipped classroom in some of its schools, as preparation for introducing this model across the university in the coming years. Hence, there is a need to study the nature and effects of flipped classrooms to address the current dearth of local research about this model. The theorization, resources, and findings from this project will also highlight Singapore’s contribution to the ongoing global discussion about this exciting pedagogy.

12 72 - PublicationOpen AccessTransformational leadership and the integration of information and communications technology into teachingInformation and communications technology (ICT) has now permeated nearly every facet of society and there is a growing need for school leaders to play a more active role in integrating ICT into teaching. While it is conceivable that transformational leadership, which has been found to be an essential form of leadership in dealing with challenges facing contemporary schools, has effects on efforts to implement school innovations such as ICT integration, to date no such study has been conducted. This study therefore field-tests a questionnaire designed to investigate teachers' perceptions of positive influence of transformational leadership practices on the integration of ICT into teaching.
1011 1988 - PublicationOpen AccessAn alternative definition of the Henstock-Kurzweil integral using primitivesWe introduce the notion of an H-primitive being the limit of a sequence of absolutely continuous functions satisfying certain conditions and use it to formulate an alternative definition of the Henstock-Kurzweil integral on a closed bounded interval. Furthermore, the definition provides a characterisation of the primitive of a Henstock-Kurzweil integrable function.
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