Now showing 1 - 10 of 17
  • Publication
    Open Access
    Passing a proof message: Student-teacher communication through a commognitive lens
    This study employs Sfard’s (2008) socio-cultural theory of Commognition to analyse student teachers’ thinking and communicating practices. Specifically, we investigate the effectiveness of the student teachers’ communication of a particular mathematical proof with reference of the four features of the commognitive framework, i.e., word use, visual mediators, narrative and routines. In this paper, we can report on the routine of the discourse to analyse the quality of mathematical discourse in two situations of “Expert-to-Novice” and “Novice-to-Novice”.
      218  207
  • Publication
    Open Access
    The delivery role and assessment role of computer-based technology in a flipped university mathematics course
    (2019) ; ;
    Wong, Khoon Yoong
    ;
    Kwan, Kang Ling
    In 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.
      153  78
  • Publication
    Open Access
    A semester-long flipped calculus course for pre-service teachers in Singapore
    (2021) ; ;
    Wong, Khoon Yoong
    ;
    Kwan, Kang Ling
    This paper reports on a study on a semester-long flipped university mathematics course (Calculus II) taught to a cohort of pre-service teachers enrolled in the Bachelor of Science (Education) programme at the National Institute of Education, which is the autonomous teacher training institute of Nanyang Technological University, Singapore. The current study is the second phase of a three-phase project which developed a comprehensive framework to guide the design of three stages of flipped learning activities: pre-class tasks; in-class interactions; and post-class consolidation. A mixed methods research design was used to collect quantitative and qualitative data over many occasions, through methods such as weekly surveys, to investigate students’ perceptions of flipped learning activities. Results of the study suggest that the students generally found the flipped learning activities helpful and enjoyable.
      75  70
  • Publication
    Open Access
    Flipped linear algebra and calculus for pre-service teachers.
    (National Institute of Education (Singapore), 2020) ;
      96  111
  • Publication
    Open Access
      374  193
  • Publication
    Open Access
    How formal should calculus in the school mathematics curriculum be: Reflections arising from an error in a calculus examination question
    This 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.
      274  175
  • Publication
    Open Access
      162  149
  • Publication
    Open Access
    Assessing mathematical competencies using disciplinary tasks
    (2012)
    Cheang, Wai Kwong
    ;
    ;
    The Singapore Mathematics Assessment and Pedagogy Project (SMAPP) is a research project conducted by the National Institute of Education and funded by the Ministry of Education. It aims to make assessment practices an integral part of teaching and learning, and broaden student learning outcomes by using authentic disciplinary tasks. As part of the project, some guidelines are provided for designing disciplinary tasks which have the distinctive features of their emphasis on contextual aspects. One of the criteria of a good disciplinary task is its ability to assess multiple mathematical competencies of students. In this paper, we will present some examples to illustrate how these competencies can be assessed. Another aim is to find out to what extent these tasks serve the purpose of assessing these competencies, by analyzing the students’ performance in a sample SMAPP task.
      220  301
  • Publication
    Open Access
    Nature and perceptions of pre-class tasks used in a flipped linear algebra course for pre-service teachers
    (2020) ; ;
    Wong, Khoon Yoong
    ;
    Kwan, Kang Ling
    In recent years, computer-based technology has enabled university lecturers to teach their courses using non-traditional pedagogies. One such pedagogy is the flipped learning model. As flipped learning is being used more frequently to teach undergraduate mathematics, instructors need to collect data to identify practices that work well to promote student mathematics achievement and favourable perceptions toward this new learning mode. This paper describes six different types of pre-class tasks for a flipped Linear Algebra II course in a Singapore university, such as short videos narrated by the instructor, synopses, summary sheets, worksheets of problems and activities, and online quizzes. The sample comprised 15 pre-service teachers, who had adequate to good mathematics backgrounds, and their participation in this project would prepare them to implement flipped learning in school mathematics in the future. On average, they spent about one hour to complete these weekly pre-class tasks, but the stronger ones reported spending less time on these tasks than the other students. Almost all the students rated very highly these tasks in terms of helping them to learn and enjoyment at mid-semester and end-of-course surveys. These perceptions had weak correlations with the course grade. Suggestions for practice and future research are discussed.
      104  76
  • Publication
    Open Access
    Comparison of pricing models with simulated demand data
    (2014)
    Soon, Wan Mei Amanda
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    ;
    Many types of pricing models incorporating different forms of demand functions have emerged in the past years. In an earlier work, a piecewise- defined Complementarity-Constrained Demand Function (CCDF) was discussed to correct certain weaknesses in commonly used demand functions. The authors introduced a Complementarity-Constrained (CC) pricing model incorporating the CCDF in that same work. However, there was a lack of numerical implementations therein. Hence in a separate work, we developed an algorithm using MATLAB to compare a generic pricing model and a CC pricing model. Experiments were performed to compare the revenues from the two models for certain ranges of parameters defining the demand function. In this work, we conduct further numerical testing by simulating the bidding behaviours of different types of customers and using simulated demand data to compare the models. We find that the use of the CC model leads to higher revenues for certain simulated scenarios.
      137  152