Now showing 1 - 8 of 8
  • Publication
    Open Access
    Teaching undergraduate mathematics: A problem solving course for first year
    In this paper we describe a problem solving course for first year undergraduate mathematics students who would be future school teachers.
      51  86
  • Publication
    Open Access
    On pre-service teachers' content knowledge of school calculus: An exploratory study
    This paper reports an exploratory study on the pre-service teachers’ content knowledge on school calculus. A calculus instrument assessing the pre-service teachers’ iconic thinking, algorithmic thinking and formal thinking related to various concepts in school calculus was administered to a group of pre-service mathematics teachers. Their performance on five of the items is reported in this paper. Other than their good performance in the iconic recognition of stationary points, their recognition on points of inflexion, differentiability and notion of minimum points was relatively poor. In addition, they appeared to lack the algorithmic flexibility in testing the nature of stationary points and the formal thinking about definition of an extremum point. The implications of the findings are discussed.
      99  121
  • Publication
    Open Access
    Comparison of pricing models with simulated demand data
    (2014)
    Soon, Wan Mei Amanda
    ;
    ;
    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  161
  • Publication
    Open Access
    Nature and perceptions of pre-class tasks used in a flipped linear algebra course for pre-service teachers
    (Association of Mathematics Educators, 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.
      106  81
  • Publication
    Open Access
    How 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, Henry
    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.
      277  178
  • Publication
    Open Access
    A semester-long flipped calculus course for pre-service teachers in Singapore
    (Association of Mathematics Educators, 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.
      77  73
  • Publication
    Open Access
    A study of pre-service teachers' performance on two calculus tasks on differentiation and limit
    The purpose of this paper is to report a part of a calculus research project, about the performance of a group of pre-service mathematics teachers on two tasks on limit and differentiation of the trigonometric sine function in which the unit of angle measurement was in degrees. Most of the pre-service teachers were not cognizant of the unit of angle measurement in the typical differentiation formula, and a number of participants recognized the condition on the unit of angle measurement but did not translate this to the correct procedure for performing differentiation. The result also shows that most of the participants were not able to associate the derivative formula with the process of deriving it from the first principle. Consequently, they did not associate it with finding . In the process of evaluating this limit, the pre-service teachers exhibited further misconceptions about division of a number by zero.
      151  208
  • Publication
    Open Access
    Hands, Head and Heart (3H) framework for curriculum review: Emergence and nesting phenomena
    In this work, we report the emergence of the Hands, Head and Heart framework that arose within the curriculum review for subject knowledge courses for primary school pre-service teachers in the National Institute of Education, Singapore. Through an initial grounded analysis of a survey of pre-service teachers and faculty focus group meeting data, the responses were broadly categorised into hands, head and heart domains and these formed an initial framework for discussions in the review committee meetings. By revisiting the data from the survey, an analysis through a complexity lens revealed the emergence of a characteristic nested self-similarity of the framework. Over the course of several committee meetings, further self-similarity was discovered. We conjecture that the Hands, Head and Heart framework and its self-similarity property provide a potential basis for a holistic approach to curriculum review. We used this framework to revise the learning objectives of the subject knowledge curriculum by resolving perspectives which previously seemed contradictory.
    WOS© Citations 2Scopus© Citations 5  110  1527