Now showing 1 - 10 of 26
  • 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.
      277  178
  • Publication
    Open Access
    Using comics to contextualise the teaching of percentages: An adaptation of a comics-based teaching package for primary school mathematics classrooms
    In this article, an adaptation of a secondary school mathematics comics-based instructional package for primary school mathematics classroom, and the teachers' and students' perceptions about the use of comics in the classroom are discussed. Further suggestions by the teachers on fine-tuning the package are also discussed.
      63  198
  • Publication
    Open Access
      24  48
  • Publication
    Open Access
    Use of real-world contexts in instructional materials designed by pre-university mathematics teachers
    (2023)
    Tan, Zheng Han Hans
    ;
    ;
    Fah, Lay Yoon
    Pre-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.
      46  57
  • Publication
    Open Access
    Fallacies about the derivative of the trigonometric sine function
    (2021) ; ;
    Tong, Cherng Luen
    In this paper, several fallacies about the extension of the formula \frac{d}{dx} (\sin x) = \cos x to the erroneous formula \frac{d}{dx} (\sin x^\circ) = \cos x^\circ are discussed. In a Commognitive Theory Framework, misconceptions by ‘newcomers’ can be traced to the use of the word “unit”.
      89  178
  • Publication
    Open Access
    Game based assessment in the mathematics classroom
    (2021)
    Leong, Eunice Ying Xuan
    ;
    The objective of this paper is to present a conceptualization and creation of a game-based assessment to address student anxiety and accelerate students’ learning through the immediate feedback given in-game. We used a revised form of Computerized Adaptive Testing in order to adapt to the test-takers’ ability and knowledge level. We adapted the Computerized Adaptive Testing to design our game-based assessment. Our design is guided by the existing education literature about student learning and the context of the game is based on the current trend of popular culture among school-going age children. We propose a game which incorporates the features of the three types of assessment: assessment for learning, assessment of learning and assessment as learning. The structure of the game-based assessment allows students to proceed as a pace which is suitable for the individuals. Through the use of a technology enhanced game-based assessment, we hope to reduce students’ anxiety related to assessment, and that they are able to progress at a customized learning.
      194  112
  • 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
    A model for scaffolding mathematical problem-solving: From theory to practice
    (2023)
    Tay, Yong Khin
    ;
    Devising 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.
      74  89
  • 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
    Teaching and learning complex numbers through problem solving
    With reference to complex numbers, it is argued in this paper that attention should not only be focused on the practical usefulness or the aesthetics of mathematics to make mathematics attractive to students. Teachers could ride on the affordance of the problem solving mathematics curriculum framework in engaging students in activities that reveal the “power” of mathematics in solving mathematics problems and generalizing the results. The paper illustrates how portions of complex numbers, a pre-university mathematics topic, could be introduced through the various stages of mathematical problem solving. The use of complex numbers is a natural progression from basic algebraic manipulation at the secondary level and could be introduced through expanding a problem in the problem solving process; students could be introduced to the power of mathematics in providing an alternative solution or proof to mathematics problems from geometry and calculus. The roots of a complex numbers can be introduced by teaching through problem solving and re-enacting the (simplified) process of how mathematicians discovered complex numbers.
      75  153