Now showing 1 - 10 of 79
  • Publication
    Open Access
    Use of practical worksheet in teacher education at the undergraduate and postgraduate levels
    (2012) ; ;
    Ho, Foo Him
    ;
    Quek, Khiok Seng
    We have applied the ‘practical paradigm’ in teaching problem solving to secondary school students. The key feature of the practical paradigm is the use of a practical worksheet to guide the students’ processes in problem solving. In this paper, we report the diffusion of the practical paradigm to university level courses for prospective and practising teachers. The higher level of mathematics content would demand higher order thinking skills. Learners without a model of problem solving would often revert to solving by referring to many examples of the same ‘type’ of problem. Polya-type problem solving skills framed by the practical worksheet was used as an attempt to elicit more effective problem solving behaviour from them. Preliminary findings show that they were able to use the practical worksheet to model their solution of problems in the courses.
      195  124
  • Publication
    Restricted
    Enhancing 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.

      14  9
  • Publication
    Open Access
    Problem solving in the school curriculum from a design perspective
    (2010-07) ; ;
    Dindyal, Jaguthsing
    ;
    Quek, Khiok Seng
    In this symposium, we discuss some preliminary data collected from our problem solving project which uses a design experiment approach. Our approach to problem solving in the school curriculum is in tandem with what Schoenfeld (2007) claimed: “Crafting instruction that would make a wide range of problem-solving strategies accessible to students would be a very valuable contribution … This is an engineering task rather than a conceptual one” (p. 541). In the first paper, we look at how two teachers on this project taught problem solving. As good problems are key to the successful implementation of our project, in the second paper, we focus on some of the problems that were used in the project and discuss the views of the participating students on these problems. The third paper shows how an initially selected problem led to a substitute problem to meet our design criteria.
      154  180
  • Publication
    Open Access
    Fine-tuning in a design experiment
    (2013)
    Ho, Foo Him
    ;
    ;
    Quek, Tay, Toh, Leong, and Dindyal (2011) proposed that a design-theory-practice troika should always be considered for a designed package to be acceptable to the research users who, in this case, are teachers and schools. This paper describes the fine-tuning to the MProSE problem-solving design made by the teachers in the school after first round of teaching. This process involved teacher input from their experience, and detailed time-consuming discussions and learning between the researcher-designers and the teacher-implementers.
      109  132
  • Publication
    Open Access
    Many pathways towards "excellence" in Singapore mathematics education
    This paper presents a snapshot of Singapore’s journey towards excellence in mathematics education by examining the role of the traditional notion of mathematics competition and other competitive activities. It could be seen using the context of mathematics competition that the notion of “excellence” has evolved over time. Excellence as a high standard for individuals to achieve or as a set of obstacles for individuals to pit against the norm has been gradually broadened to include excellence as an internal goal for an individual to achieve, and even excellence as a goal for the mathematics education landscape.
  • Publication
    Open Access
    The roles of mathematics competition in Singapore mathematics education
    The roles of mathematics competitions in Singapore mathematics education have expanded beyond helping the country in identifying and supporting of mathematical talents. In this note, test items from the past years mathematics competition were examined. It was proposed that mathematics competitions can potentially play three important roles in Singapore mathematics education: to (1) stretch students to explore mathematics beyond the usual school curriculum; (2) set direction in higher order thinking skills could be infused into the usual classroom teaching; and (3) preserve the “elementary mathematics” within the constantly evolving national mathematics curriculum. This note further presents some episodes of students’ responses to some competition questions from previous years. It was found that some students developed incomplete or incorrect mathematical reasoning but gave the correct answers to these questions, which is contradictory to the intention of setters of the questions. Readers are cautioned to the existence of a mismatch between the intentions of these competition questions and the actual format and structure of the competitions.
      299  574
  • Publication
    Open Access
    On in-service mathematics teachers’ content knowledge on kinematics
    (The Education University of Hong Kong, 2005)
    This paper reports a preliminary study on in-service Additional mathematics teachers' knowledge of kinematics concepts. A survey consisting of TRUE/FALSE questions was issued to the participating teachers. The questions were collations of the common misconceptions identified by some local Physics teachers among the local Physics students. The participants were asked to supply the answers to the questionnaire with their answers substantiated with reasons. In this paper, we discuss the results of the survey done on a group of twenty six in-service Additional mathematics teachers and classify the teachers' misconceptions of kinematics concepts. The finding of this initial survey could be useful to spur further research on Mathematics teachers' subject content knowledge on kinematics. Pragmatically it would also be useful for any agency which is planning for any content upgrading workshops for in-service teachers.
      123  148
  • 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.
      49  69
  • Publication
    Open Access
    Stratonovich-Henstock integral for the operator-valued stochastic process
    (2022)
    Canton, Recson
    ;
    Labendia, Mhelmar
    ;
    In this paper, we introduce the Stratonovich-Henstock integral of an operator-valued stochastic process with respect to a Q-Wiener process. We also formulate a version of Ito's formula for this integral.
      39  49