Now showing 1 - 10 of 29
  • Publication
    Open Access
    On a certain vector crank modulo 7
    (2015)
    Hirschhorn, Michael D.
    ;
    We de ne a vector crank to provide a combinatorial interpretation for a certain Ramanujan type congruence modulo 7.
      120  106
  • Publication
    Open Access
    Four solutions of a geometry problem
    This article focuses on a challenging geometry problem that was originally posed to primary school students. Four solution approaches, ranging from elementary to advanced, are discussed. Reflections on these approaches and the problem solving processes are also shared.
      316  126
  • 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.
      112  142
  • Publication
    Open Access
    Constructing an exemplary mathematical justification: Why is it so hard for mathematics teachers?
    (National Institute of Education (Singapore), 2019)
    Chua, Boon Liang
    ;
    ;
    Yap, Von Bing
      103  85
  • Publication
    Open Access
      374  191
  • Publication
    Open Access
    Scaffolding cards: A strategy for facilitating groups in problem solving
    (2013) ;
    Dindyal, Jaguthsing
    ;
    Ho, Foo Him
    Problem solving task design is not only the design of a non-routine problem to be solved by the students. Our task design also requires a supporting document, the practical worksheet, which would act as a cognitive scaffold for the students in the initial stages of the problem solving process before they can internalize the metacognitive strategies and automate the use of these strategies when faced with a new problem. A further enhancement of the scaffolding that can be provided by the teacher as she facilitates forty or more students working on the practical worksheet is a set of scaffolding cards. In this paper, we describe the cards and the preliminary use of these cards to facilitate problem solving for teachers in a professional development workshop.
      121  108
  • Publication
    Open Access
    Twelve erroneous proofs
    Assessing how well students understand proofs is difficult. One way to achieve this is to present an erroneous proof and require students to identify the error. Twelve erroneous proofs on various topics in mathematics at the Secondary school level are presented as examples.
      100  72
  • Publication
    Open Access
    Mathematical problem solving for everyone: Infusion and diffusion (MInD)
    (Office of Education Research, National Institute of Education, Singapore, 2020) ; ; ;
    Quek, Khiok Seng
    ;
    ;
    Dindyal, Jaguthsing
    ;
    Ho, Foo Him
    This research project is an attempt to realise the ideals of mathematical problem solving, which is at the heart of the Singapore mathematics curriculum in the daily practices of mainstream mathematics classrooms. This work builds on the foundation of M-ProSE (OER 32/08 TTL) to diffuse the findings to the mainstream school curriculum. Our work involves three steps: (1) initialisation of problem solving as an essential part of the mathematics curriculum in a school at the foundational year; (2) infusion of problem solving as an embedded regular curricular and pedagogical practice across all year levels in the school, and (3) diffusion of this innovation from this school to the full range of schools in Singapore. In each of the above steps, we take a complex systems approach and include curriculum, instructional practices, assessment and teacher professional development in our overall design research process. Our current project builds upon the initial foundation of MProSE to scale out (infuse) and scale up (diffuse) the innovation to mainstream schools in Singapore, hence the project is named MInD. With the experience and data collected from MProSE research school, the design needs to be re-adjusted in order for problem solving to be diffused throughout the mainstream schools. The importance and relevance of this research project to schools is readily observed by the schools' responses: To the researchers' pleasant surprise, four mainstream schools readily expressed their commitment to participate in this research as the school leaders see the relevance of this project to their school curriculum. Further, the Principal of MProSE research school expressed his interest to get his school involved for the infusion phase(step (2)) of the research. The research team of MInD consists of the original researchers from MProSE and two more new team members. The entire team consists of expertise from different fields: mathematicians, mathematics educator, educational psychologist, curriculum specialist, senior teacher, a school principal (who is also a mathematician), an expert of change management and leadership studies, a senior MOE curriculum specialist.
      120  14
  • 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  173
  • Publication
    Open Access
    Weighted generalized crank moments for k-colored partitions and Andrews-Beck type congruences
    (2021)
    Lin, Bernard L. S.
    ;
    Peng, Lin
    ;
    Recently, Beck studied a new partition statistic which involves counting the total number of parts of a partition with certain rank or crank. Andrews proved two of Beck's conjectures related to ranks. Chern subsequently proved several results involving weighted rank and crank moments and deduced a number of similar Andrews-Beck type congruences. In this paper, we show that some of Chern's results can be explained by a simple combinatorial argument, and extend this approach to the study of k-colored partitions. As a consequence, we derive a large number of new Andrews-Beck type congruences for k-colored partitions.
    WOS© Citations 10Scopus© Citations 11  268  27