Now showing 1 - 6 of 6
  • 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  148
  • 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  582
  • Publication
    Open Access
    Mathematical problem solving for everyone: A new beginning
    (2012)
    Dindyal, Jaguthsing
    ;
    ; ; ;
    Quek, Khiok Seng
    Mathematical problem solving has been at the core of the Singapore mathematics curriculum framework since the 1990s. We report here the features of the Mathematical Problem Solving for Everyone (M-ProSE) project which was carried out in a Singapore school to realise the learning of mathematical problem solving and as described by Pólya and Schoenfeld. A mathematics problem solving package comprising “mathematics practical” lessons and assessment rubric was trialled in the school for Grade 8 in 2009. Responses from three students show mixed perceptions to the module, but an end-of-module assessment shows that the students were able to present their solutions along Pólya’s four stages. We also describe teacher preparation for teaching the module. After the trial period, the school adopted the module as part of the curriculum and it is now a compulsory course for all Grade 8 students in that school.
      550  722
  • Publication
    Open Access
    From the past to the future of technology in mathematics education in Singapore
    (Hanoi National University of Education, 2023)
    This paper discusses the changes in classroom instructions due to technology over the years in mathematics education, and how these changes have impacted mathematics learning and teaching. The impact on learning can be seen over a few phases in Singapore: The use of scientific and graphing calculators has allowed the focus on the developing of higher order thinking skills, while at the same time de-emphasizing the routine computation. With the introduction of various computer softwares such as spreadsheets, mathematics teaching and learning has moved towards the next level of emphasis on coding and computational thinking. Technology can and has been harnassed by teachers to enhance student learning. These will be discussed in details in the talk, with particular reference to the Singapore education context.
      18  356
  • Publication
    Open Access
    Concretisations: A support for teachers to carry out instructional innovations in the mathematics classroom
    (2019) ; ; ;
    Quek, Khiok Seng
    ;
    Yap, Romina Ann Soon
    We recognize that though teachers may participate in various forms of professional development (PD) programmes, learning that they may have gained in the PD may not always lead to corresponding perceivable changes in their classroom teaching. We offer a theoretical re-orientation towards this issue by introducing a construct we term “concretisation”. Concretisations are resources developed in PD settings which can be converted into tangible tools for classroom use. In theorising such resources, we contribute in informing the design process of teacher professional development for better impact into actual classroom practice. We purport principles of design which render concretisations effective. Subsequently, we test these principles by presenting a specific case of teaching mathematical problem solving.
    WOS© Citations 4Scopus© Citations 4  135  172
  • 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  75