Now showing 1 - 10 of 15
  • Publication
    Open Access
    Mathematical problem solving for integrated programme students
    (2006-05) ;
    Quek, Khiok Seng
    ;
    ;
    Lee, Tuo Yeong
    ;
    Lim-Teo, Suat Khoh
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    ;
    Ho, Foo Him
      150  247
  • Publication
    Open Access
    Mathematical Problem Solving for Everyone (MProSE)
    (Office of Education Research, National Institute of Education, Singapore, 2020) ;
    Quek, Khiok Seng
    ;
    ; ;
    Dindyal, Jaguthsing
    This project involves the development and implementation of a problem solving package (M-ProSE) in the secondary school mathematics curriculum. It aims to induct secondary school mathematics students into the discipline of mathematics via a programme that turns well established theories of mathematical problem solving into praxis. In contrast with conventional training for mathematics competitions which tend to be restricted to a small number, M-ProSE is designed for all mathematics students Development of the project: In a pilot study conducted over two years in an Integrated Programme of a junior college, the research team observed that students were generally resistant to following the stages of Polya's model. In an attempt to 'make' the students follow the Polya model, especially when they were clearly struggling with the problem, we decided to construct a worksheet like that used in science practical lessons and told the students to treat the problem solving class as a mathematics 'practical' lesson. In this way, we hoped to achieve a paradigm shift in the way students looked at these 'difficult, unrelated' problems which had to be done in this 'special' class. Practical work to achieve the learning of the scientific processes has a long history of at least a hundred years. It is certainly conceivable that similar specialised lessons and materials for mathematics may be necessary to teach the mathematical processes, including and via problem solving. Implementation of the project: M-ProSE is an attempt to teach problem solving in 'practical' setup. Students will be taught Polya's model and problem solving in general in two or three dedicated lectures. The main mode of learning is then through a series of 'mathematics practical' lessons. Students work on usually one or at most two problems which have to be worked out on a special worksheet which requires the student to systematically and metacognitively go through the Polya model. M-ProSe is to be implemented as part of the mathematics curriculum and will be assessed. In order to implement M-ProSE, we need to build the teachers' capacity first to solve non-routine mathematics problems and thereafter to teach problem solving to their students. This involves the researchers conducting a series of workshops for the school teachers to widen their repertoire of problem solving resources. Next, we will develop with the teachers the instructional strategies to teach problem solving to their students, by means of a lesson study approach. Some of the researchers will initially teach some student classes as a model for the teachers before they take over entirely. To contribute to the understanding of teaching mathematical problem solving in general, the researchers will collect data over some cohorts which will enable them to further improve the package and make the package useful to other schools. The evidence collected will provide the basis for pedagogical practices in the mathematics classrooms.
      141  31
  • Publication
    Open Access
    Reconceptualising problem solving in the school curriculum
    (2009-07)
    Dindyal, Jaguthsing
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    ;
    Quek, Khiok Seng
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    ;
    In this paper, we discuss the development of a very specific problem solving curriculum in an independent school in Singapore as part of the first phase of our research project. We are using a design research methodology to fine-tune the problem solving curriculum in which we are introducing the mathematics practical, an idea borrowed from science education.
      98  138
  • 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
    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  21
  • Publication
    Open Access
    Teacher preparation for a problem solving curriculum
    (2009) ; ;
    Quek, Khiok Seng
    ;
    Dindyal, Jaguthsing
    ;
    The role of the teacher is central to the success of any curriculum innovation. Thus, teachers’ professional development has become an increasingly important subject of discussion in recent education literature. In the design and implementation of the project reported here, teachers’ preparation for the problem-solving curriculum featured prominently. This paper discusses the challenges of selecting a suitable problem and ways of using it productively within a professional development programme that the authors carried out for the teachers involved in the project.
      301  172
  • Publication
    Open Access
    Assessment in a problem solving curriculum
    (2009) ;
    Quek, Khiok Seng
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    ;
    Dindyal, Jaguthsing
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    In this paper we elaborate on the ways for assessing problem solving that goes beyond the usual focus on the products of the problem solving process. We designed a ‘practical’ worksheet to guide the students through the problem solving process. The worksheet focuses the solver’s attention on the key stages in problem solving. To assess the students’ problem solving throughout the process, we developed a scoring rubric based on Polya’s model (1954) and Schoenfeld’s framework (1985). Student response to the practical worksheet is discussed.
      310  341
  • Publication
    Open Access
    Concretisations: A support for teachers to carry out instructional innovations in the mathematics classroom
    (Springer, 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  192
  • Publication
    Open Access
    Infusing problem solving into mathematics content course for pre-service secondary school mathematics teachers
    (Association of Mathematics Educators, 2013) ;
    Quek, Khiok Seng
    ;
    ; ; ;
    Ho, Foo Him
    ;
    Dindyal, Jaguthsing
    This paper presents a re-design of an undergraduate mathematics content course on Introductory Differential Equations for pre-service secondary school mathematics teachers. Based on the science practical paradigm, mathematics practical lessons emphasizing problem-solving processes via the undergraduate content knowledge were embedded within the curriculum delivered through the traditional lecture-tutorial system. The pre-service teachers' performance in six mathematics practical lessons and the mathematics practical test was examined. They were able to respond to the requirements of the mathematics practical to go through the entire process of problem solving and to carry out "Look Back" at their solution: checking the correctness of their solution, offering alternative solutions, and expanding on the given problem. The use of Mathematics Practical has altered the pre-service teachers’ approach in tackling mathematics problems in a positive direction.
      219  498
  • Publication
    Open Access
    Mathematical problem solving for everyone: A new beginning
    (Association of Mathematics Educators, 2012)
    Dindyal, Jaguthsing
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    ; ; ;
    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.
      552  732