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Relooking "Look Back": A student`s Attempt at Problem Solving using Polya`s Model
( Leong Yew Hoong ),( Dindyal Jaguthsing ),( Toh Tin Lam ),( Quek Khiok Seng ),( Tay Eng Guan ) 한국수학교육학회 2011 수학교육 학술지 Vol.2011 No.1
Against the backdrop of half a century of research in mathematics problem solving, Polya`s last stage is especially conspicuous-by the scarcity of research on it! Much of the research focused on the first three stages (e.g., Francisco & Maher 2005; Taylor & Mcdonald, 2007), with little or no successful attempts at following through with the subjects. In this paper, we describe a case study of how the innovation of a "Practical Worksheet" within a new paradigm of a "Mathematics Practical" enabled a high-achieving student to push beyond getting a solution for a problem to extending, adapting and generalising his solution. The findings from this study indicate promise in achieving the learning of Polya`s model with notable success in the fourth stage, Look Back.
Mathematical Problem Solving for Everyone: A Design Experiment
( Quek Khiok Seng ),( Dindyal Jaguthsing ),( Toh Tin Lam ),( Leong Yew Hoong ),( Tay Eng Guan ) 한국수학교육학회 2011 수학교육연구 Vol.15 No.1
An impetus for reviving research in mathematical problem solving is the recent advance in methodological thinking, namely, the design experiment ([Gorard, S. (2004). Combining methods in educational research. Maidenhead, England: Open University Press.]; [Schoenfeld, A. H. (2009). Bridging the cultures of educational research and design. Educational Designer. 1(2). http://www.educationaldesigner.org/ed/volume1/issue2/]). This methodological approach supports a "re-design" of contextual elements to fulfil the overarching objective of making mathematical problem solving available to all students of mathematics. In problem solving, components critical to successful design in one setting that may be adapted to suit another setting include curriculum design, assessment strategy, teacher capacity, and instructional resources. In this paper, we describe the implementation, over three years, of a problem solving module into the main mathematics curriculum of an Integrated Programme school in Singapore which had sufficient autonomy to tailor-fit curriculum to their students.
Teachers Solving Mathematics Problems: Lessons from their Learning Journeys
( Tay Eng Guan ),( Quek Khiok Seng ),( Dindyal Jaguthsing ),( Leong Yew Hoong ),( Toh Tin Lam ) 한국수학교육학회 2011 수학교육연구 Vol.15 No.2
This paper reports on the learning journeys in mathematical problem solving of 21 teachers enrolled on a Masters of Education course entitled Discrete Mathematics and Problem Solving. It draws from the reports written by these teachers on their personal journeys: the commonalities and differences among them in terms of how they look at their own problem solving experiences, what language they employ in talking about problem solving, and what impact the course has on their views about problem solving. One particular aspect of problem solving instruction, a pedagogical innovation called the Practical Worksheet, is addressed in some detail. These graduate students are full-time mathematics teachers with at least two years of classroom experience. They include primary and secondary teachers.
Teachers Solving Mathematics Problems : Lessons from their Learning Journeys
( Tay Eng Guan ),( Quek Khiok Seng ),( Dindyal Jaguthsing ),( Leong Yew Hoong ),( Toh Tin Lam ) 한국수학교육학회 2011 수학교육 학술지 Vol.2011 No.1
This paper reports on the learning journeys in mathematical problem solving of 21 teachers enrolled on a Masters of Education course entitled Discrete Mathematics and Problem Solving. It draws from the reports written by these teachers on their personal journeys: the commonalities and differences among them in terms of how they look at their own problem solving experiences, what language they employ in talking about problem solving, and what impact the course has on their views about problem solving. One particular aspect of problem solving instruction, a pedagogical innovation called the Practical Worksheet, is addressed in some detail. These graduate students are full-time mathematics teachers with at least two years of classroom experience. They include primary and secondary teachers.
( Feng Deng ),( Eng Guan Tay ),( Tin Lam Toh ),( Yew Hoong Leong ),( Khiok Seng Quek ),( Pee Choon Toh ),( Jaguthsing Dindyal ),( Foo Him Ho ) 한국수학교육학회 2015 수학교육연구 Vol.19 No.1
Previous studies indicated that students tended to hold less satisfactory beliefs about the discipline of mathematics, beliefs about themselves as learners of mathematics, and beliefsabout mathematics teaching and learning. However, only a few studies had developed curricular interventions to change students`` beliefs. This study aimed to examine the effect of a problem-solving curriculum (i.e., Mathematical Problem Solving for Everyone, MProSE) on Singaporean Grade 7 students`` beliefs about mathematical problemsolving (MPS). Four classes (n =142) were engaged in ten lessons with each comprising four stages: understand the problem, devise a plan, carry out the plan, and look back. Heuristics and metacognitive control were emphasized during students`` problem solving activities. Results indicated that the MProSE curriculum enabled some students to develop more satisfactory beliefs about MPS. Further path analysis showed that students`` attitudes towards the MProSE curriculum are important predictors for their beliefs.