Browsing by Author "Ng, Luan Eng"
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- PublicationOpen AccessMPCK variables valued by schools’ mathematics department heads(2006-11)
;Lim-Teo, Suat Khoh ;Ng, Luan EngChua, Kwee GekMathematics Pedagogical Content Knowledge (MPCK) affects classroom practices which in turn affects learning by pupils. While there are many desirable practices which demonstrate strong MPCK, teachers' adoption and use of these practices in part depend on the value placed on them by the school management. This paper presents the quantitative and qualitative findings of a survey as well as insights from interviews of primary schools' Mathematics department heads on their perceptions of the importance of various teachers' practices in contributing towards effective mathematics teaching and learning. The study shows that the department heads value practices which contribute towards conceptual learning and pupil motivation to learn which go beyond achievement in performance tests.393 160 - PublicationRestrictedRepresentation of problem solving in Singaporean primary mathematics textbooks with respect to types, Polya's model and heuristics(2002)Ng, Luan EngThis study aims to investigate how a series of mathematics textbooks entitled "Primary Mathematics" represent problem solving. This series of textbooks were used by all the primary schools at all grade levels in Singapore from 1981 to 2000. Although schools have adopted new textbooks for their Primary One pupils starting 2001, the textbooks in this series will only be phased out gradually level by level and completely phased out by the end of 2005.
Given that problem solving occupies a central role in mathematics education as well as the mathematics curriculum in Singapore, the purpose of this study is to examine the representation to two important aspects of mathematical problem solving - the process of problem solving and problem types. With regard to the problem-solving process, the researcher focused on the general and specific problem-solving strategies. The representation of general problem-solving strategy was analysed using Polya's model, which is marked by these key phases: (a) understanding the problem, (b) devising a plan, (c) carrying out the plan, and (d) looking back. The specific strategies used in solving problems were examined using the set of heuristics stated in the mathematics syllabus (Ministry of Education, 1990). In addition to the analysis of process of solving problems, an examination of the problem-solving environment provided by this series of textbooks was conducted. Specifically, the researcher sought to obtain a picture of the problem-solving experience provided to textbook users by examining the distribution of these problems types:
● routine problems versus non-routine problems
● open-ended problems versus close-ended problems
● application problems versus non-application problems
● problems with exactly sufficient or extraneous or insufficient information
● single-step problems versus multi-step problems
The coding of problems using the above mentioned framework presented these key findings:
● The first three phases of Polya's problem-solving model were represented in about 64% of the worked examples. However, the fourth phase "Looking back" was not modeled in all the worked examples.
● Not all the heuristics stated in the Ministry of Education (1990) mathematics syllabus were represented in the problem-solving process in the textbooks. Three heuristics: "Use a diagram", "Act it out", and "Use a model" were predominantly modeled in the problem-solving process of the worked examples. Three heuristics "Make a supposition", "Work backwards", and "Restate the problem in another way" were not represented.
● All problems contained exactly sufficient information.
41.5% of the problems were application problems. 99% of the problems were routine problems. 2.6% of the problems were open-ended problems. 72.6% of the problems were single-step problems.
In the light of these findings, the researcher makes the following recommendations to textbook writers in improving the representation of problem solving in textbooks:
● Where applicable, the "Looking back" phase be modeled in the process of solving a problem. This would demonstrate to problem solvers the importance of reflecting and improving on their problem-solving process.
● There should be a representation of the full range of the heuristics listed in the mathematics syllabus. When problem solvers are exposed to the full range of heuristics, they would have the benefit of learning how to apply all the different heuristics.
● The problem-solving environment could be made more challenging and diverse by incorporating a higher proportion of non-routine problems, open-ended problems and problems with insufficient or extraneous information.584 156