Metacognition and mathematical problem solving – Teaching and learning at the primary levels [metamaps (primary)]
Translating productive failure in the Singapore A-level statistics curriculum
Mathematics education in Singapore
Mathematics education in Singapore is a shared responsibility of the Ministry of Education (MOE) and the National Institute of Education (NIE) . The MOE overseas the intended, implemented and attained curriculum in all schools while the NIE is involved in teacher preparation and development and also research in mathematics education. Therefore this report has two sections respectively , the first describes the education system and school mathematics curricula while the second briefly provides relevant information on teacher preparation and development and mathematics education research in Singapore.
Translating productive failure in the Singapore A-level statistics curriculum
In the recommendations made to the revised Singapore-Cambridge General Certificate of Education Advanced Level (A-level) Mathematics curriculum (Ministry of Education (MOE): Curriculum Planning and Development Division (CPDD), 2015a, 2015b), an emphasis was placed on the use of constructivist pedagogy to deepen students’ understanding of concepts and appreciation of the disciplinarity of the subject, and the development of students’ critical and inventive thinking capacities that are relevant to the 21st century. Current practices in the Junior Colleges (JCs), with its lecture and tutorial system, remain largely didactic with direct instruction being the main pedagogical approach. To support the shift in pedagogical approach, empirically-tested learning designs that embody the constructivist principles, and were proven effective in Singapore’s classrooms were needed.
This project proposed the use of Productive Failure (PF), a learning design that embodies constructivist principles, empirically tested, and proven effective and tractable in Singapore mathematics classrooms (Kapur, 2008, 2010, 2011, 2012, 2014a; Kapur & Bielaczyc, 2012). Given PF’s positive learning outcomes and its alignment to the recommendations made in the revised A-level curriculum, the MOE’s CPDD’s Mathematics Unit collaborated with the PF research team, and through MOE’s existing processes and structures, worked with the JCs to translate the learning design across key concepts in the Singapore A-level Statistics curriculum.
Infusing thinking skills through the use of graphic organizers in primary mathematics to enhance weak pupils’ learning
A popular topic for local mathematical research is investigating the factors underlying difficulties encountered by weak pupils in word problem solving. With the emphasis on infusing thinking skills into English, Mathematics, Science and Social Studies in primary classes, there is now an urgent need to look for alternative ways of helping weak pupils to learn thinking skills through mathematics word problem solving. Thinking strategies such as the use of graphic organizers that build thinking skills have been successfully used to teach English, Science and Social Studies to slow learners. The organizers have helped pupils to decompose problems into smaller parts for easier understanding, to organize information into schemata and to establish links between the schemata. This paper attempts to show that weak pupils in primary school could be helped to learn and think in mathematics classes through the use of graphic organizers while solving word problems. The thinking processes illustrated are part-whole, sequencing, comparing and contrasting, decision making and predicting.
Children making sense during word problem solving
This is a workshop on word problems in primary mathematics. The workshop is based on a paper derived from an investigation into children’ responses to standard and non-standard mathematics word problems before and after an intervention programme. Standard word problems can be solved by identifying the correct operation and performing the necessary computation. The story context does not affect the solution. In solving non-standard word problems the story context is important in obtaining a correct solution. Primary Three children in five Singapore schools participated in a year-long intervention where their teachers used several lessons that included non-standard problems. The children were asked to solve standard and non-standard word problems at the start and at the end of the school year. Among these word problems, there were those that were similar to, those that were similar in the mathematical structure to but different in the superficial features from, and those that were different in mathematical structure from the problems in the intervention programme. The responses from four intact classes were selected for analysis. It was found that the children were able to make sense of their computation results. However, in situations that went beyond computation, many children were not able to make sense. Intervention and use of concrete materials were found to encourage sense-making.
The use of video recording as a research tool and feedback: Advantages and disadvantages
The use of video-recording as a means of research in psychology is not new but it is not often used in Singapore for a number of reasons. Manpower, lack of technical assistance and time constraints are some comely cited reasons for the reluctance to use video-taping as a form of record taking. But the extensive use of video-recording by Prof. Jim Stigler in a substudy of the TIMSS on the comparison of classroom practices has given compelling evidence on the versatility of the use of video-recording in comparative research. Encouraged by the powerful evidence provided by the TIMSS, the writers have attempted video-recording in a comparative study of classroom practices in primary mathematics. The process of video analysis is undoubtedly time-consuming, but it is also an invaluable learning experience. This paper attempts to discuss the advantages and disadvantages of using video-recording as a form of research record keeping and for feedback in learning–teaching situations.
Living and feeling mathematics learning
School mathematics has often been taught in a rather mechanical manner, and frequently outside the context of everyday life. Frequent over-emphasis on arithmetic, manipulation of algebraic expressions, and pure memorisation of facts and theorems have left many students feeling that mathematics is mechanical, abstract, and unsuitable for the common person's consumption. This is ironical, since mathematics has developed out of the pure necessity of a routine of daily life - counting. Learning need not be fun at every stage. However, as teachers, we could create contexts at each stage of learning so that students' learning of mathematics does not become merely a mechanical process, but consists of experiences that they could live and feel. In this paper, I will share experiences in my mathematics classrooms that evoke emotions of some strength, so that mathematics will become part of the repository of unforgettable memories in students' lives. This is, in fact, in line with the findings of brain research which reveal the important role that emotions play in learning.
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