Lee Ngan Hoe

There is a number of definitions to the term "global citizenship". To the young and trendy, it means international exposure through extensive travelling and having an overseas education. But a philosophical and sociological review of the term in a global and multiracial society like Singapore indicates that matters like knowledge of other cultures, races, religions, economic issues, health issues, unemployment, critical review of information from a wide range of media, justice and integrity should be of concern to a global citizen. Compassion, respect and social responsibility transcend beyond geographical borders, race, language , gender and religious barriers Developing Singaporean students into global citizens may not be easy as many aim single mindedly for good grades, a well-paid job and speedy promotion. Howard Gardner published Five Minds for the Future in 2006. In his book, he stresses that for people to move forward in the 21st Century, they need to have a: 1) Disciplined Mind for lifelong learning; 2) Synthesized Mind to critically select and integrate relevant information; 3) Creative Mind to develop new products and new approaches to problem solving; 4) Respectful Mind to appreciate diversity; and 5) Ethical Mind to ensure integrity and justice. Conscious attempts to develop the Five Minds in students may help to promote global citizenship.

The Concrete-Pictorial-Abstract (C-P-A) sequence is a key instructional strategy for the development of primary mathematics concepts in Singapore. However, the way to go about teaching and learning with the C-P-A sequence is unclear. As a result, the benefits of this sequence cannot be fully capitalized. This paper aims to (1) expound from learning theories of Bruner, Dienes and Piaget, and literature on representations, how learning takes place with representations and (2) using the insights gleaned, propose how teaching with representations looks like. It concludes with segments of a series of classroom lesson plans crafted using the proposed model of teaching and learning with representations for the concept of equivalent fractions in Primary Three.

Pupils have consistently fared poorly in solving non-routine Mathematical problems and the main obstacle is in understanding problems fully and planning for an effective problem-solving approach. The present study explored the impact of a metacognitive scheme on pupils' ability to solve non-routine Mathematical problems. Using a pretest-posttest design involving 63 pupils from two intact mixed-ability Primary Four classes, pupils' findings revealed that the intervention was effective, to a small extent, in improving pupils' awareness of problems, personal control of their problem-solving behaviour and emotions as well as regulation of their own thinking. Pupils also became more confident and engaged in problem solving, and they ultimately achieved greater problem-solving success. Limitations and instructional implications were discussed.

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.

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.