We introduce the notion of an H-primitive being the limit of a sequence of absolutely continuous functions satisfying certain conditions and use it to formulate an alternative definition of the Henstock-Kurzweil integral on a closed bounded interval. Furthermore, the definition provides a characterisation of the primitive of a Henstock-Kurzweil integrable function.

Students’ attitudes toward mathematics and mathematics learning and their implications for mathematics instruction have long been a commonly shared interest among mathematics educators. To assess Singapore students’ attitudes toward mathematics and mathematics learning, we have recently conducted, as part of a larger research project, a survey of more than one thousand secondary students in eight schools. Overall, the results suggest that Singapore secondary students have generally positive attitudes toward mathematics and mathematics learning. However, they hold relatively negative attitudes about work on challenging problems and about the usefulness of mathematics in their adult life. The paper also includes discussion on the implications of the findings from the survey for the teaching and learning of mathematics and offers relevant suggestions.

In Singapore, one topic of great interest in mathematics teacher education is the subject knowledge (SK) in mathematics of teachers. This topic has arisen in other places, often under the name “mathematical knowledge for teaching”, or “MKT.” Many mathematicians and mathematics educators believe that teachers should be given more content knowledge in mathematics. Such content knowledge should not be just higher mathematics but mathematics that is connected to mathematics teaching. In other words, it should be mathematics for teaching. Many books have been published on this subject in the United States during the past few years. McCrory (2006) provides a review of twenty such books. In addition, the Fall 2005 issue of American Educator features the topic of mathematics for teaching (for example, see Ball, Hill, & Bass, 2005).

In this paper, a brief account on the development of integrating technology in the mathematics curriculum in Singapore over the last decade is first discussed. The impact of such an initiative in the mathematics classroom, on teaching and learning of mathematics in Singapore, and in the training of mathematics teachers is considered. Future directions and projects are also briefly presented.

How do we create an enriching learning environment that promotes learning? One way to move our students from learning mathematical concepts and skills in isolation to seeing how they are inter-linked is a paradigm shift that will cause our students to learn mathematics holistically and even to appreciate its intrinsic beauty. This paper discusses how mathematics teachers can stimulate the visual thinking or geometrical intuition of our students by looking at algebraic problems through the lens of geometry.

In this paper, we describe how we can compute the integrals of a class of so called improper Riemann integrals and a class of non-absolute Henstock-Kurzweil integrals, which are highly oscillatory and are not Lebesgue integrable.

Posing or raising appropriate problems is necessary and important for active and deep learning in mathematics. However, students rarely make effort to find thinking problems by themselves. Such an attitude and behavior often lead to passive learning and cause various difficulties and problems in mathematics teaching. The main objective of this paper is to explore the ways to develop students’ ability to find and pose good mathematical problems and thus to promote more active learning in mathematics.

Metacognifion is often regarded as a higher order thinking skill that benefits mainly higher achieving students. Weaker students, on the other hand, often encounter mathematics as a form of drill and practice exercise. It is no wonder that many weaker mathematics students become school dropouts and live to believe that mathematics is beyond the common folk. As we enter into the new knowledge-based economy, we need to raise the educational level of the masses - we need to seek breakthroughs. This paper takes a look at some strategies to promote the use and learning of metacognitive skills for weaker students.

In this article, we present a case study of six Singaporean elementary school teachers working in a Lesson Study team that prepared them for problem solving instruction. The Lesson Study process included preparing, observing, and critiquing mathematics lessons in the context of solving fractions tasks. By conducting Lesson Study, we anticipated that these teachers would develop greater insight into students’ mathematics, which would influence their classroom practices. Through the process of planning, observing and critiquing and by purposefully listening to students’ explanations, the teachers began to better understand their students’ learning, which in turn could help them develop their students' mathematical knowledge.

A research project entitled "Calculus Education at the Junior College and Tertiary Levels in Singapore" was begun in 1996 to study the current status of teaching and learning of calculus in Singapore. As part of the project, a survey was carried out to determine the general attitude of Junior College and Tertiary students' attitude towards mathematics in general and towards calculus in particular. This paper reports the findings of the part of the survey dealing with student attitude towards mathematics. In general, tertiary and junior college students who do Mathematics have a positive attitude towards mathematics in that very few of them have mathematics anxiety and majority enjoy mathematics. However, some of the findings of the students' view of mathematics and their approaches to learning mathematics give cause for concern.

As the educational system in Singapore shifts from an efficiency driven approach to one that is ability driven, there is now a more urgent need to look at individual students' learning style. The concept of multiple intelligences, as proposed by Howard Gardner, fits in well as a framework for such a consideration. Since teachers are found to teach the way they were taught, this study looks at the reaction of trainee teachers’ reaction to the use of musical intelligence in learning activities for lower primary mathematics. In this study, the teachers were brought through the steps of such a lesson as part of their pre-service training. A short video clip of the session will be used to illustrate participatory level of the teachers in such a session.

The use of control groups in experimental designs allows the researcher to determine whether a treatment has had an effect or whether one treatment is more effective than another. This is particularly the case for medical and psychological research. However, the use of 'intact classes' in educational research, resulting in the cases of quasi-experimental design, control groups pose a number of threats to the internal validity of such designs. This paper discusses the issues of such designs and the related threats, and proposes a design which incorporates instead suitable use of multiple 'comparison groups' in such designs from the perspective of a study on the mathematical learning and achievement of lower secondary students using metacognitive strategies. It will also be shown how such a use of multiple 'comparison groups' allows for a more cautious and reliable basis for acceptance and rejection of hypotheses, thus providing a way of examining common threats to the internal validity of such studies.

The author describes the current scene of the use of technology in schools and tertiary institutes, and gives his personal views on the use of technology in mathematics teaching and learning. In short, he put forth his conviction on whither technology goes.