This paper reports an innovative approach to teaching problem solving in secondary school mathematics classrooms based on a specifically designed problem-solving module.This approach adopts the science practical paradigm and rides on the works of Polya and Schoenfeld in order to give greater emphasis to the problem solving processes. We report the…

"Limit" is a difficult mathematical concept, even for good students. It is also a key foundational idea for the study of advanced mathematics. It holds a central position as a foundation of the theory of approximation, of continuity, and of differential and integral calculus. However, the difficulty for teachers is how to organise…

In this paper the teachers' learning journey on designing a mathematics problem that involves a real-life context is reported. This is part of a larger project undertaken in a primary school in Singapore where the teachers were engaged in planning, observing and critiquing mathematics lessons to investigate teaching and learning. These unique…

Women are underrepresented in science, technology, engineering and mathematics (STEM) areas in university settings; however this may be the result of attitude rather than aptitude. There is widespread agreement that quantitative problem-solving is essential for graduate competence and preparedness in science and other STEM subjects. The research…

The teaching of mathematics for the development of numeracy is emerging to be an important goal of recent reforms. In broad terms, numeracy involves the application of mathematical concepts and procedures in the understanding and solution of a range of problems including real-life problems. Teaching for numeracy, thus calls for skills in…

Trends in the curriculum reform propose that algebra should be taught throughout the grades, starting in elementary school. The aim should be to decrease the discontinuity between the arithmetic in elementary school and the algebra in upper grades. This study was conducted to investigate and characterise upper elementary school students…

Technology has become a major force in developing curricula and educational practice in mathematics education internationally. While many technologies are important in affluent developed countries, the hand-held calculator continues to be the technology most likely to be available to students when and where they need it. Modern calculators have…

It has long been recognised that successful mathematical learning comprises much more than just knowledge of skills and procedures. For example, Skemp (1976) identified the advantages of teaching mathematics for what he referred to as "relational" rather than "instrumental" understanding. More recently, Kilpatrick, Swafford and Findell (2001)…

Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes…

In this paper we demonstrate that "lesson study" may be adapted from its primary use as a professional development strategy for use as a research strategy, especially to identify principles of good lesson design. We report on a project undertaken in two Australian secondary schools where lesson study research was used to investigate the design of…

The objective of the present study is to describe how students discover rules underlying a certain phenomenon under question and the process in which they mathematically justify such discovery by way of utilizing tables and graphs in the use of the cell reference function of spreadsheets when a problem is not easily solved through simple symbol…

This paper reports on a study to examine mental computation strategies used by Year 1, Year 2, and Year 3 students to solve addition and subtraction problems. The participants in this study were twenty five 7 to 9 year-old students identified as excellent, good and satisfactory in their mathematics performance from a school in Penang, Malaysia.…

The purpose of this study was to examine the changes in novice and experienced mathematics teachers' questioning techniques. This study was conducted in Sarawak where ten (experienced and novice) teachers from two schools underwent the lesson study process for fifteen months. Four data collection methods namely, observation, interview, lesson…

Newman (1977, 1983) defined five specific literacy and numeracy skills as crucial to performance on mathematical word problems: reading, comprehension, transformation, process skills, and encoding. Newman's Error Analysis (NEA) provided a framework for considering the reasons that underlay the difficulties students experienced with mathematical…

This paper discusses results from a design research in line with Realistic Mathematics Education (RME). Daily cycles of design, classroom experiments, and retrospective analysis are enacted in five days of working about division by fractions. Data consists of episodes of video classroom discussions, and samples of students' work. The focus of…