The understanding of the relationships between pattern recognition and mathematical abilities is important for students in their learning of mathematics and mathematics teachers in the design of their teaching pedagogies. This study examines the connections between pattern recognition and mathematical abilities of students from four Singapore…

This study investigated the role of the bar model method, a significant aspect of the Singapore mathematics curriculum, in the remediation of seventh-grade students' errors on algebra word problems. To accomplish this purpose, we first assessed students' errors on a written test involving algebra problems and identified ten students based on the…

This study analysed the designs of algebraic problems in elementary mathematics textbooks used in Finland, Indonesia, Malaysia, Singapore, and Taiwan. This study employed a content-analysis method that focused on four dimensions: representational forms, cognitive demand levels (CDLs), contextual features, and types of responses. The result of the…

Whole number arithmetic is the foundation of higher mathematics and a core part of elementary mathematics. Awareness of pattern and underlying problem structure promote the learning of whole number arithmetic. A growing consensus has emerged on the necessity to provide students with the opportunity to engage in algebraic reasoning earlier in their…

This paper outlines an approach to definitively find the general term in a number pattern, of either a linear or quadratic form, by using the general equation of a linear or quadratic function. This approach is governed by four principles: (1) identifying the position of the term (input) and the term itself (output); (2) recognising that each…

The article provides a report on the comparison of Opportunities to Learn algebra and eighth grade students' algebra achievement in three countries: Botswana, Singapore and the United States. The study used student and teacher data from the Trends in International Mathematics and Science Study (2011 and 2015). By using a multilevel regression…

This study describes an online method of measuring individual students' collaborative problem-solving abilities using four interactive mathematics-based tasks, with students working in pairs. Process stream data were captured from 3,000 students who completed the tasks in the United States, Australia, Canada, Costa Rica, Singapore, and Finland.…

The international comparison of students' mathematics knowledge and competencies is an effective method of evaluating students' mathematics performance and developing policies to improve their achievements in mathematics. Trends in International Mathematics and Science Study (TIMSS) are among the most well-recognized international comparisons that…

Mathematics assessment and testing are increasingly situated within digital environments with international tests moving to computer-based testing in the near future. This paper reports on a secondary data analysis which explored the influence the mode of assessment--computer-based (CBT) and pencil-and-paper based (PPT)--and visuospatial ability…

The authors are a team of teachers and teacher educators who are deeply interested in helping mathematically-challenged students improve in their learning of mathematics. In Singapore, depending on their performance at the end of a nationwide Year 6 examination, students are channelled into three ability streams for Years 7 to 10: Express (60%),…

The evolution of Singapore's school mathematics curriculum is in tandem with developments in the education system of Singapore. In the last six decades, economic policies of the government that are necessary for the survival of Singapore in a fast changing world have shaped the aims of the school mathematics curriculum. The present day curriculum…

This study examined 361 Chinese and 345 Singaporean sixth-grade students' performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies…

A purpose of this study was to explore the inter-relations among eighth grade mathematics student achievements in the content domains of "Number, Algebra, Geometry, and Data & Chance" and the cognitive domains of "Knowing, Applying, and Reasoning," in the context of the Trends in International Mathematics and Science Study…

Elementary school students often exhibit a wide variety of different conceptions associated with algebraic thinking that their teachers fail to recognize or understand (Smith, diSessa, & Roschelle, 1994). It is crucial that elementary school teachers possess knowledge of the variety of different student conceptions and also boast abilities to…

Much of the neuroimaging research has focused on how mathematical operations are performed. Although this body of research has provided insight for the refinement of pedagogy, there are very few neuroimaging studies on how mathematical operations should be taught. In this article, we describe the teaching of algebra in Singapore schools and the…