Singapore Mathematics Curriculum Research Articles

싱가포르 중학교 수학교과서에서의 빅 아이디어 접근 구현 사례 연구

Big Ideas approach is gaining attention as a design and implementation perspective for curriculum that intends connected and coherent mathematics learning. This study conducted quantitative and qualitative analysis on horizontal connections between mathematical content in middle school mathematics textbooks of Singapore where Big Ideas approach was applied. The quantitative analysis revealed the strength of horizontal connections within strands and within topics by Big Ideas. Among the eight Big Ideas in Singapore mathematics curriculum, “diagrams” and “notations” aided generally high level of horizontal connections, while “functions,” “invariance,” and “models” promoted generally lower level. The qualitative analysis distinguished between process-oriented and concept-oriented Big Ideas. Horizontal connections by process-oriented Big Ideas were further classified into “connections by conventional mathematical practices” and “connections through non-routine mathematical reasoning”, while horizontal connections by concept-oriented Big Ideas were classified as “deductive connections based on definitions” and “inductive connections based on awareness of structure”. Results are discussed and implications for the implementation of Big Ideas approach in the 2022 revised mathematics curriculum are suggested.

Use of Real-World Contexts in Instructional Materials Designed by Pre-University Mathematics Teachers

Pre-university education in Singapore serves as a bridge between secondary and university education. Despite its importance and the popularity of mathematics as a subject, few studies have been conducted on Singapore pre-university mathematics. We also notice that problems in real-world contexts have been increasingly emphasised in the Singapore mathematics curriculum. In this paper, we study the infusion of real-world contexts in the instructional materials of a typical pre-university institution, with a focus on the topic of vectors. The word problems used in the instructional materials involving real-world contexts are categorised into neutral contexts and basic real-life experiences, and the benefits of utilising these problems are discussed. The benefits include the potential to raise students’ awareness that mathematics can be used as a resource to solve real-world problems or explain real-world phenomena. The alignment of these word problems to the Singapore mathematics curriculum and 21st Century Competencies is also discussed.

Primary school students' perceptions of using comics as a mode of instruction in the mathematics classroom

ABSTRACT A research project on using comics for teaching mathematics was initiated in one Singapore primary school. One class of Grade 5 (students of age 11–12) students was exposed to comics for mathematics instruction. This paper reports a case study of seven students’ perception of the features of the comics instructional package and how these features impacted their learning of mathematics. The students’ responses in an interview with the researchers were analysed using Thematic Analysis and presented using the Singapore mathematics curriculum framework. Four main features of the comics instructional package: (1) humour; (2) story narrative; (3) scaffolding provided by the questions and (3) visuals and four main themes: Increase in (a) enjoyment; (b) understanding; (c) appreciation of real-world applications of mathematics and (d) participation during lessons; were uncovered. The use of comics could potentially impact positively on developing students’ Attitudes, Skills, Concepts and Processes of the Singapore mathematics curriculum framework in learning mathematics.

The role of the Singapore bar model in reducing students’ errors on algebra word problems

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 errors they demonstrated. These students were then offered instruction on how to use the bar model method. Following the instruction, we did clinical interviews and observed that the Singapore bar model method helped students understand the problem and transform words into mathematical expressions. Hence, the bar model served as an assistive tool for the remediation of students’ errors in algebra word problems by facilitating students’ comprehension and transformation.

School calculus curriculum and the Singapore mathematics curriculum framework

School calculus curriculum and the Singapore mathematics curriculum framework

Türkiye (5-8. Sınıflar) ve Singapur (P5-6., S1-2. Sınıflar) Matematik Öğretim Programlarının Cebir Öğrenme Alanı Bağlamında Karşılaştırılması

The purpose of this research is to compare the mathematics curricula of the 5th-8th grades in Turkey and the same level of grades in Singapore with respect to the learning domain of algebra. For this purpose, these curricula are compared in terms of the sub-learning domains, the number of outcomes, contents of outcomes, the order in which they are taught, the grade level and application guidelines of outcomes, and their classification in the Bloom Taxonomy. The pattern of this research is a document review. Under this pattern, the horizontal approach is used to compare the curricula of the two countries. In the research, the data were analyzed through content analysis and descriptive analysis methods. The research findings indicate that both curricula differ in terms of sub-learning areas, the number, content, and ranking of outcomes, especially their implementation guidelines and classification in the Bloom taxonomy. The Singapore Mathematics Curriculum with the context of algebra learning domain handle everyday life problems as a sub-learning domain, includes the relatively more difficult topics at the secondary school level, includes more outcomes, includes the content of the Turkish Mathematics Curriculum, but also includes additional topics, differs from the Turkish Mathematics Curriculum in the teaching of the concept of 'variable' which constitutes the basis of algebra, and the fact that the cases of equality and inequality are addressed together; clearly provides guidance for the learning and teaching process by offering direct applications, software, function machines, table use, working with groups and game suggestions in the application guidelines, places more emphasis on high-level cognitive skills.

Towards a professional development framework for mathematical modelling: the case of Singapore teachers

Despite the incorporation of mathematical modelling in the Singapore mathematics curriculum framework since 2007, Singapore teachers still face readiness issues concerning the use of open-ended real-world problems. This paper presents some preliminary findings from an exploratory study undertaken within a professional development programme on mathematical modelling for experienced secondary mathematics teachers who are tasked to lead their schools in mathematical modelling. The research aims to gain insights into teachers’ efforts at designing and assessing modelling activities, and their perceptions about facilitation challenges, for the purpose of proposing future directions in professional development towards more sustained, concerted efforts at incorporating mathematical modelling in Singapore schools.

Implementing the Singapore Mathematics Curriculum in South Africa: Experiences of Foundation Phase Teachers

This paper reports on the findings from individual interviews and focus group discussions involving six teachers implementing the Singapore Mathematics Curriculum (SMC) in the Foundation Phase (Grade R to Grade 3) in a school in South Africa. The interviews presented an opportunity to explore teachers’ experiences with their attempts to use the SMC approach in their classrooms. By the same token, it highlighted the challenges faced by the teachers as they implemented the curriculum, and informed recommendations for the effective implementation of the Singapore mathematics curriculum in South Africa. The SMC identifies problem solving as central to mathematics learning. It defines problem solving as the acquisition and application of mathematics concepts and skills in a wide range of situations, including non-routine, open-ended and real-world problems. Furthermore, the textbook activities are built on a progression from Concrete experience (through the use of manipulatives), to a Pictorial stage (in which learners draw models) and finally to the level (this is known as the CPA approach). This sequence allows learners to gain a concrete understanding of basic mathematical concepts and relationships before they start working at the abstract level. The teachers identified the following features of the SMC and the textbooks as having a positive impact on implementation: the teachers’ guides are user-friendly; the various representations of mathematical concepts, and the connections made between various topics in the Singapore textbooks, supported conceptual understanding; the CPA approach fostered deeper understanding of mathematics and was effective when teaching learners who have special needs and a language barrier; the Singapore framework has significantly fewer topics and follows a spiral organisation in which one layer of content is built on the next; and the use of the manipulatives offered visual and tactile stimulation for the learners and helped improve learning. One of the key challenges identified by the teachers was that they struggled to implement a problem-solving approach and that the learners struggled when engaged in problem-solving activities. The learners also found the bar model drawing challenging. The findings also highlight the problems associated with implementing the SMC simultaneously in all grades and advocate a grade-by-grade implementation strategy.

Reviving Pólya's “Look Back” in a Singapore school

This study is based on the stance that Pólya's “Look Back,” though understudied, remains relevant to Mathematics curricula that place emphasis on problem solving. Although the Singapore Mathematics curriculum adopts the goal of teaching Look Back, research about how it is carried out in actual classroom practice is rare. In our project, we focus on a redesign of a teacher development programme that is targeted to help teachers realize Pólya's original vision of Look Back in the classroom. We report the cases of two teachers who have participated in the teacher development programme: their thinking about Look Back (through interview records) and their interpretation of Look Back in their classroom practice (through video records). By bringing these two spheres of data together, we discuss their degree of ‘buy-in’ to Look Back in the overall problem solving enterprise.

Teacher preparation for a problem-solving curriculum in Singapore

Problem solving is at the heart of the Singapore Mathematics curriculum. However, it remains a challenge for teachers to realise this curricular goal in practice. Here, we review the efforts of Singapore mathematics teacher educators in incorporating problem-solving (teaching) competency in teacher education and PD programmes. We discuss conceptual and practical issues, actions taken and changes made in building teachers’ capacity to enact a problem-solving curriculum in a school-based design experiment project. In the project, teachers learnt problem solving, observed and then carried out lessons, using the “Mathematics Practical”—akin to the science practical—as key to instruction and assessment.

Should the U.S. Emulate Singapore's Education System to Achieve Singapore's Success in the TIMSS?

Since the release of the timss results, a call has been issued to emulate the curriculum, if not the educational practices, of Asian countries that have done well on the TIMSS. California has even stated that its “new” mathematics curriculum will be fashioned after the “rigorous” Singapore mathematics curriculum. Before endorsing such views, it would be instructive to look at some possible reasons that Singapore's eighth graders performed so well in the TIMSS and some possible implications. I list five possible reasons for Singapore students' success in the eighth-grade TIMSS and ask the reader to reflect on the implications to mathematics teaching and learning in the United States under “Questions to ponder.”