Cheng, Lu Pien

Mathematical connections are true relationships and are important for deep mathematical understanding. Connections are also important components of successful problem solving. At the heart of effective teaching and learning of mathematics is task design. This chapter unpacks the different types of mathematical connections through concrete examples to address aspects of task design that draw attention to connections. The relationships between task design, anticipated pedagogies and student learning are also illustrated for teachers to make links and connections explicit in the primary mathematics classrooms.

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.

The Concrete-Pictorial-Abstract (CPA) approach, based on Bruner’s conception of the enactive, iconic and symbolic modes of representation, is a well-known instructional heuristic advocated by the Singapore Ministry of Education since early 1980’s. Despite its ubiquity as a teaching strategy throughout the entire mathematics education community in Singapore, it is somewhat surprising to see a lack of an account of its theoretical roots. This paper is an attempt to contribute to this discussion on the CPA strategy and its potential role in continuing advancement of quality mathematics education.

In Singapore, education is regarded as an investment instead of a social service. Singapore’s Education System has evolved over time and so have school mathematics curricula in Singapore. Mathematics education in Singapore schools in the twenty-first century is still going through a period of change. Mathematics is a compulsory subject up to Grade 10 in Singapore schools. The present-day School Mathematics Curriculum is based on a pentagonal framework with mathematical problem solving as its central focus. In this chapter, we review the developments of Singapore school mathematics curriculum for the past sixty years and describe some of the important features of the intended, attained and implemented aspects of the mathematics curriculum in Singapore. The implementation of the 2019 secondary mathematics syllabus and the 2020 primary mathematics syllabus began in 2020 and 2021, respectively. This chapter also examines the implications and issues related to the implementation of these two syllabuses.

It is easy to dismiss the work of “teaching students to apply formula” as a low-order priority and thus trivialises the professional knowledge associated with this practice. Our encounter with an experienced teacher—through the examination of her practices and elaborations—challenges this simplistic assumption. There are layers of complexities that are as yet under-discussed in the existing literature. This paper reports a case study of her practices that reflect a complex integration of relevant theories in task design. Through examining her praxis around the theme of “recognise the form”, we discuss theoretical ideas that can potentially advance principles in the sequencing of examples for the purpose of helping students develop proficiency in applying formula.

In this article, an adaptation of a secondary school mathematics comics-based instructional package for primary school mathematics classroom, and the teachers' and students' perceptions about the use of comics in the classroom are discussed. Further suggestions by the teachers on fine-tuning the package are also discussed.