Mathematics Instructional Practices in Singapore Secondary Schools

This collection of research papers presents to the reader an overview of mathematics instruction in Singapore.  The text details the instruction used in schools with a focus on the instructional core, practices promoting mastery, development of conceptual knowledge, mathematical reasoning, and developing mathematical problem-solving skills.  Throughout the text, there is a wealth of documentation of classroom instruction with data and proven impact on student learning.  As pointed out on page 2 in the opening overview chapter, Singapore is a key enabler of social mobility and the system provides equal opportunity for every child.  All institutions are required to be registered with the Ministry of Education (MOE) and all public schools are taught in English except for the “Mother Tongue” language paper.  Figure 1.1 on page 5 presents an overview of the pathways and possible lateral transfers among courses with the Primary School Leaving Examination (PSLE) and figure 1.2 on page 7 presents the curriculum framework in a pentagon shape.  These are essential in understanding how the primary mathematics curriculum is set up for continuous learning and the metacognitive skills need for problem-solving.

The collection contains 17 research papers divided into four main parts, Global Features of Practice, Enactment of the Intended Curriculum, Tasks and Tools, and Conclusion.  Chapter 2 in the mathematics curriculum in Singapore secondary schools is a key chapter as it explores the pedagogies adopted by experienced teachers when enacting the set curriculum and the use of materials for enacting the set curriculum.  Thirty experienced teachers were selected for the first phased and other 691 for the second.  Figure 2.1 on page 21 details the model of the curriculum enactment process.  The video segment was most interesting for me with the three-camera approach.  This way, with the teacher, student, and whole-class cameras (page 26), reflections and key idea questions (pages 27-28) can be asked to continuously improve teaching and learning.  These reflections are also emphasized in Figure 5.2 on page 83, which details the phases of mathematics lessons with an introduction, development, consolidation, and conclusion.

Throughout the text, real-life applications are used.  Some of the highlights include the use of the Law of Sines on pages 94-95, the applications from the Integrated Programme class on pages 129-130, and the volume of a cylinder on page 215.  Each of these examples provides the reader with a deeper sense of how mathematics is taught, with exact comments from teachers and students, in Singapore.  One great example of a teacher-student conversation is presented on pages 262-263 regarding the connection between Quadratics, x-intercepts, and real zeros together with the Quadratic Formula.

In the concluding chapter, the pentagon model is revisited with the main outcome: Singapore secondary mathematics teachers do not think (nor enact) the Skills apart from the other relevant components of the pentagon.  The “paradox” is also summarized with the history of East and West Asia counterparts presented for the reader to consider.  The final point made is that  “working hard” and “ being ready for changes” are critical  To be globally competitive, teachers are always being innovative to meet the demands of today’s students based on modern and current events.  Teachers are also ready to change and constantly improve and are not happy with low performing students.  As pointed out on the final page of the text, page 344, the teachers are “driven” to help students be all they can be.  This is a goal we all have as educators.  I highly recommend this book to gain an international perspective on how Singapore teaches their students to pass along these practices to your classes.

Peter Olszewski, M.S., is a Mathematics Lecturer at The Pennsylvania State University, The Behrend College, an editor for Larson Texts, Inc. in Erie, PA, and is the 362nd Chapter Advisor of the Pennsylvania Alpha Beta Chapter of Pi Mu Epsilon. His research fields are in mathematics education, Cayley Color Graphs, Markov Chains, and mathematical textbooks. He can be reached at pto2@psu.edu or www.personal.psu.edu/pto2. Outside of teaching and textbook editing, he enjoys playing golf, playing guitar and bass, reading, gardening, traveling, and painting landscapes.