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Yeo, Joseph B. W.
Unpacking the big idea of equivalence
2021, Yeo, Joseph B. W.
Equivalence is one of the eight clusters of big ideas proposed for the 2020 secondary school mathematics syllabus in Singapore. In this chapter, I will unpack the meaning of equivalence: the idea of an equivalence relation, the differences between equivalence and equality, and the usefulness of equivalent equations and equivalent statements in solving mathematical problems. In particular, I will examine the solutions of some types of equations which do not seem to produce equivalent equations in subsequent steps, e.g. the introduction of an extraneous solution when solving some equations involving surds or logarithms, and the elimination of a variable when solving a pair of simultaneous equations in two variables, and explain how the solutions of these equations can still produce equivalent equations in subsequent steps. In other words, the transformation or conversion from one equation to another equivalent equation is still the basis of the method for solving any kinds of equations. In addition, this chapter will discuss how to teach secondary school students the big idea of equivalence without teaching the abstract idea of an equivalence relation.
Singapore mathematics pedagogies for developing future-ready learners
2024, Yeo, Joseph B. W., Choy, Ban Heng, Kaur, Berinderjeet
The dawn of the fourth industrial revolution ushers in a highly volatile and uncertain world, which demands educators and students to master both disciplinary and transdisciplinary competencies that are essential for navigating this ambiguity and complexity. Mathematics learning provides learning experiences for students to develop these key competencies necessary for the 21st-century workplace. In this chapter, we will highlight some of the innovative pedagogies used in Singapore mathematics classrooms that engender the development of such competencies. We first describe the Singapore Mathematics Curriculum Framework, often referred to as the Pentagon Model, which highlights the five interrelated aspects of mathematics education that support the central goal of mathematical problem-solving: concepts, skills, processes, metacognition, and attitudes. Next, two general pedagogies, the Concrete-Pictorial-Abstract (C-P-A) approach and inquiry-based learning are described and illustrated using examples used in Singapore classrooms. We then conclude by arguing how these innovative pedagogical approaches can help cultivate a productive mathematical mindset in our students so that they are empowered to look at the world through the lens of mathematics, beyond learning mathematical facts and formulae.
Cultivation of positive attitudes by experienced and competent mathematics teachers in Singapore secondary schools
2021, Yeo, Joseph B. W.
Use of technology by experienced and competent mathematics teachers in Singapore secondary schools
2021, Yeo, Joseph B. W.