Many pathways towards "excellence" in Singapore mathematics education
This paper presents a snapshot of Singapore’s journey towards excellence in mathematics education by examining the role of the traditional notion of mathematics competition and other competitive activities. It could be seen using the context of mathematics competition that the notion of “excellence” has evolved over time. Excellence as a high standard for individuals to achieve or as a set of obstacles for individuals to pit against the norm has been gradually broadened to include excellence as an internal goal for an individual to achieve, and even excellence as a goal for the mathematics education landscape.
An experienced and competent teacher's instructional practice for normal technical students: A case study
This paper presents a case study of an experienced and competent mathematics teacher’s classroom instructional practice in a Normal Technical Mathematics course. The topic that was observed was Volume and Surface Area of a Pyramid, a subtopic within the mensuration topic in Secondary Two syllabus. The teacher used a video clip on the Egyptian Pyramids to integrate students’ prior knowledge on pyramids, which raised their attention on the topic. This was followed by engaging the students in hands-on activity to understand the formulae.
Enacting a problem-solving lesson using scaffolding to emphasize extending a problem
In this paper, we describe our conceptualization of teaching mathematical problem-solving at the upper primary level, emphasizing Polya’s Stage Four in extending a problem. Geometry is used as a context of the presentation. The objective is to engage pupils more metacognitively in their problem-solving process. By reviewing existing education literature, features that will support authentic problem solving were identified. The frameworks explored in this study include Polya’s 4-step problem-solving model, Schoenfeld’s framework, and the synthesis of the two frameworks through “Making Mathematics Practical” which utilize an extensive use of teacher scaffolding. The proposed scaffolding stresses pupils to problem solve beyond finding a solution as well as independently check and expand the given mathematics problem.
Scaling up the education research: Magical (SUPERMAGICAL): use of comics in teaching mathematics.
Fallacies about the derivative of the trigonometric sine function
In this paper, several fallacies about the extension of the formula 𝑑/𝑑𝑥 (sin 𝑥) = cos 𝑥 to the erroneous formula 𝑑/𝑑𝑥 (sin 𝑥°) = cos 𝑥° are discussed. In a Commognitive Theory Framework, misconceptions by ‘newcomers’ can be traced to the use of the word “unit”.
Mathematics: Connection and beyond: Yearbook 2020 association of mathematics educators
This book contains 11 chapters from various experts all over the world on mathematics education. It provides different perspective of how to establish connection within mathematics and beyond. The ideas are from different authors internationally and is practice-oriented, based on empirical studies conducted by the various authors. This is a good illustration of linking theory with practice.
School calculus curriculum and the Singapore mathematics curriculum framework
In this paper, the Singapore school calculus curriculum at the upper secondary and the pre-university levels is examined in the light of the Singapore mathematics curriculum framework. Three key features of the calculus content are discerned: (1) an intuitive approach to calculus supported by the use of technology; (2) an emphasis on techniques; and (3) an emphasis on procedural over conceptual knowledge. Following that analysis, a review of the performance of a group of pre-university students on selected calculus tasks in a calculus survey prior to and after their learning of pre-university calculus is discussed. The students’ performance in the survey shows that many students did not visually identify calculus concepts that were studied procedurally. They demonstrated a lack of conceptual understanding of the calculus procedures. This study suggests that the partial calculus knowledge acquired in the early upper secondary levels might not necessarily facilitate the acquisition of a more complete concept at the pre-university level. Furthermore, the students’ procedural knowledge of calculus did not seem to develop their procedural fluency or flexibility.
A study of pre-service teachers' performance on two calculus tasks on differentiation and limit
The purpose of this paper is to report a part of a calculus research project, about the performance of a group of pre-service mathematics teachers on two tasks on limit and differentiation of the trigonometric sine function in which the unit of angle measurement was in degrees. Most of the pre-service teachers were not cognizant of the unit of angle measurement in the typical differentiation formula, and a number of participants recognized the condition on the unit of angle measurement but did not translate this to the correct procedure for performing differentiation. The result also shows that most of the participants were not able to associate the derivative formula with the process of deriving it from the first principle. Consequently, they did not associate it with finding . In the process of evaluating this limit, the pre-service teachers exhibited further misconceptions about division of a number by zero.
Models of instruction and mathematics teaching in classrooms of Singapore secondary schools
In this chapter, we discuss the comics package we have developed to teach lower secondary school statistics of the mathematics curriculum. Most people would think that comics for classroom instruction can at most stop at arousing students’ interest in the subject, especially among the low-attaining students. However, we assert that using comics in teaching lower secondary statistics can introduce the students to much of the statistical processes within contexts that are meaningful to students, invite them to engage in higher order thinking tasks in order to develop their critical thinking ability. We also discuss snapshots of how one teacher enacted the statistics lessons based on our comics teaching package, and two teachers’ response to the comics package.