Now showing 1 - 10 of 31
  • Publication
    Open Access
    Redesigning pedagogy for mathematics with the help of technology
    Many teachers have experienced at one time or another the frustrations of trying to impart their knowledge to their students but the latter somehow seem not to grasp the full meaning of the content taught. This may be due to the constructivists’ belief that knowledge cannot be transmitted from teachers to learners but is actively constructed by the learners themselves as they attempt to make sense of their experiences. So this paper attempts to look at how mathematics teachers can redesign their pedagogy by taking into account new teaching methods that are made possible by technology. The paper will also give a few examples of how to use various mathematical software to guide pupils to explore mathematical concepts so that they can construct their own knowledge.
      122  167
  • Publication
    Restricted
    The effect of exploratory computer-based instruction on secondary four students' learning of exponential and logarithmic curves
    The study investigated the effect of exploratory computer-based instruction on pupils' conceptual and procedural knowledge of graphs, and the affective issues towards the use of computers in mathematics. Many previous studies compared the effect of computer-assisted instruction with traditional teacher-directed teaching and any difference in performance might be due to a different pedagogical approach instead of the use of information technology (IT). In this study, both the experimental and control classes were taught using a guided discovery method to explore the characteristics of the exponential and logarithmic curves. One class used an interactive computer algebra system called LiveMath, while the other did not have access to IT. The findings indicated a significant difference in pupils' conceptual and procedural knowledge although there was no significant difference in their affect towards mathematics in general and towards the topic in particular. The pupils in the experimental class also showed a moderately positive affect towards the use of IT. This seemed to suggest that there was an inherent advantage of using IT to explore mathematical concepts.
      165  15
  • Publication
    Open Access
    Using LIVEMATH to bring mathematics alive
    Joseph B. W. Yeo describes an interactive algebra computer system to help students explore algebra and calculus.
      117  170
  • Publication
    Open Access
    Specialising and conjecturing in mathematical investigation
    This paper introduces a new framework to model the interactions of the processes of specialising and conjecturing when students engage in mathematical investigation. The framework posits that there is usually a cyclic pathway alternating between examining specific examples (specialising) and searching for pattern (conjecturing), instead of a linear pathway as in many other theoretical models. The framework also distinguishes between observing a pattern and formulating it as a conjecture, unlike most models that treat an observed pattern as a conjecture to be proven or refuted. I will then use the framework to analyse and explicate a secondary school student's specialising and conjecturing processes while he attempted an open investigative task.
      173  239
  • Publication
    Open Access
    By teaching we learn
    (National Institute of Education (Singapore), 2022) ;
    Dindyal, Jaguthsing
    ;
    ;
    Seto, Cynthia
    ;
    Choon, Ming Kwang
      294  104
  • Publication
    Open Access
    Making visible a teacher’s pedagogical reasoning and actions through the use of pedagogical documentation
    (2022) ;
    Dindyal, Jaguthsing
    ;
    Mathematics education research has focused on developing teachers’ knowledge or other visible aspects of the teaching practice. This paper contributes to conversations around making a teacher’s thinking visible and enhancing a teacher’s pedagogical reasoning by exploring the use of pedagogical documentation. In this paper, we describe how a teacher’s pedagogical reasoning was made visible and highlight aspects of his thinking in relation to his instructional decisions during a series of lessons on division. Implications for professional learning are discussed.
      55  74
  • Publication
    Open Access
    Mathematical investigation: Task, process and activity
    (2009) ;
    Yeap, Ban Har
    Many writers believe that mathematical investigation is open and it involves both problem posing and problem solving. However, some teachers feel that there is a sense of doing some sort of investigation when solving problems with a closed goal and answer but they are unable to identify the characteristics of this type of investigation. Such confusion will affect how teachers teach their students and how researchers conduct their research on investigation. Therefore, this article seeks to clarify the relationship between investigation and problem solving by providing an alternative characterisation of mathematical investigation as a process involving specialisation, conjecturing, justification and generalisation. It also distinguishes between mathematical investigation as a process and as an activity: investigation, as a process, can occur when solving problems with a closed goal and answer, while investigation, as an activity involving open investigative tasks, includes both problem posing and problem solving. Implicit support for this alternative characterisation of mathematical investigation is gathered from some existing literature as these writers did not state this perspective explicitly. The article concludes with some implications of this alternative view on teaching and research.
      3319  2384
  • Publication
    Open Access
    Motivating mathematics students and cultivating the joy of learning mathematics
    The underlying basis of the self-determination theory (SDT) is that people are inherently motivated to learn if their basic psychological needs of autonomy, competence and relatedness are met. The theory also provides a comprehensive taxonomy on the different types of extrinsic and intrinsic motivations. For example, identified and integrated extrinsic motivations are based on a sense of value while intrinsic motivation is based on interest. In this article, I will put the theory into practice, suggesting in more concrete terms how teachers could motivate their students to learn mathematics. First, I will describe some applications within mathematics and in the real world which could be used to motivate students extrinsically by helping them see the value of what they are studying. Moreover, real life examples might also help students relate mathematics to their own experiences. Then I will provide some examples of catchy mathematics songs and amusing videos which could be used to motivate students intrinsically by arousing their interest. I will also discuss how to build up students’ competence in mathematics by developing concepts using examples and not definitions, and by using guided discovery learning and guided proofs, which could also provide autonomy support for the students. I will examine how the practice of procedural skills could be structured more effectively and how mathematics puzzles and gamification could make such practice more enjoyable. Lastly, I will draw on a research study to inform what Singapore teachers are doing to motivate their students.
      152  248
  • Publication
    Open Access
    Using LiveMath as an interactive computer tool for exploring algebra and calculus
    Many mathematics educators in Singapore secondary schools are aware that The Geometer’s Sketchpad, a dynamic geometry software, can be used to explore geometry. But most of them do not know of any computer algebra system (CAS) that can be used to explore algebra and calculus. Traditionally, most mathematicians, scientists and engineers have always used a CAS, such as Maple, to perform symbolic manipulations in order to solve algebraic and calculus problems. However most educators do not see any purpose in their pupils learning a CAS to perform symbolic manipulations, such as factorisation, differentiation and integration, when formal assessments still require them to perform such skills by hand. But with the advance of LiveMath (previously known as Theorist and MathView), an intriguing CAS that provides “a unique user interface that allows one to perform ‘natural’ algebraic maneuvers even more ‘naturally’ than one can achieve them on paper” (Kaput, 1992), there is now another way of using a CAS in the teaching and learning of mathematics, i.e., to explore algebraic and calculus concepts. Moreover the capability of LiveMath templates to be interactive even on Web pages opens up an exciting chapter in online mathematics learning. This paper looks at some examples of how educators can use LiveMath as an interactive tool for their pupils to explore algebra and calculus. It also provides some research evidence to suggest that the use of LiveMath for exploring mathematics may enhance pupil learning.
      162  119