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Qualitative research for education: An introduction to theories and methods

미국의 “전국 수학 교사 협의회”(National Council of Teachers of Mathematics, NCTM)는 1989년부터 〈학교 수학의 교육과정과 평가 규준〉(1989), 〈수학 가르침(교수)의 전문성 규준〉(1991), 〈학교 수학의 평가(시험) 규준〉(NCTM, 1995), 〈학교 수학의 원리와 규준〉(2000)을 출판하여 미국의 수학 교육 의 전망(목표, 나아갈 길)과 규준(실행 지침)을 제시하였다. 수학 교사들로 구성된 미국의 NCTM은 학생, 학부모, 학교 행정가 등 많은 사람들과 힘을 합하여 모든 학생들에게 수준 높은 수학 교육을 받을 수 있는 여건(환경, 기회)을 조성하는 데 구심점의 역할을 하였다. 한편 많은 관련 단체들은 여러 배경과 능력을 가진 학생들이 전문성을 지닌 교사(특수 교사를 일컫는 밀이 아니다. 수학 교과를 이해하고 수학의 전문성과 특수성을 가르칠 수 있는 일반 교사를 일컫는 말이다.)로부터 미래를 대비해 평등하고, 진취적이며, 지원이 잘 이루어지고, 공학 도구(IT)가 잘 갖춰진 환경에서 중요한 수학적 아이디어를 이해하면서 학습할 수 있는 수학 교실(미국에서는 우리나라처럼 수학 교사가 수학 시간에 학생의 방(교실: Homeroom)에 찾아가지 않고 학생들이 선생의 방(수학 교실: Classroom)을 찾아온다. 전형적인 수학 교실의 사진은 2쪽에 나와 있다.)을 만들기 위해 함께 힘썼다. NCTM에서 출간한 여러 규준들은 우리나라의 제6차와 제7차 교육과정에도 큰 영향을 미쳤다. 이 글에서는 NCTM(2000)에서 제시한 학습 원리를 간단히 살펴본 다음 이를 중심으로 현재 미국 수학 교육의 교수ㆍ학습 이론의 동향을 살펴본다.

미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론

List of Figures List of Tables Foreword Introduction Robin P. Fawcett, M.A.K. Halliday, Sydney M. Lamb and Adam Makkai 1 Language as Code and Language as Behaviour: A Systemic-Functional Interpretation of the Nature and Ontogenesis of Dialogue M.A.K. Halliday 2 Metaphors of Information John Regan 3 How Universal is a Localist Hypothesis? A Linguistic Contribution to the Study of 'Semantic Styles' of Language Yoshihiko Ikegami 4 Some Speculations on Language Contact in a Wider Setting Jeffrey Ellis 5 Ways of Saying: Ways of Meaning Ruqaiya Hasan Index

Language as social semiotic

The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

Digraphs Theory Algorithms And Applications

Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions

For a graph or digraph G, let be the family of strong orientations of G; and for any , we denote by d(D) the diameter of D. Define . In this paper, we survey the results obtained and state some problems and conjectures for the parameter .

Optimal Orientations of Graphs and Digraphs: A Survey

Teachers today are expected to be able to apply a wide range of digital technologies in the  classroom.  Initial  teacher  education  programs  should  prepare  teachers  to  apply them with confidence. Pre-service teachers in Singapore responded to a survey on use of  technologies  in  their  personal  lives  and  in  their  teaching,  and  how  confident  they were  in  using  them.  Among  17  applications,  the  most  frequently  used  were  those related  to  computer  technology such  as  checking  an  online  dictionary,  web  browsing and searching,  emailing,  and using computer  software.  Participants’  use of computer software  was  frequent;  however  it  was  more  so  in  their  personal  lives  than  in  their teaching.  The  least  used  items  included  audio  recording,  video  recording  and  global positioning  system  (GPS).  Usage  was  found  to  be  positively  correlated  with confidence, and while participants often had confidence in using the applications, their confidence was relatively low for items such as video and audio recording which the yused  the  least.  While  teachers’  use  of  computers  is  important,  their  ability  and confidence  to  use  other  modern  technologies  for  effective  teaching  should  not  be neglected.

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Relating use of digital technology by pre-service teachers to confidence : a Singapore survey

Latent profile analysis of students' motivation and outcomes in mathematics: an organismic integration theory perspective.

Problem solving is at the heart of the Singapore Mathematics curriculum. However, it remains a challenge for teachers to realise this curricular goal in practice. Here, we review the efforts of Singapore mathematics teacher educators in incorporating problem-solving (teaching) competency in teacher education and PD programmes. We discuss conceptual and practical issues, actions taken and changes made in building teachers’ capacity to enact a problem-solving curriculum in a school-based design experiment project. In the project, teachers learnt problem solving, observed and then carried out lessons, using the “Mathematics Practical”—akin to the science practical—as key to instruction and assessment.

Teacher preparation for a problem-solving curriculum in Singapore

Mathematical Problem Solving Scheme of Work and Assessment of the Mathematics Practical Detailed Lesson Plans Scaffolding Suggestions, Solutions to the Problems and Assessment Notes.

Eng Guan Tay

Papers

Optimal Orientations of Graphs and Digraphs: A Survey

Relating use of digital technology by pre-service teachers to confidence : a Singapore survey

Latent profile analysis of students' motivation and outcomes in mathematics: an organismic integration theory perspective.

Teacher preparation for a problem-solving curriculum in Singapore

Making Mathematics Practical: An Approach to Problem Solving