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The ninth International Congress on Mathematics Education (ICME) will be held in Makuhari, Japan from July 31 to August 6, 2000. (Makuhari is in Tokyo, about half way between the downtown area and Narita International Airport - about 40 km from central Tokyo.)
This page has information on the WGA1: Mathematics Education in Pre- and Primary School. This is a working document that will change up until the date of the conference. It is intended as a place for collecting suggestions from those interested in taking part in the working group and for keeping you informed about the progress of the group. The Organizing Team for WGA1 hope to update this page regularly.
The International Program Committee (IPC) for ICME-9 has established WGA1 and invited us, Linda Sheffield of the United States and Ann Anderson of Canada, to serve as Co-Chief Organizers of this Working Group. This is a call for those interested in mathematics education in pre- and primary school to contact us with their views on issues appropriate for WGA1.
Over the span of three 120-minute sessions, we plan to pursue one focused idea per session, with the assistance of two invited speakers to get each session started, speakers from different parts of the world who have different views on the topic. We plan to have these speakers each present for 20 - 25 minutes. We would like these presenters to have a written paper that we could disseminate to our WGA by early June, 2000 via email to give the participants a chance to think about the issues before ICME. For the last hour of each session we will break into three subgroups to discuss the issues that have been raised. We have invited people with interest and expertise in these areas to lead the discussions in each of the three groups. These discussion leaders might briefly (5 minutes or less) present work on their own related to the topic, but the focus of their task is to ask leading questions and conduct the discussion of the group based on the issues of the day. In this way, WGA1 proposes to stimulate focused, perhaps controversial, and lively discussions on topics that are of utmost concern to teachers and researchers of children from preschool through age twelve. Currently, we have planned the following broad topics for the sessions. The speakers who have accepted our invitations as major presenters and the discussion leaders are also listed for each topic.
1.Understanding and Assessing Children's Mathematical Thinking - coming to know and understand children's mathematical thinking and doing, determining standards for assessment and accountability.
Focus questions: How might we best understand or assess children's mathematical reasoning: through formal, standardized means or through more informal methods? What should be the main purpose of this: understanding children's thinking or assessing, standardizing and reporting results?
Major Presenters: Ian Thompson, Great Britain and Hanlie
Murray, South Africa
Discussion Leaders: Graham Jones, Australia; Karen Usiskin,
USA; and Constance Kamii, USA
Presenter: Hanlie Murray
Title: In-depth Assessment of Children's Mathematical Reasoning
Abstract: The title of this presentation carries implications about beliefs and value judgements that must be made explicit. Firstly, if the need is felt for information about students’ mathematical reasoning, it implies the conviction that mathematics learning consists of a series and combinations of students’ processes of personal and social constructions that build directly on previous constructions, that are constrained by the qualities of previous constructions, by the beliefs of the student about he nature of mathematics and what type of behavior is required from her, and by the types of tasks and the learning culture to which she is exposed. Secondly, it implies a willingness from the educational system both at macro (educational design) and at micro (classroom level), to adjust learning programs according to the information obtained on students’ thinking, whether it be from minute-to-minute in classroom situations or in four- or five-year cycles by official policy-makers.
Aspects of students’ reasoning that should influence the above decision processes are:
- Describing levels of development in specific concepts
- Identifying emerging mathematical ideas (e.g. theorems in action) in students’ thinking so that they can be clarified, shared, and formalized
- Identifying misconceptions, inconsistencies, and limiting constructions in students’ conceptions of a particular topic
- Identifying likely reasons for the above problems
- Identifying mathematical structures (problem types) that are essential for students’ constructions of powerful mathematical ideas
- Identifying suitable take-off situations for learning trajectories
- The effect of different contexts, classroom culture, and wider cultural considerations on students’ reasoning.
The above list may (correctly) be seen as a description of most of the major issues in current research on mathematics education. I would like to suggest some tools appropriate for classroom use to obtain information of the above kind, together with extensive examples of student responses. The major questions to be discussed are:
- Do curriculum designers and teachers share this idea about learning and about assessment as a means to inform their practice?
- If we believe in this idea, how can we share the idea of in-depth assessment informing practice with curriculum designers and teachers?
To see the full text click here.Presenter: Ian Thompson
Title: Mental Calculation and Mathematical Thinking
Abstract: Over the last fifteen years successive governments have been vigorous in introducing a wide range of changes aimed at raising standards in the English education system. Two particular innovations that are relevant to the theme of this Working Group are National Curriculum testing and the National Numeracy Strategy. In addition to our traditional GCSE examinations for 16-year-olds and Advanced level examinations for 18-year-olds, all children are now formally tested at 7, 11 and 14 years of age. The most recent innovation, implemented in every school in the land from 1st September 1999, is the National Numeracy Strategy with its framework of detailed, structured programmes of study for each primary school year and, soon, for the first few years of secondary school.
An important aspect of both of these innovations is the place within them of mental calculation - named in this way in order to distinguish it from the more traditional, formal and 'fear-inducing' mental arithmetic. In 1998 the testing of mental calculation was introduced into the national tests for 11 and 14-year-olds using pre-recorded audio cassette tapes. In addition to this, one of the four key principles underpinning the NNS is named as 'an emphasis on mental calculation'. It could be argued that each of these innovations takes a different approach to the assessment of mental calculation: the national tests are summative, whereas the NNS approach, with its emphasis on interactive whole class teaching, rich questioning and the importance of discussion, is much more formative in nature.
This paper will consider research in England that has investigated children's mental strategies for two-digit addition and subtraction, and will argue that an awareness of individual children's mental calculation strategies at different stages of their development can provide useful information about their mathematical thinking.
To see the full text, click here.
2. Developing Children's Mathematical Power - building on children's mathematical understanding, encouraging the development of their mathematical thinking, using appropriate tools to develop mathematical reasoning.
Focus questions: How might we best develop children's mathematical power: via establishing a good classroom culture or by using good tasks? What are some examples or prototypes of these? Should technology take a major role?
Major Presenters: Nobohiko Nohda, Japan and Erna Yackel,
United States
Discussion Leaders: John Edgell, USA; Munirah Ghazali,
Malaysia and Yoshinori Hayakawa, Japan; and Agnes Macmillan,
Australia
Presenter: Erna Yackel
Title: Creating a Mathematics Classroom Environment that Fosters the Development of Mathematical Argumentation
Abstract: Taking the symbolic interactionist perspective that meaning is constituted as individuals interact with one another, it is essential to consider the nature of the interactions that occur in the mathematics classroom. Explicit attention to classroom social and soicomathematical norms and to classroom discourse can result in advancing children's development of mathematical argumentation. As children learn to explain and justify their thinking to others they develop intellectual autonomy and, in the process, mathematical power.
In this presentation I deal with issues related to classroom norms, the interactive constitution of meaning and argumentation. Examples from a number of primary school classrooms are used to clarify and illustrate the main issues.
To see the full text, click here.Presenter: Nobohiko Nohda
Title: A Study of "Open-Approach" Method in School Mathematics Teaching
Abstract: Our study on analyzing students' strategies and difficulties in problem solving is considered indispensable to improve teaching and learning in mathematics classroom activities. It seems that these strategies and difficulties are influenced greatly by some social and cultural factors, such as languages, symbols and representations etc.. This study is planned in order to make exact the effects of the 'Open-Approach' method on teaching and learning of teacher and students who engage in problem-solving, particularly with reference to the sharing of mathematical ideas of problem and use of mathematical patterns involved in problem solving. We have to become more aware of the information processes that consist of the communications and interactions between the teacher's explanations and pupil's approach to problem-solving.
To see the full text, click here.
3. Supporting Teachers in Understanding, Assessing, and Developing Children's Mathematical Abilities - developing support systems for both new and experienced teachers.
Focus questions: How might we best best support teachers: via solid mathematical content or by helping teachers to learn how children think? How might this best be accomplished?
Major Presenters: Hsin-Mei E. Huang, Taiwan and Barbara
Clarke, Australia
Discussion Leaders: Nobuki Watanabe, Japan and Alena
Hospesova, Czech Republic; Joan Cotter, USA and Tad Watanabe, USA
Presenter: Barbara Clarke
Title: Supporting Teachers in Understanding, Assessing and Developing Children's Mathematics through Sharing Children's Thinking
Abstract: In this session, the argument will be made that in contrast to providing teachers with a deep understanding of higher-level mathematics, a framework that focuses on a clear understanding of key mathematical "growth points" in children's learning may be a more critical need. Such a framework can offer an enhanced understanding of the mathematics that teachers need to teach, and a lens through which they can view their own children's growth. Using the example of the Early Numeracy Research Project in Victoria, Australia, I will illustrate the power of a framework for mathematical learning in understanding, assessing, and developing children's mathematical thinking. At the beginning of the school year, teachers use a task-based interview with every child one-to-one for approximately thirty minutes, providing detailed information on individual children's mathematical understanding. Teachers meet throughout the year at school, district and statewide professional development, during which they share insights and are presented with ideas for the classroom from research and the wisdom of other teachers. Implications of this approach for preservice and inservice teachers will be discussed, as will early data from the project.
To see the full text, click here.Presenter: Hsin-Mei Edith Huang
Title: Supporting Elementary School Teachers In Understanding, Assessing and Developing Children's Mathematical Abilities In Taiwan
Abstract: Educational reform has been promoted in full flourish in Taiwan for the past few years. The Curriculum Guidelines for the Compulsory Education that were announced in 1999 are considering the desirability of a more integrated curriculum and the relationship between the curriculum of the school and the world outside (Ministry of Education, 2000). The new curriculum, including mathematics will be started for grade one students in 2001. The school mathematics curriculum that we are using now is 1993-curriculum, which was strongly influenced by the curriculum and evaluation standards of school mathematics from American (NCTM, 1989; 1991). Though there are differences between new curriculum and 1993-curriculum standards, both curricula take the modern constructivist's point of view that meaningful learning occurs only when children actively construct the information from new experience and connect it to their own knowledge. In addition, children's ability to solve mathematical problems is also emphasized in both curricula (Ministry of Education, 1993; 2000).The views that interpret how mathematics knowledge is learned by children are fully exploited in the 1993-curriculum of elementary school mathematics (Huang, 1996). It is a big change for a teacher's role from a direct teaching mode to a constructivist approach. What is involved in bringing about significant and worthwhile change in integrating student-centered learning, assessing and developing children's mathematical ability are our important issues in teacher education. For the purpose of supporting elementary school teacher professional development and understand children's mathematical thinking, the programs include the following:
1. Small cooperative group discovery project and topic-based work.
2. Integration as a relationship between the mathematics curriculum and the classroom outside.
3. Mathematical task-based assessment.
4. Problem posing and solving activities.
5. Teacher as an educational action researcher.Getting teachers to change is difficult (Duffy & Roehler, 1986). In order to help children to achieve more meaningful learning, teacher-effectiveness scholars have tried various approaches in supporting and changing teachers' teaching practice as well as understanding children's mathematical thinking. Working with teachers is quite a meaningful approach for both researchers' and teachers' professional development.
References
Huang, M. F. (1996). Elementary school mathematics education in Taiwan. Paper presented at NCTM 74th Annual Meeting at San Diago, Aprial 27, 1996.
Ministry of Education. (2000). Curriculum standards for national elementary schools in Taiwan. Taiwan, Taipei: Author. (In Chinese).
Ministry of Education. (2000). The Curriculum Guidelines for the Compulsory Education: The First Stage. Taiwan Taipei: Author. (In Chinese).
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, Va.: NCTM.
National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, Va.: NCTM.
Duffy, G. & Roehler, L. (1986). Constraints on teacher change. Journal of Teacher Education, 36, 55-58.
To see the full text click here.
This is a call for those interested in mathematics education in pre- and primary school to contact us about their interest in participating in WGA1.
At this point, the invited speakers, discussion leaders and the topics for each session have been decided upon. We are inviting others interested in WGA 1 to participate in two ways.
1. Paper by Distribution (PbyD): We are interested in having members of the WGA 1 distribute papers describing their work in the area of Mathematics Education in Pre and Primary School, especially as it relates to the focus topics listed below. These papers will not be presented orally, but will be distributed before the conference to WGA 1 members via the Internet using email and web sites and/or at the conference as a paper copy.
If you are interested in writing a paper to distribute to the members of the WGA 1, it would be your responsibility to bring copies of the paper to ICME, and if possible, to post your paper on a web site so WGA members can read it before the conference. Please email one of the members of the Organizing Team by June 30, 2000 to let us know if you would like to participate by distributing a paper. Include the topic of your paper, the topic of the day that your paper is most closely related to, and whether you would be able to post your paper on a web site. Please see the main ICME site at http://www.ma.kagu.sut.ac.jp/~icme9/ for more information on PbyD. You must follow all the guidelines for a PbyD that are listed at http://www.ma.kagu.sut.ac.jp/~icme9/PbyD.html.
2. Working Group Discussants: Even if you do not lead one of the small group discussions or distribute a paper, you can still be a very important part of WGA 1 by being an active participant in the small group discussions. If you are interested in doing this, be sure to mark WGA 1 when you register for the conference.
Audience
WGA1 is designed to give a forum for mathematics educators interested
in the mathematics teaching and learning of pre- and primary-aged
students, those from approximately age three to age twelve. The
primary language of the conference will be in English.
Publication
A summary of the work of WGA1 will be presented at the end of the
Congress and published in the conference proceedings. In addition to
this, we hope to have a more detailed publication (perhaps an
electronic one) to include the main papers presented as well as
additional information. Suggestions from potential participants,
authors, and publishers would be welcome.
Associate Organizers
In addition to the Co-Chief Organizers of WGA1, Ann Anderson and
Linda Sheffield, the Organizing Team (OT) for this WGA has three
Associate Organizers. They are Wan Kang of Korea <wkang@ns.seoul-e.ac.kr>,
Christoph Selter of Germany <Christoph.Selter@t-online.de>,
and Shizumi Shimizu from Japan <ssimizu@ningen.human.tsukuba.ac.jp>.
Please feel free to contact them as well as Ann or Linda with any
concerns or suggestions. We will all be working together in
preparation for our WGA.
How to contact us
We would like to hear from you regarding any aspect of the activities
of WGA1. Whether you wish to make a formal presentation to the group
or not, please let us know if you are interested in WGA1 so that we
can begin to set up some networks to facilitate our work before,
during, and after the conference. If you prefer to send email in
German, Korean, or Japanese, please contact the appropriate Associate
Organizers listed above.
Linda Sheffield
School of Education
Northern Kentucky University
Highland Heights, KY 41099, USA
Phone: 606-572-5431 email: sheffield@nku.edu
Ann Anderson
Department of Curriculum Studies
University of British Columbia,
Vancouver, BC Canada V6T 1Z4
Tel: 604-822-5298 e-mail: ann.anderson@ubc.ca.
This page last updated on July 23, 2000
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