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!,!0!= R'4' ' vw,m!m!!ttttD DG 3: Mathematics for whom and why? The balance mathematics for all and for high level mathematics
Team Chairs: Lena Lindenskov, Danish University of Education, Copenhagen, Denmark
Marta Villavicencio, Ministry of Education, Lima, Peru
Team Members: Sol(omon) Garfunkel, COMAP, Lexington, USA
Gerardus Polla, Bina Nusantara University, Jakarta, Indonesia
Anita Rampal, Delhi University, India
Worldwide the Ministries of Education, institutions and education societies are trying to answer the hot and controversial headline theme in different ways. Discussion Group 3 recognised both the diversity of social, economics, political and cultural problems in the different countries and at the same times some similarities in the hopes and aims for mathematical education. We centred on the debate related to five questions:
Question 1: Who should receive what kinds of mathematics education, why, and with what goals?
Question 2: Is the dichotomy between 'mathematics for all' and 'for high-level mathematics genuine?
Question 3: How can 'mathematics education for all' embrace opportunities for 'high-level mathematical activity'? But also: How can 'mathematics for high level activity' embrace opportunities for 'mathematics education for all'?
Question 4: How can instructional practices support the development of highly motivated mathematics learners as well as mathematics for all?
Question 5: What is the mathematical literacy? Must mathematical literacy be the same for all? If not, that means mathematical literacy depending on each socio-cultural group? Why?
Organisation
Discussion Group 3 organized its work this way: In the first part of the session 1, L. Lindenskov made a presentation in Power Point of: i) the purposes of the discussion group; ii) the answers given by the group of panellists R. Askey, S. Carreira, Y. Namikawa and R.Vital, who in a plenary session at ICME 10 had expounded their points of view on the headline theme; iii) the questions asked by the Organizing Team and divulged through the ICME web page; and iv) the contents of the documents presented as materials in the same web page related to the asked questions by organizing team and by G. Malaty, V. Freiman and B. Evans. In the second part of the session 1, the partakers made groups freely, in order to exchange points of view with respect to the ideas expounded by the panellists.
In the session 2, S. Garfunkel synthesized what the DG 3 advanced in the previous session, and the Team Chairs asked partakers to divide in four groups to continue with the discussion and to give an answer to the questions. Each subgroup handed in the result of their work at the end of the session. Having as a base these products, M. Villavicencio and L. Lindenskov systematized the answers that were obtained and elaborated a work document.
In the session 3, this document was handed in. This document was presented by M. Villavicencio in Power Point and served as a base for the discussion in the plenary meeting. Owing to the lack of time to agree with all that was presented, the Organizing Team considered appropriate to continue the discussions electronically among the partakers after the Congress through e-mails.
Discussions and recommendations
Following up, the main themes in the discussions as seen by the organizers and contributors - through discussions in the DG 3 with respect to the five questions and answers and recommendations for the formulation of politics are displayed. Later on elaborated results from the e-mail discussions will be displayed on the website.
Question 1: Who should receive what kinds of mathematics education, why, and with what goals?
Everybody should receive mathematics education, because they need thinking tools for work, everyday life and citizenship that can be developed by learning mathematics, and because mathematics gives them possibilities for enjoyment, creativity and for personal development. Math makes use of a universal language to describe the nature, the human society, and so on, and it helps to train logic and abstract thinking; and given that it uses math models, helps to learn systematically to understand things or to solve problems.
In order to ensure mathematics for all, unequal opportunities in mathematics education have to be overcome. That means that it is crucial to give more attention to and guarantee appropriate math education for:
- Female children - such actions are necessary, for instance, because male-centred traditional customs usually guide girls, even though mathematically talented, to choose the college departments unrelated with mathematical fields. Parents and even teachers do not expect girls to learn mathematics as well as boys
- People in the rural areas, particularly for native people who speak their mother tongue and have traditional cultural and minority social-cultural groups (e.g. immigrants). Generally, rural areas, compared with urban areas, have an educationally inferior environment in aspects of teachers' teaching and math competency and parents' educational expectation and educational information, and so on.
- Those that have special needs, i.e. who are blind or handicapped should be given special attention.
- To children and adults, illiterates and other vulnerable groups in society.
We recommend that educational system should emphasize:
- Cultivating mathematical ability and curiosity, and not isolated skills and knowledge.
- Providing students with experiences that put emphasize on the math problem solving and thinking abilities (reasoning and communication).
- Providing students with experiences that give a broad perspective to the mathematics content structure and the relations among the various structural branches, starting from the young age.
- Supporting teachers overcoming eventual own bad learning experiences.
Mathematics education like other subjects - must support universal social values (solidarity, tolerance, openness, inclusiveness and attitudes to maintain a dialogue in our own social group and with others) seeking for the well being of mankind.
Question 2: Is the dichotomy between 'mathematics for all' and 'for high-level mathematics genuine?
It seems to the organizers that with question 2 and 3 the partakers faced the biggest challenges in their efforts to interpret and understand each others viewpoint. Some partakers defended the viewpoint that a solid mathematical ground is a necessary prerequisite before engaging with any use of mathematics; others defended that learners can develop both areas simultaneously. The majority of the partakers tended to give the following answer to question 2:
No, the dichotomy between 'mathematics for all' and 'for high-level mathematics is not genuine? It is not genuine, because high-level learners also need mathematical literacy. While everybody needs mathematical literacy, it is not needed that all people acquire high-level mathematics. But the scientific, technological and welfare development of the world need a great many responsible mathematicians, who must be capable also in mathematical literacy.
Especially for adults, mathematics education must answer to their needs, expectations and intentions.
Question 3: How can 'mathematics education for all' embrace opportunities for 'high-level mathematical activity'? How can 'mathematics for high level activity' embrace opportunities for 'mathematics education for all'?
It might be a common belief that Math education for all should and could ensure, at the same time, the development of capabilities and high levels of performance for some learners. We share this belief, and in this sense, math education for all can embrace opportunities for high-level mathematical activity by teaching with challenging situations accommodations to different kinds of students.
The opposite direction is not so commonly demonstrated. In our view, however, Mathematics for high-level activity also ought to embrace opportunities for 'mathematics education for all' to ensure that also high achieving learners learn more than abstract de-contextualised math knowledge, also they should be given opportunities to acquire mathematical literacy by problem posing and solving in authentic contexts.
This supposes to reflect on what math education must be given, on which interesting ideas must be displayed? Which tools must be used? Which questions must be asked? How to support an appropriate teachers mathematics knowledge and their ability to create a meaningful learning environment in which each student would be given opportunity to realize her full potential? And also particularly in the developing countries, what information and training must be provided for the teachers of different basic education levels?
Question 4: How can instructional practices support the development of highly motivated mathematics learners as well as mathematics for all?
Instructional practices can be supportive to all groups of learners by:
- Considering different learning styles and using a variety of instructional strategies and materials. Developing and nurturing mathematical critical and creative thinking is not possible solely with routine, say, arithmetical tasks, and applying algorithms told how to be used by the teacher.
- Emphasizing a participatory role for learning, that means use mathematical language, oral discussion, and writing, listening and observing skills; create mutual respect and equal treatment regardless of ability; expand career and economic horizons; incorporate technology as thinking and learning tool; to assess performance through a variety of evaluation techniques.
- Valuing the learners creativity and supporting discussions and co-flections on different strategies and the use of different means.
Question 5: What is the mathematical literacy? Must mathematical literacy be the same for all? If not, that means mathematical literacy depending on each socio-cultural group? Why?
Mathematical literacy could be defined as "An individual's capacity to identify and understand the role that mathematics [practice and knowledge] plays [and could play] in the world, to make well-founded mathematical judgements and to engage in mathematics, in ways that meet the needs of that individual's current and future life as a constructive, concerned and reflective citizen" (Mathematical Literacy defined in Programme for International Student Assessment, HYPERLINK "http://www.pisa.oecd.org/pisa/math.htm" http://www.pisa.oecd.org/pisa/math.htm, July 2004, were we suggest to add the expressions in brackets)
This definition is valid for the human being as a citizen of the world, in a world in accelerated process of globalisation; and given that this global village would be unique in the diversity, the mathematical literacy must be the same for all.
In actual practice, we are very far from this math literacy as something which is the same for all. As the first step it might be appropriate for members of the mathematics education community to refer to a more local math literacy that can be national or regional, according to the environment for which the person's math capabilities are functional, that is, that permits him/her to respond to the needs of his/hers current and future life as a constructive, responsible and reflective citizen in his/her country or region. Such necessities evidently vary from one community to another, and from one epoch to another, because, for example, the social-economic and cultural reality of a European city requires that a person acts with knowledge and math capabilities very different to those which an inhabitant of the Peruvian mountains needs to unfold with efficiency, efficacy and effectiveness in his own social-cultural context; and the requirements of today's corresponding populations are different to those of fifty years ago. From this point of view, math literacy is relative; it depends on the demands of the persons' social economic and cultural reality in a given environment and time.
From a viewpoint as mathematics education as a means to enhance intercultural understanding, however, mathematical literacy in a broader sense could be realized by providing students from, say, European cities with knowledge of math culture of, say, Peruvian peers living in rural area and vice versa.
Conclusion
DG 3 seems to
Have succeeded in giving room for an open and engaging exchange of different views
Have succeeded in formulating some answers and some recommendations
Time did not allow us to focus on questions such as: Is there sometimes a tendency to say what not everyone can learn, nobody should learn? Does every student need to take mathematics courses every year? What is the future of mathematics as an education subject in a changing world dominated by technology? Is better, or?
This report has been prepared by Lena Lindenskov, Danish University of Education, Copenhagen, Denmark and Marta Villavicencio, Ministry of Education, Lima, Peru with the assistance of Sol(omon) Garfunkel, COMAP, Lexington, USA, and Gerardus Polla, Bina Nusantara University, Jakarta, Indonesia. They are happy to be contacted for further information on the work of this Discussion Group at
HYPERLINK "mailto:lenali@dpu.dk" lenali@dpu.dk; HYPERLINK "mailto:lena.lindenskov@gmail.com" lena.lindenskov@gmail.com;
HYPERLINK "mailto:villavicencio.mr@pucp.edu.pe" villavicencio.mr@pucp.edu.pe; HYPERLINK "mailto:villavicenciomr@yahoo.com" villavicenciomr@yahoo.com;
HYPERLINK "mailto:sol@comap.com" sol@comap.com;
HYPERLINK "mailto:GerardP@binus.ac.id" GerardP@binus.ac.id
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