ICMI News(letter) 25, October/ November 2013 available
ICMI News 25: October/ November 2013,
A Newsletter from the ICMI-International Commission on Mathematical Instruction
Editors: Abraham Arcavi (ICMI Secretary General) and Cheryl E. Praeger (ICMI Vicepresident)
Email addresses: ICMI_Secretary-General@mathunion.org / Cheryl.firstname.lastname@example.org
October 31, 2013
1. Editorial – From the desk of ICMI Vice-President Angel Ruiz
2. ICMI Study 22 on Task Design
3. A letter from Barbara Jaworski, PME President
4. Mathematics Education at the ICM, Seoul 2014
5. MENAO at ICM
6. ICME 14, July/ August 2020
7. Klein Workshop held in Berlin, September 2013
8. CANP Mekong Sub-Region held in Cambodia, October 2013
9. Have you read?
FROM THE DESK OF ICMI VICE- PRESIDENT ANGEL RUIZ
Signed: Angel Ruiz, Vice-President of ICMI
President Interamerican Committee of Mathematics Education
Reform in Mathematics Education and the Praxis Perspective in developing countries. The case of Costa Rica
School curriculum reforms in developing countries like Costa Rica acquire some special dimensions. In many of these countries political opportunity is perhaps more decisive: the willingness of high government officials is necessary to jump-start a reform process. There is no automatic process that arises from the natural evolution of the same education system and its institutions. Secondly, time and pace of reforms must be very fast especially in the early stages, as it is necessary to use the existing positive political will to achieve the reforms. A change of government can halt or roll back reforms indefinitely. This is so because there is often little continuity of public policies. It is not unusual for governments to bury what was the work of a former minister, or to modify the curriculum without much theoretical or social foundation. For the reformers the pressure is very strong to reach a “no-return point” before the change of a government that has been positive. That is a point where it is politically not profitable to go back.
To complement this, it is not unusual for there to be groups of local power in the education system that see as a threat curriculum changes that have not been proposed by them. Therefore, decisions of higher political authorities do not necessarily get implemented. And the chances of negative reactions in these feuds are inversely proportional to the time remaining for a government. As the change of government approaches the role of these groups becomes stronger. For the reformers this also has implications: first, it becomes relevant to use all the possible time when negative local feuds have less strength. Second, reformers should seek a social base of teachers and ministerial staff who are committed to the education reform. This is essential to find a positive balance of the forces for change. However, this affects the timing of the reform. A smooth and linear protocol cannot be followed.
A strong reaction to changes by some teachers is also normal, not only because of a general condition of fear of the new. There are other factors: i) a very weak initial preparation of teachers is predominant in these countries, and ii) it is also common that there are almost no hours during the working day of teachers for in-service professional development (almost all the work load for a teacher is composed of classroom contact hours with no other time for training, research or collective construction of better lessons). These two factors make it difficult to implement educational change or to get unanimous support for it, especially if the changes are significant.
To this must be added that there are teachers unions and associations that do not normally support curriculum change because in these national contexts these agencies rarely have academic or pedagogical motivations and their struggles are often limited to improving wages or working conditions.
Apart from few adequate materials and resources (texts, guides, counseling), there is political uncertainty, adverse feuds and union bureaucrats, teachers not well prepared and little time for in-service training, all of which undoubtedly create a complex reality in which to attempt educational reform. However, within this scenario, a first aim should be to get a significant segment of teachers to support the change, in order to generate a social basis for education reform. If this base can be articulated with sufficient force, it would be possible to move a few steps ahead. This requires curriculum design to be attractive, and though challenging appear implementable by teachers. Not all curricula would serve that purpose. The curriculum that must be attractive to students must also contain sufficient indications for teachers; it cannot be just a list of contents or curricular objectives, or a set of general orientations. You also need to quickly provide complementary resources to teachers to make them feel the nature of the reform and have direct support of their action in the classroom. In the absence of collections of text, or the existence of a weak educational culture to use them (which is usual), there needs to be specific documents that include the new elements oriented towards the classroom activity. It is also essential to develop some in-service training processes in the same direction to complement all actions; this process should reach out to as many people as possible in the shortest time.
On the other hand, in theory, ensuring the future of reform requires institutions that provide initial training for teachers to adjust their programs to curriculum changes. This would provide new teachers who support the new approaches. However, that takes many years, more than the length of a period of a government administration (the time to secure the reform). Besides, it is not certain that these entities want to make such adjustments, because they share many of the same weaknesses as the rest of the educational system (power feuds, intellectual inertia, negative reaction to change, union protests). If reform succeeds politically in reaching a “point of no-return”, or if a new government supports the educational reform, there can be a valuable additional support from teacher training institutions. But it would not be adequate to wait for training institutions to reform themselves and generate new teachers before starting a general educational reform.
Now, after this extensive preamble we turn to Costa Rica. In late 2010, the Minister of Education of Costa Rica asked Angel Ruiz to lead the design of a new curriculum for all pre-university education, which he performed with the assistance of a team of researchers from the Center for Research and Preparation in Mathematics Education (http://www.cifemat.org) and also from primary and secondary in-service teachers. This curriculum was approved by the Higher Council of Education in May 2012 and is being gradually implemented in classrooms beginning in 2013.
The same team (with the reinforcement of other professionals in the areas of virtual education) is the main instrument that Costa Rica adopted to implement the new curriculum. They developed the project named Reform of Mathematics Education in Costa Rica. It will last until 2015 (www.reformamatematica.net). This project is funded by the Foundation for Cooperation Costa Rica United States, CRUSA (http://www.crusa.cr), although the Ministry of Education provides an important counterpart. Reformers in Costa Rica have denominated their curricular orientation as the Praxis Perspective in Math Education.
The main focus of the new curriculum is a pedagogical strategy that the authors called “Problem Solving with Emphasis in Real Contexts” which essentially proposes the organization of the lesson to build learning through carefully selected problems. Its emphasis is not adding or subtracting content. It is a break with the teaching style of teaching of mathematics through lessons that are initiated through theory, examples, routine practice and sometimes challenging or contextualized problems. The new paradigm is reinforced with curricular emphasis operationalized explicitly: to promote positive attitudes and beliefs about mathematics, an intense use of digital technologies (albeit gradual and adequate), and the use of the history of mathematics. It is proposed to create higher cognitive abilities in students and mastery of specific abilities associated with mathematical areas through an appropriate teaching mediation which involves mathematical tasks of increasing complexity and cognitive transversal activities (which are designated as “mathematical processes”). It is an integrated curriculum from the first year of Primary to the last of Secondary organized through five areas of mathematics: Number, Geometry, Measurement, Relations and Algebra, and Statistics and Probability.
The proposal incorporates original research findings and international experience in mathematics education, such as a reading of the Japanese experience in problem solving, ideas of the National Council of Teachers of Mathematics (USA), Realistic Mathematics Education (Freudenthal Institute, Netherlands), the PISA theoretical framework, and results of the French School of Didactics of Mathematics. The curriculum bases itself on the “progress of mathematics education in the world”, but without losing sight of the conditions of the local context.
This Praxis Perspective emphasizes that a curriculum cannot be designed “in vitro” and then implemented, but implementation should illuminate the design from its inception: a good curriculum is one that can be implemented in a local reality responding to a specific socio-political context, although taking into account the findings and international experience. Content, main focus, and curricular axes as potential implementation actions were established based on this reality, establishing appropriate times and timing.
The scenario of Mathematics Education in Costa Rica has been substantially modified by the action of this group of reformers who received government support. The country now has not only a high quality official curriculum adapted to the national context (and able to enlist the support of teachers), it also has developed important implementation actions. This project has created blended courses: including face-to-face sessions, independent study of documents and virtual online sessions (self-assessment practices and tests). Even before the formal adoption of new programs, it started a training program each year for thousands of in-service teachers in primary and secondary schools (something which had never been done before in the country). These blended courses use “two times”: one for leaders and one for large groups of teachers taught by the leaders (the course is essentially the same for leaders and massive populations). This strategy allows articulating a set of teachers as a social base for educational reform.
The teacher preparation has been amplified through Massive Online Open Courses (MOOC), that reinforce the blended courses. The MOOCs, which internationally were originally linked more to higher education, served here for teacher training. Among their advantages are the use of videos (which are attractive and useful) and a pedagogical structure that allows an easy design.
To construct a common reference and a social identity, the reformers of Costa Rica created a Virtual Community of Mathematics Education. This is an efficient tool for dealing with concerns and approaches of teachers in the country and for coordinating educational activities.
The heavy use of communication technologies has become a powerful ally for working with large populations of in-service teachers in a relatively very short time and to ensure proper quality and consistency in the preparation given to all regions of the country.
These various actions, intended to have great synergy, seek to achieve a “point of no-return” in the following months, as there will be a change of government in Costa Rica in May 2014. The best possible scenario would be to have future new political authorities support further this educational reform process (which is very possible), but that still is uncertain.
The actions so far taken have changed the conditions under which teaching and learning of mathematics are developed in this country: curriculum, teacher training, and use of technology. This scenario pushes universities that prepare teachers to adjust their initial training programs in line with the reform, but it will take several years before this can have an impact on the classroom. This reform has opened a new stage of Mathematics Education in Costa Rica. However, amid a developing country an absolute success cannot be taken for granted. There is a significant level of uncertainty. If the reformers in Costa Rica are more successful, this experience could become a model to study when attempting to develop a reform in Mathematics Education in other countries. However the Costa Rican experience up to now may be already useful for other national or regional contexts which have similar socioeconomic and cultural characteristics (many details of this reform are described in revistas.ucr.ac.cr/index.php/cifem/issue/view/1186).
2. ICMI STUDY 22: TASK DESIGN IN MATHEMATICS EDUCATION
The mathematics education community has been engaged for many years in designing curriculum, and more specifically, designing tasks, problems and activities aimed at learning concepts, practicing procedures, solving problems and exploring mathematical phenomena. However, it is only in the last decade that task design became a focus of theoretical and empirical scrutiny. Thus, ICMI decided to commission an ICMI Study on Task Design and to appoint an International Program Committee co-chaired by Anne Watson (Oxford University, UK) and Minoru Ohtani (Kanazawa University, Japan). The IPC convened the ICMI Study conference which took place in Oxford, UK, in July 22nd-26th, 2013. This conference gathered a sample of the international efforts invested in these directions. The proceedings of this conference can be accessed through the ICMI website or directly from hal.archives-ouvertes.fr/hal-00834054
Materials from the plenary activities at this conference (lectures, panel and workshop) can be accessed at
Many lively discussions were carried on throughout the working groups. The leaders of the different working groups submitted a brief summary of their sessions, which are quoted below.
Theme A: Tools and Representations
Leaders: Allen Leung and Janete Bolite Frant.
“Theme A concerns designing teaching-learning tasks that involve the use of tools and representations in the mathematics classroom and, in the way it connects to how mathematical knowledge can be represented by tools. Major issues addressed in the discussion were how relaxing conditions and different types of feedbacks could enhance or create hurdles for learning, how (un)intentional disturbances resulting from tool usage could be used as opportunities for learning, affordances and constraints, boundary of mathematical and pedagogical fidelity, multi-representations, the potentials of tools in inclusive mathematics education, and instrumental/semiotic functions of tools.”
Theme B: Student Perspectives in Task Design
Leaders: Janet Ainley and Claire Margolinas
“Focusing on student perspectives on task design, the discussion in Theme B was guided by the two overarching questions of how the gap between teachers' intentions and students’ activity can be minimised, and how students perceive the purpose of the tasks they work on. We considered two ‘triangular’ relationships, between teacher, student and task, and between teacher, student and researcher/task designer. Members of the group presented rich examples of the adaptation and shaping of tasks in response to student reactions.”
Theme C: Design and use of Text-Based Resources
Leaders: Denise Thompson and Anne Watson
“Aspects of text-based tasks can be organized around three nodes: 1) the nature and structure of the text, including different kinds of physical text materials, the authorship and voice of tasks, the coherency of tasks in published collections, and organization of content; 2) the pedagogic/didactic purpose of a task, including principles about learning, relationships between pedagogic purpose and layout, and content aims; and 3) the intended mathematical activity, including the relationship between purpose and activity, and grain sizes of tasks. We expect to expound on these issues with varied examples and issues raised during the working group.”
Theme D: Principles and Frameworks for Task Design
Leaders: Carolyn Kieran, Michiel Doorman, and Minoru Ohtani.
“In the book chapter related to the reflections and work of this group, the author-coordinators will attempt, first, to situate current thinking on task design within a wider frame, going back to the 1960s when research in the learning and teaching of mathematics began to emerge as a discipline in its own right. The chapter will then focus on specific frameworks for task design, or more broadly didactic design, and the nature of the principles/heuristics/tools
associated with these frameworks. Two central parts of the chapter will be devoted to examples of how designers go about conceptualizing and designing tasks and task-sequences, and case studies of the dynamic relation between frameworks and principles, on the one hand, and task design on the other hand. The chapter will also touch upon the diversity of design approaches across cultural communities and will conclude with a synthesis of the current state of the art and offer suggestions for further research.”
Theme E: Features of Task Design
Leaders: Peter Sullivan and Yudong Yang
“This theme addressed the features of task design that informed teachers’ decisions about goals and pedagogies. Threads in the discussions included the importance of explicit articulation of mathematical goals, the nature of the authority and autonomy of the teacher in creating and implementing tasks, processes for task development, problematic aspects of converting tasks from one culture to another, issues in the development of task sequences, and aspects of pedagogy connected to task design.”
3. A LETTER FROM BARBARA JAWORSKY, PME PRESIDENT
PME is the International Group for the Psychology of Mathematics Education and is affiliated with ICMI. I write as PME’s new President, elected in August 2013. It is a great honour to hold this office in a society which is well established and highly respected throughout the Mathematics Education world.
The main focus of PME is Research in Mathematics Education; this includes psychological research and also extends to research linked to other disciplinary areas, social, philosophical, anthropological and scientific. In 2006, we celebrated 30-years of PME with a Handbook showcasing research presented at PME over these years (Gutierrez and Boero, 2006); including sections on cognitive and social aspects and use of technology in learning and teaching mathematics together with professional aspects of teaching mathematics and the education of new teachers. We are about to embark on a new volume of research from our ‘fourth decade’. In some countries (e.g., Denmark, Norway) having a paper published in PME equals a journal paper (in terms of bibliometric points) and is the only conference proceedings in mathematics education which has this possibility.
PME employs an Administrative Manager and is led by an International Committee (IC) of 16 members from a range of countries, plus the President. It holds a conference each year in a different country led by a local organising committee in cooperation with the IC. A proceedings of accepted papers is published for each conference. Between conferences, the IC continues the work of PME, ensuring a smooth transition from year to year and dealing with issues that arise.
Two of the main goals of PME relate to Quality and Inclusion in mathematics education research. Quality ensures the highest academic/scientific standards in our research and publication; a rigorous reviewing system seeks to accept only papers which demonstrate this quality. Inclusion ensures the openness and democratic principles that bring researchers from all over the world to PME, attracts researchers from under-represented countries and supports financially those who find it difficult to meet the costs of attending PME. Currently PME’s Skemp Fund provides financial support in these areas and it is our intention to extend the range of support in future years.
There are many issues to address in ensuring quality and inclusion together. For example, PME’s rigorous reviewing system might act against the acceptance of papers from new or early career researchers. A Pre-Submission Support process allows prospective participants in a PME Conference to receive comments from experienced researchers in PME in time to modify their paper before submission. A variety of conference sessions – research forums, research reports, short oral reports, seminars, working and discussion groups -- supports a wide range of participation in a wide range of research areas. A new initiative in 2014 will be a Young Researchers’ Day (‘young’=early career) to take place directly before the conference. This will be organized by a combination of local and international experts in mathematics education research and tailored directly to the needs of inexperienced researchers. A further initiative is to make past PME proceedings more accessible to researchers throughout the world by electronic access. Over the coming years, proceedings will gradually be digitized year by year from the most recent to those past.
The next PME conference will be held in Vancouver, Canada in 2014 (July 15 to 20) (www.pme38.org). Conferences in years after 2014 are under discussion and will be clarified soon; please refer to www.igpme.org for up-to-date information or contact the PME Administrative Manager (Dr. Bettina Roesken-Winter) at email@example.com.
Barbara Jaworski, PME President 2013-2016
4. MATHEMATICS EDUCATION AT THE ICM
The International Congress of Mathematicians will take place in Seoul, August 13-21, 2014. Section 18 will be devoted to "Mathematics Education and Popularization of Mathematics". Two well known mathematicians will deliver plenary lectures: Étienne Ghys (France) and Günter M. Ziegler (Germany). Three panels will address the following themes which are of great interest to both mathematicians and mathematics educators:
- The risks of assessment and comparisons in mathematical education (Moderator: William Schmidt; Panelists: Konrad Krainer, Gilah Leder and Mogens Niss).
- How should we teach better? (Moderator: Deborah Ball; Panelists: William Barton, Werner Blum, Jean-Marie Laborde and Man Keung Siu).
- Mathematics is everywhere (Moderator: Christiane Rousseau; Panelists: Eduardo Colli, Fidel Nemenzo and Konrad Polthier).
5. MENAO AT ICM
The International Mathematical Union (IMU) announces the one day event: MENAO - Mathematics in Emerging Nations: Achievements and Opportunities, COEX Convention & Exhibition Center, Seoul, Korea, Tuesday, August 12, 2014.
The MENAO event features approximately 100 participants and is open to an additional 350 observers. It will take place on the day immediately preceding the opening of the 2014 International Congress of Mathematicians (ICM).
The MENAO event will feature personal stories of mathematicians, country-specific development stories, both from the perspective of mathematicians in developing countries and from the perspective of their international partners, as well as an in-depth look at the Korean story as narrated by key figures in the various stages of its mathematical development.
The Republic of Korea (South Korea), the host country for ICM 2014, has experienced a remarkable mathematical development over the last 50 years, one that proceeded hand-in-hand with its economic and educational development. As an act of solidarity with their colleagues in emerging nations, the Korean ICM hosts are inviting 1,000 mathematicians and advanced mathematics graduate students (as part of the "NANUM 2014" invitation program) from the developing world to attend ICM 2014. The participation of these invitees in the Congress will be fully paid for by Korean corporate sponsorship and other donors. For further information see:
It is expected that the presence and participation of many NANUM invitees will enrich the discussions that are intended to be an essential part of the MENAO event.
The goal of the MENAO event is to listen to the voices of mathematicians and aspiring advanced students of mathematics from the developing world, to share success stories of development via partnerships between the local mathematical communities, their governments, and international agencies and foundations, and to review the current status of those efforts and future needs.
Bringing together, in an environment like this, those who are in need with those who are willing to support may create a stimulus for partnerships that will benefit the developing world and mathematics in general.
Finally, the relationships between mathematical development and economic development elsewhere in the world will be explored.
MENAO participants will take part by invitation; observers will be admitted via registration on a first-come first-served basis. The registration process will be explained in a future announcement.
The leadership of the International Mathematical Union wishes to make MENAO a premier event, of compelling interest to all organizations, governmental agencies, and individuals that have contributed to international mathematical development or are potentially interested in doing so.
For further questions please contact the CDC Administrator in the IMU Secretariat in Berlin: firstname.lastname@example.org
Reported by C. Herbert Clemens, CDC (Commission for Developing Countries) Secretary for Policy.
6. INTERNATIONAL CONGRESS ON MATHEMATICAL EDUCATION (ICME)14, 2020
ICMI invites its state representatives, national/regional organisations and academic institutions to consider the possibility of organising and hosting the International Congress on Mathematical Education in July/August 2020. Further details regarding requirements and suggestions can be found at
Letters of intent should be submitted to the ICMI Secretary General by December 1, 2013.
7. KLEIN WORSHOP BERLIN
Workshops are periodically held as part of the Klein Project and its many international branches. The last workshop took place in Berlin in September 17-20, 2013, under the title "Elementary Mathematics from an Advanced Standpoint - Felix Klein and Mathematics for Teachers", organized by Prof. Dr. Hans-Georg Weigand (Germany). The workshop devoted a special day for Mathematics teachers from the Berlin area at the Humboldt University. The overarching goal of the meeting (as well as of the Klein Project at large) was to bring together mathematicians, mathematics educators and teachers in order to discuss ways and opportunities and barriers to enrich teacher education and mathematics classrooms with contemporary mathematics, and to imbue higher levels of education with the spirit of contemporary mathematics. For more details see
8. CANP MOEKONG SUB-REGION HELD IN CAMBODIA
The Capacity and Network Project (Mekong Sub-Region) Workshop, known as CANP(MSR), was held from 14th to 25th October in Phnom Penh in Cambodia. Thirty-three participants from Cambodia, Laos, Thailand and Viet Nam, and an international support team of eight, completed a full programme of workshops in mathematics and mathematics education, as well as national presentations and other events, including a full social programme.
The CANP(MSR) Workshop was opened by the Secretary of State for the Ministry of Youth Education and Sport, His Excellency Pit Chamnan. A delegation later met again with the Secretary of State, presenting a report on their recommendations with respect to three questions about mathematics education in Cambodia. In addition, four members of the international team gave presentations at Kemarak university to a group of 150 teachers.
The Workshop has formed a regional grouping, yet to be given a formal name, and plans to meet in 2014, as well as mount other regional activities.
For some more information please go here: www.mathunion.org/icmi/other-activities/outreach-to-developing-countries/canp-project-2013-south-east-asia/
Reported by Bill Barton, Past-President of ICMI.
9. HAVE YOU READ?
The International Journal of Mathematical Education in Science and Technology published an issue devoted to the teaching and learning of calculus (2103, Vol. 44 (5)).
The issue is based on the presentations at the Topic Study Group 13 at ICME-12 which included: 16 papers and 10 posters from 17 different countries. The selection (8 papers) provides insights into the developments on the teaching and learning of calculus at the upper secondary and tertiary level, describing pedagogical advances, new trends and recent research studies.
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