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Topic: ICMI News 25: October/ November 2013 / A Newsletter from the ICMI
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Jerry P. Becker

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Registered: 12/3/04
ICMI News 25: October/ November 2013 / A Newsletter from the ICMI
Posted: Nov 6, 2013 1:09 PM
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Sent at the request of Lena Koch.
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:
<> / <>

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
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?

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
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
This project is funded by the Foundation for
Cooperation Costa Rica United States, CRUSA
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

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

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
in <>

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
. 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

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

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

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."

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)
(<> ).
Conferences in years after 2014 are under
discussion and will be clarified soon; please
refer to <> for
up-to-date information or contact the PME
Administrative Manager (Dr. Bettina
at <>
Barbara Jaworski, PME President 2013-2016

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).

See <>

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
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: <>
Reported by C. Herbert Clemens, CDC (Commission
for Developing Countries) Secretary for Policy.

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.

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

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: <>
Reported by Bill Barton, Past-President of ICMI.

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.

Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
625 Wham Drive
Mail Code 4610
Carbondale, IL 62901-4610
Phone: (618) 453-4241 [O]
(618) 457-8903 [H]
Fax: (618) 453-4244

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