February 16th, 2015
At Tsukuba, Tokyo
Professional competence and professional
community in mathematics education：
Does competence belong to an individual
or a community?
Takuya BABA
Hiroshima University
Contents
1. Mathematics teacher’s professional
competence
2. Mathematics education community and its
competence
4. Beyond mathematics education community
1. Mathematics teacher’s professional
competence
• To bridge between Pedagogy and Content is an
important task in the teacher education.
PCK (Hill et al., 2008)
It is not enough to have just this knowledge but it is more
important to integrate and implement them into the
actual lesson.
The affective aspect of teacher’s competence such as
attitudes and willingness is not seen in this framework.
TEDS-M 2008 Framework
Teacher Education and Development Study in Mathematics
(TEDS-M)
In this framework, what are the belief and the professional
motivation?
Strengths and weaknesses of perceiving the
individual professional competence
[Strengths]
・To measure and to be aware of each described competence,
・To grow the weak component of competence intentionally, and
・To plan the pre-service education to grow each component
systematically
[Weaknesses]
・To tend to perceive it fragmentarily. In an actual lesson, it will
not work individually.
・To be less attentive to what is not expressed.
・To be less attentive to long term (developmental) perspective.
Consideration of the weaknesses
We perceive it as cross-section of knowledge at a certain
time and not as more subtle and complicated professionalintegrative knowledge embedded in the teaching practice.
In order to describe this more subtle knowledge, inevitably
we use more philosophical and holistic term to express the
complicated whole. In this expression, being simple (e.g.
listen to children’s voice) and being philosophical (e.g.
interactionism, social constructivism) may look quite
opposite but close to each other.
Competence embedded in groups
This professional knowledge has two ways:
an individual teacher polishes his/her knowledge and skills
through professional life
the group appreciates it and support growing it
Even at the vague stage of feeling, the invisible thing is formed
through visible things and handed over to next group through
repeated implementation of lesson and reflection over it.
Especially this invisible thing will function like as air.
2. Mathematics education community
and its competence
Knowledge and values held by the groups
• An individual teacher think based on the knowledge and
values shared by the group. In Japan, through the lesson study
newly recruited teachers are expected to feel and acquire
these knowledge and values embedded in the daily practice.
• Some Japanese professional knowledge such as Kyo-zaikenkyu and Kikan-junshi is known. Journal of Japan Society of
Mathematics Education (2010) edited the anthology of shared
knowledge.
• Sharing and verbalizing like this has strength of going beyond
the context. What is important as well is the process of
knowledge creation and values behind it.
Anthology of shared knowledge
Strength and limitation of verbalizing the
essence (slogan)
• Many countries promote the education reform using the
slogan “child-centeredness”. It has an impact on reconsidering
the old knowledge. It, however, does not reach the point to
form a new knowledge yet. What is easily conveyed is only
conveyed and remains at very superficial level. In other words,
what is important is not conveyed.
• Then what is the most important thing to convey? In short, it
is putting the child’s learning at the center of mathematics
lesson. It, however, only produces the tautological effect.
Again consequently, it remains very abstract and superficial.
(Example Japanese community)
(Ueda, 2013)
Mathematical thinking, evaluation
method of higher objectives and
open ended approach, textbook
change, treatment of diversified
mathematical thinking,
have made a impact on sharing
such value. Historical research can
provide an important perspective
to grasp values formed within
mathematics education community.
Textbooks
Textbook in 1973 (S48)
Textbook in 1980 (S55)
Textbooks
Textbook in 1985 (S60)
Textbook in 2010 (H22)
Process of Curriculum Development and
national assessment
6. Identification of problems
7. Revision of curriculum
1. Identification of problems
2. Curriculum development
3. Dissemination of curriculum
5. Assessing the curriculum
4.Implementation of curriculum
3. Beyond present community of mathematics
education
Present community and community beyond
time and space
• If the knowledge as a result is simply transferred to
other community, it may remain superficial. To
overcome it, the community condenses the
knowledge through reflection over thousands
practices and contains the values and passions of
many people.
• As time passes, the community may transform,
passions and values behind the knowledge and
experience are transmitted with some modification
and reconstructed by the following generation of
community.
Wenger’s Community of Practice
1) Meaning: about our (changing) ability – individually and
collectively - to experience our life and the world as meaningful.
2) Practice: about the shared historical and social resources,
frameworks, and perspectives that can sustain mutual engagement.
3) Community: about the social configurations in which enterprises
are defined as worth pursuing and our participation is recognizable
as competence.
4) Identity: about how learning changes who we are and creates
personal histories of becoming in the context of our communities.
Learning as
belonging
Learning by
doing
Learning as
becoming
Learning as
experience
Important points to consider
• Invisibility: Not all aspects can be seen and some critical
aspects cannot be easily measured.
• Collectivity: Not only individuals but also group have a
competence. The latter enables individuals to think more
deeply/ shallowly and appreciates/ depreciates their efforts.
• Formativeness: The group forms knowledge (competence).
This should be interpreted as a process not as a product.
Through this process, the group attach a lot meaning and
values into the knowledge and values, and they can be shared
among the members.
• Historicity: This and formativeness may complement each
other. The formation process is long and
Fixation and attention-calling functions of
describing the competence
• Describing the professional competence such as SEARS-MT
will provide the direction and goal beyond the diversity of this
area’s common characteristics. It can provide many reference
points and make objective clear in each country.
• On the other hand, the above discussion pose the problem
how to make it possible to discuss the invisible professional
competence by the community in a long run.
• Shiono Naomichi in 1930s called the newly-revised syllabus
“pomace”. He rather values its discussion process.
• Hopefully, describing the professional competence can be
interpreted as continuous process of externalization and selfreferential over shared knowledge.
Reference
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Views about Education on Mathematics Lesson at Primary Schools, 2004-2006
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for Educational Development Report of the International Experience Sharing
Seminar(2) -Actual Status and Issues of Teacher Professional Development, CICE,
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Inprasitha,M. 2013. “Open Approach: Japanese Mathematics Education from
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Wenger 2002 Community of Practice. Harvard Business School Press.