The professional development of teachers of mathematics€¦ · The professional education and...
Transcript of The professional development of teachers of mathematics€¦ · The professional education and...
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The professional development
of teachers of mathematics
Ruhama Even
Weizmann Institute of Science
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Teaching development of
practicing mathematics
teachers
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Teaching development of practicing
mathematics teachers (or professional
development of teachers)
• Key to improving students' opportunities to
learn mathematics.
• Supporting practicing teachers’ learning is
not a trivial task.
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Challenges associated with
supporting practicing teachers’
learning
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Relevant issues
• The nature of the field of mathematics
teaching development of practicing teachers.
• The practice of mathematics educators who
work in this field.
• The professional education and development
of these educators.
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The nature of the field of
mathematics teaching development
of practicing teachers
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The nature of the field
• Ill defined
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The nature of the field: ill defined (1) • Teaching development of practicing
teachers is not part of a systematic
institutionalized practice.
• In many countries: • insightful and innovative initiatives,
• local and temporary,
• dependent on the particular individuals who
initiate, design, lead, and operate them.
• In contrast to teaching children at school.
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The nature of the field: ill defined (1) • Teaching development of practicing
teachers is not part of a systematic
institutionalized practice.
• In many countries: • insightful and innovative initiatives,
• local and temporary,
• dependent on the particular individuals who
initiate, design, lead, and operate them.
• Some countries adopt a different approach.
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Teaching development of practicing teachers
as a systematic institutionalized practice
• Lesson study in Japan.
• Teaching research system in China.
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Teaching research system in China
• “Well-established, multi-tiered teaching research
system through which teachers and teaching
researchers work together to design, deliver, and
revise lessons to promote a high quality of
student learning” (Huang, Su, & Xu, 2014).
• Mathematics teaching researchers work with and
help teachers improve their teaching by
mentoring and assessing teaching, conducting
teaching research activities, and supporting
implementation of new curricula.
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The nature of the field: ill defined (2) No agreed-upon name for those working in the field:
• Teachers of teachers
• Teacher educators
• Teacher mentors
• Facilitators
• Professional development (PD) leaders
• Professional development (PD) providers
• Teacher-leaders
• Teaching researchers (China)
• Coaches
• Didacticians • …מוביליםמורים , מדריכים, מנחים
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No agreed-upon name
These people are not recognized as
members of an identifiable group whose
members share a profession, by:
• Others.
• Themselves.
• In contrast to the name teachers in the field
of teaching children at school.
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The nature of the field: ill defined (2) No agreed-upon name for those working in the field:
• Teachers of teachers
• Teacher educators
• Teacher mentors
• Facilitators
• Professional development (PD) leaders
• Professional development (PD) providers
• Teacher-leaders
• Teaching researchers (China)
• Coaches
• Didacticians • …מוביליםמורים , מדריכים, מנחים
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An attempt to change current situation
Didacticians:
“…mathematics (teacher–) educators who work
with practising teachers to promote
developments in teaching and learning
mathematics: the term includes university
faculty, teaching researchers, curriculum
development coordinators, master teachers,
mathematics coaches, and so on”.
Jaworski & Huang, 2014
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The name Didacticians
• Calls attention to the problem of lack of a
shared identity.
• Proposes a means of altering current
situation.
• Does not straightforwardly convey the
meaning associated with it.
• Time will tell whether the community at
large will adopt the proposed name.
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The nature of the field
We need to better understand:
• The characteristics of different teaching
development systems.
• Who educates practicing teachers of
mathematics in different countries.
• The advantages and the disadvantages of
different systems.
• The extent to which they relate to cultural and
societal factors.
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The practice of mathematics
educators who work in the field
of mathematics teaching
development of practicing teachers
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The practice of those working in the field
Substantial increase in scholarship on
teaching development of practicing
mathematics teachers:
• Rich descriptions of successful programs
and activities.
• Limited empirical research-based
information about the practice of those
working in the field.
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Some practices of those working in the field (ZDM, 2014)
• Engaging teachers in analyzing videos of classroom instruction.
• Inviting groups of teachers to compare and contrast public presentations of same content lessons.
• Modeling teaching.
• Providing positive feedback to teachers.
• Engaging teachers in examining student work.
• Engaging teachers in studying curriculum materials.
• Encouraging teachers’ systematic gathering and analysis of evidence from their classes.
• Presenting math tasks with the potential to stimulate discussions among teachers of all grade levels.
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Limited empirical research-based information
Problem 1: Research focus
• Teacher learning.
• Not the practice of those working in the field.
• In contrast to research on school teaching.
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Limited empirical research-based information
Problem 2: Sources of information
• Those working in the field on their own work.
• Those who publish in scholarly publications.
• Mainly from countries where English is a
national language.
• Adler et al. (2005), Gellert et al. (2013).
• In contrast to research on school teaching.
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Limited empirical research-based information
Problem 3: Nature of information
• Lack of information on practices that are not
effective for facilitating teaching development.
• In contrast to research on school teaching.
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Some practices of those working in the field (ZDM, 2014)
• Engaging teachers in analyzing videos of classroom instruction.
• Inviting groups of teachers to compare and contrast public presentations of same content lessons.
• Modeling teaching.
• Providing positive feedback to teachers.
• Engaging teachers in examining student work.
• Engaging teachers in studying curriculum materials.
• Encouraging teachers’ systematic gathering and analysis of evidence from their classes.
• Presenting math tasks with the potential to stimulate discussions among teachers of all grade levels.
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The practice of those working in the field
We need to better understand:
• What practices are common.
• What practices facilitate teaching development.
• What practices impede teaching development.
• Advantages and disadvantages of different
practices.
• Supporting and obstructing conditions.
• The extent to which effective practices are
related to cultural and societal factors.
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The professional education and
development of educators
working in the field of
mathematics teaching development
of practicing teachers
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The professional education and
development of educators working in
the field of mathematics teaching
development of practicing teachers
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The professional education and
development of mathematics teachers
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The professional education and
development of mathematics teachers
Immense international attention in the last
three decades:
• Establishment of the international Journal of
Mathematics Teacher Education (1998).
• Plenary sessions at ICME meetings (since 2004).
• One of five research domains in the 2nd PME
milestone book (2006); missing in the 1st (1990).
• ICMI study 15 (Conference 2005,Volume 2009).
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The professional education and
development of educators working in the
field of mathematics teaching
development of practicing teachers
• Almost neglected until recent years.
• Review of JMTE 1998-2002 (prospective &
practicing teachers):
• Halai (1998) – Own work as mentor.
• Even (1999) – Formal preparation program.
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Becoming an educator working in the field
of mathematics teaching development
Traditionally
• Through practice.
• No formal education that explicitly aimed at preparing, educating or developing mathematics teacher educators in general, and those working with practicing teachers in particular.
In recent years
• Growing attention to structuring the education and professional development of educators of practicing teachers.
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Growing international attention
• Publication of The International Handbook of
Mathematics Teacher Education: The
Mathematics Teacher Educator as a
Developing Professional (2008).
• One of three main problems that needs to be
addressed, ICMI Study 15 Volume (2009).
• Themed issue of ZDM (2014).
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What should educators working in the field of mathematics teaching development learn?
• Discussions about the preparation of
educators tend to start with questions of
knowledge:
What should future educators know?
• Work in the field of teaching development is
something one does, not just knows.
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Knowtice (knowledge+practice)
• The integration of knowledge, skills,
dispositions and practices situated in the
practice of mathematics teaching
development (Even, 2005, 2008).
• The essence of what teachers – as well as
educators working in the field – need to learn
and develop.
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The case of MANOR (1993-2003)
Main goal
• Preparation of, and support for, practice-based
educators working in the field of secondary
school mathematics teaching development.
Even (1999, 2005, 2008)
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The case of MANOR (1993-2003)
Knowledge base (1)
• Preparation of, and support for, practice-based
educators working in the field of secondary
school mathematics teaching development.
Even (1999, 2005, 2008)
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The case of MANOR (1993-2003)
Knowledge base (2)
• Preparation of, and support for, practice-based
educators working in the field of secondary
school mathematics teaching development.
Even (1999, 2005, 2008)
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The case of MANOR (1993-2003)
Knowledge base (3)
• Preparation of, and support for, practice-based
educators working in the field of secondary
school mathematics teaching development.
Even (1999, 2005, 2008)
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How might practice-based educators in
the field of mathematics teaching
development develop knowtice?
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MANOR’s main components
• Two-year formal preparation program.
• Monthly graduate forum.
• Bi-annual national conferences.
• Individual support.
• Resource Files.
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MANOR’s main components
• Two-year formal preparation program.
• Monthly graduate forum.
• Bi-annual national conferences.
• Individual support.
• Resource Files.
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Two-year formal preparation program
• Weekly 6-hour sessions at the Weizmann
Institute.
• Weekly 2-hour PD for teachers at a school or
at a regional teacher center.
• Extensive work outside formal meetings.
• Yearly portfolios.
• 3 groups – 75 graduates from all over the
country.
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MANOR’s main components
• Two-year formal preparation program.
• Monthly graduate forum.
• Bi-annual national conferences.
• Individual support.
• Resource Files.
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Monthly graduate forum
• Long term
• Shared responsibility of participants and staff
for the content and framework of the sessions.
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MANOR’s main components
• Two-year formal preparation program.
• Monthly graduate forum.
• Bi-annual national conferences.
• Individual support.
• Resource Files.
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Bi-annual national conferences
• For all practice-based educators in the field of
mathematics teaching development.
• Shared responsibility of participants and staff
for the content and framework of the sessions.
• Presentation of work, discussions of
professional issues, sharing ideas and
materials with each other.
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MANOR’s main components
• Two-year formal preparation program.
• Monthly graduate forum.
• Bi-annual national conferences.
• Individual support.
• Resource Files.
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MANOR’s main components
• Two-year formal preparation program.
• Monthly graduate forum.
• Bi-annual national conferences.
• Individual support.
• Resource Files.
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Resource Files: Topics
• Algebra
• Functions
• Limits
• p
• Teaching mathematics in heterogeneous
classes.
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Resource Files: Major themes
• Historical view on the main topic of the file.
• Selected mathematical aspects relevant to the
topic.
• Students' conceptions and ways of learning
and thinking.
• Aspects of mathematics lessons and teaching.
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Resource Files: Characteristics
• Detailed suggestions for teaching
development meetings.
• Several models for teaching development
meetings.
• Classified list of articles, books, journals, and
other references.
• Serve as a resource, model and guide.
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Developing knowtice: theoretical orientations
Drawing on and inspired by:
• Constructivist and socio-cultural approaches to
student learning of mathematics adopted to
learning to work with secondary school math
teachers on developing their teaching.
• Situated learning approach (Lave & Wenger, 1991).
• Framework of three types of teacher
development: personal, professional and social
(Bell & Gilbert, 1994).
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Developing knowtice: MANOR’s approach
• Providing a supportive and intellectually and
professionally demanding environment.
• Designing activities where participants needed to
solve real problems of practice, combined with
opportunities for reflecting on and analyzing these
solutions, in the light of academic and practical
knowledge.
• Developing norms of interaction that encourage
the study and critique of one’s own and others’
practice, combined with the actual enactment of
knowledge. © All rights reserved
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Providing a supportive and intellectually and
professionally demanding environment
Inclusion of an advanced academic component.
Requirements of high commitment and work
investment outside formal meetings: • Experimenting with innovative learning materials.
• Reading research articles.
• Conducting small scale research studies.
• Writing papers.
• Conducting weekly PD activities for teachers.
• Initiating change in school mathematics teaching.
• Preparing portfolios.
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Designing activities where participants needed to
solve real problems of practice, combined with
opportunities for reflecting on and analyzing these
solutions, in the light of academic and practical
knowledge
• What are good problems in school mathematics?
• What are students’ learning processes in algebra?
• How might students’ difficulties addressed?
• What is teachers’ knowledge about functions?
• What PD activities are useful in a specific context?
• How can I work with teachers on change initiatives?
• …
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Developing norms of interaction that encourage the
study and critique of one’s own and others’
practice, combined with the actual enactment of
knowledge
• Reflecting on one’s own and discussing others’ PD
activities, and suggesting reasoned modifications.
• Collaborating on planning, implementing and
evaluating activities, sharing and discussing ideas,
difficulties and challenges related to change
initiatives in mathematics teaching and learning.
• Suggesting alternative solutions to problems of
practice, explaining reasoning to peers, examining
each other’s solutions.
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The professional education and development of educators working in the field of mathematics teaching development
We need to better understand: • What “these” people need to learn.
• When and how they should learn that.
• How preparation and continuous development programs might be organized.
• What might be useful learning experiences, and for what purposes.
• What kinds of support are helpful.
• The extent to which effective programs are related to cultural and societal factors.
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