Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
ISSN 1309-6591
Editor-in-Chief
Abdullah Kuzu,
Anadolu University, Turkey
Associate Editors
Cindy G. Jardine
University of Alberta, Canada
Işıl Kabakçı
Anadolu University, Turkey
Franz Breuer
Westfälische Wilhems-Universität Münster, Germany
Jean McNiff
York St John University, United Kingdom
Ken Zeichner
University of Washington, USA
Wolff-Michael Roth
University of Victoria, Canada
Yavuz Akbulut
Anadolu University, Turkey
Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
Advisory Board
Abdullah Kuzu, Anadolu University, Turkey
Ahmet Saban, Selçuk University, Turkey
Ali Rıza Akdeniz, Rize University, Turkey
Ali Yıldırım, Middle East Technical University, Turkey
Angela Creese, University of Birmingham, United Kingdom
Angela K. Salmon, Florida International University, USA
Antoinette McCallin, Auckland University of Technology, New Zealand
Arif Altun, Hacettepe University, Turkey
Asker Kartarı, Hacettepe University, Turkey
Aytekin İşman, Sakarya University, Turkey
Benedicte Brøgger, The Norwegian School of Management BI, Norway
Bronwyn Davies, University of Melbourne, Australia
Buket Akkoyunlu, Hacettepe University, Turkey
Cem Çuhadar, Trakya University, Turkey
Cemalettin İpek, Rize University, Turkey
Cesar Antonio Cisneros Puebla, Universidad Autonoma Metropolitana Iztapalapa, Mexico
Cindy G. Jardine, University of Alberta, Canada
Claudia Figueiredo, Institute for Learning Innovation, USA
Durmuş Ekiz, Karadeniz Technical University, Turkey
Elif Kuş Saillard, Ankara University, Turkey
Fawn Winterwood, The Ohio State University, USA
Ferhan Odabaşı, Anadolu University, Turkey
Franz Breuer, Westfälische Wilhems-Universität Münster, Germany
Gina Higginbottom, University of Alberta, Canada
Gönül Kırcaali İftar, Professor Emerita, Turkey
Hafize Keser, Ankara University, Turkey
Halil İbrahim Yalın, Gazi University, Turkey
Hasan Şimşek, Middle East Technical University, Turkey
Işıl Kabakçı, Anadolu University, Turkey
İlknur Kelçeoğlu, Indiana University & Purdue University, USA
Jacinta Agbarachi Opara, Federal College of Education, Nigeria
Jean McNiff, York St John University, United Kingdom
José Fernando Galindo, Universidad Mayor de San Simón, Bolivia
Ken Zeichner, University of Washington, USA
Mustafa Yunus Eryaman, Çanakkale Onsekiz Mart University, Turkey
Nedim Alev, Karadeniz Technical University, Turkey
Nigel Fielding, University of Surrey, United Kingdom
Nihat Gürel Kahveci, Istanbul University, Turkey
Petek Aşkar, Hacettepe University, Turkey
Pranee Liamputtong, La Trobe University, Australia
Richard Kretschmer, University of Cincinnati, USA
Roberta Truax, Professor Emerita, USA
Selma Vonderwell, Cleveland State University, USA
Servet Bayram, Marmara University, Turkey
Sevgi Küçüker, Pamukkale University, Turkey
Shalva Weil, Hebrew University of Jerusalem, Israel
Soner Yıldırım, Middle East Technical University, Turkey
Udo Kelle, Philipps-Universität Marburg, Germany
Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
Ümit Girgin, Anadolu University, Turkey
Wolff-Michael Roth, University of Victoria, Canada
Yang Changyong, Sauthwest China Normal University, China
Yavuz Akbulut, Anadolu University, Turkey
Yavuz Akpınar, Boğaziçi University, Turkey
Review Board
Abdullah Adıgüzel, Harran University, Turkey
Abdullah Kuzu, Anadolu University, Turkey
Adeviye Tuba Tuncer, Gazi University, Turkey
Adile Aşkım Kurt, Anadolu University, Turkey
Ahmet Naci Çoklar, Selçuk University, Turkey
Ahmet Saban, Selçuk University, Turkey
Ali Rıza Akdeniz, Rize University, Turkey
Ali Yıldırım, Middle East Technical University, Turkey
Angela Creese, University of Birmingham, United Kingdom
Angela K. Salmon, Florida International University, USA
Antoinette McCallin, Auckland University of Technology, New Zealand
Arif Altun, Hacettepe University, Turkey
Asker Kartarı, Hacettepe University, Turkey
Aytekin İşman, Sakarya University, Turkey
Aytaç Kurtuluş, Osmangazi University, Turkey
Bahadır Erişti, Anadolu University, Turkey
Belgin Aydın, Anadolu University, Turkey
Benedicte Brøgger, The Norwegian School of Management BI, Norway
Bronwyn Davies, University of Melbourne, Australia
Buket Akkoyunlu, Hacettepe University, Turkey
Cem Çuhadar, Trakya University, Turkey
Cemalettin İpek, Rize University, Turkey
Cesar Antonio Cisneros Puebla, Universidad Autonoma Metropolitana Iztapalapa, Mexico
Cindy G. Jardine, University of Alberta, Canada
Claudia Figueiredo, Institute for Learning Innovation, USA
Dilek Tanışlı, Anadolu University, Turkey
Durmuş Ekiz, Karadeniz Technical University, Turkey
Elif Kuş Saillard, Ankara University, Turkey
Eren Kesim, Anadolu University, Turkey
Esra Şişman, Osmangazi University, Turkey
Fawn Winterwood, The Ohio State University, USA
Ferhan Odabaşı, Anadolu University, Turkey
Figen Ünal, Anadolu University, Turkey
Figen Uysal, Bilecik University, Turkey
Franz Breuer, Westfälische Wilhems-Universität Münster, Germany
Gina Higginbottom, University of Alberta, Canada
Gönül Kırcaali İftar, Professor Emerita, Turkey
Gülsün Kurubacak, Anadolu University, Turkey
Hafize Keser, Ankara University, Turkey
Halil İbrahim Yalın, Gazi University, Turkey
Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
Handan Deveci, Anadolu University, Turkey
Hasan Şimşek, Middle East Technical University, Turkey
Işıl Kabakçı, Anadolu University, Turkey
İlknur Kelçeoğlu, Indiana University & Purdue University, USA
Jacinta Agbarachi Opara, Federal College of Education, Nigeria
Jale Balaban, Anadolu University, Turkey
Jean McNiff, York St John University, United Kingdom
José Fernando Galindo, Universidad Mayor de San Simón, Bolivia
Ken Zeichner, University of Washington, USA
Mehmet Can Şahin, Çukurova University, Turkey
Meltem Huri Baturay, Gazi University, Turkey
Meral Ören Çevikalp, Anadolu University, Turkey
Mine Dikdere, Anadolu University, Turkey
Mustafa Caner, Ondokuz Mayıs University, Turkey
Mustafa Nuri Ural, Afyon Kocatepe University, Turkey
Mustafa Yunus Eryaman, Çanakkale Onsekiz Mart University, Turkey
Müyesser Ceylan, Anadolu University, Turkey
Nedim Alev, Karadeniz Technical University, Turkey
Nigel Fielding, University of Surrey, United Kingdom
Nihat Gürel Kahveci, Istanbul University, Turkey
Nilüfer Köse, Anadolu University, Turkey
Osman Dülger, Bingöl University, Turkey
Pelin Yalçınoğlu, Anadolu University, Turkey
Petek Aşkar, Hacettepe University, Turkey
Pranee Liamputtong, La Trobe University, Australia
Richard Kretschmer, University of Cincinnati, USA
Roberta Truax, Professor Emerita, USA
Selma Vonderwell, Cleveland State University, USA
Sema Ünlüer, Anadolu University, Turkey
Semahat Işıl Açıkalın, Anadolu University, Turkey
Serap Cavkaytar, Anadolu University, Turkey
Servet Bayram, Marmara University, Turkey
Servet Çelik, Karadeniz Technical University, Turkey
Sevgi Küçüker, Pamukkale University, Turkey
Sezgin Vuran, Anadolu University, Turkey
Shalva Weil, Hebrew University of Jerusalem, Israel
Soner Yıldırım, Middle East Technical University, Turkey
Şemseddin Gündüz, Selçuk University, Turkey
Tuba Yüzügüllü Ada, Anadolu University, Turkey
Udo Kelle, Philipps-Universität Marburg, Germany
Ümit Girgin, Anadolu University, Turkey
Wolff-Michael Roth, University of Victoria, Canada
Yang Changyong, Sauthwest China Normal University, China
Yavuz Akbulut, Anadolu University, Turkey
Yavuz Akpınar, Boğaziçi University, Turkey
Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
Language Reviewers
Mehmet Duranlıoğlu, Anadolu University, Turkey
Mustafa Caner, Ondokuz Mayıs University, Turkey
Administrative & Technical Staff
Elif Buğra Kuzu, Anadolu University, Turkey
Serkan Çankaya, Anadolu University, Turkey
The Turkish Online Journal of Qualitative Inquiry (TOJQI) (ISSN 1309-6591) is published quarterly
(January, April, July and October) a year at the www.tojqi.net.
For all enquiries regarding the TOJQI, please contact Assoc.Prof. Abdullah KUZU, Editor-In-Chief,
TOJQI, Anadolu University, Faculty of Education, Department of Computer Education and Instructional
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Phone #:+90-222-3350580/3519, Fax # :+90-222-3350573,
E-mail : [email protected]; [email protected].
Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
Table of Contents
Post-Colonial Theory and Action Research
Jim B. Parsons
Kelly J. Harding
Collaborative Action Research: Teaching of Multiplication and Division in the
Second Grade
Eda Vula
1
7
Lirika Berdynaj
Preservice Secondary Mathematics Teachers’ Knowledge of Students
17
Hülya Kılıç
Acting and Teacher Education: The BEING Model for Identity Development
Kemal Sinan Özmen
36
Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
Post-Colonial Theory and Action Research
Jim B. Parsons
The University of Alberta, Canada
[email protected]
Kelly J. Harding
The University of Alberta, Canada
Abstract
This essay explores connections between post-colonial theory and action research. Post-colonial
theory is committed to addressing the plague of colonialism. Action research, at its core, promises
to problematize uncontested ‘colonial’ hegemonies of any form. Both post-colonial theory and
action research engage dialogic, critically reflective and collaborative values to offer a fuller range
of human wisdom. The authors contend that post-colonialism theory calls for justice and seeks to
speak to social and psychological suffering, exploitation, violence and enslavement done to the
powerless victims of colonization around the world by challenging the superiority of dominant
perspectives and seeking to re-position and empower the marginalized and subordinated. In similar
ways, action research works to eradicate oppression, powerlessness and worthlessness by affirming
solidarity with the oppressed, helping humans move from passive to active and by fundamentally
reshaping power. Because both post-colonial theory and action research position the insider or
oppressed in an ethic of efficacy, it values community, relationships, communication and equality,
and is committed to reciprocity, reflexivity and reflection. Thus, both hold the potential to help
reconstruct conditions for a more democratic and just society.
Keywords: Post-colonial theory; action research; colonialism; powerlessness; worthlessness
Introduction
“The collapse of the great European empires; their replacement by the world economic hegemony
of the United States; the steady erosion of the nation state and of traditional geopolitical frontiers,
along with mass global migrations and the creation of so–called multicultural societies; the
intensified exploitation of ethnic groups within the West and ‘peripheral’ societies elsewhere; the
formidable power of the new transnational corporations: all of this has developed spaces since the
1600’s, and with it a veritable revolution in our notions of space, power, language, identity ”
(Eagleton, 1996, 204).
19th century British Prime Minister William Gladstone stated that “justice delayed is justice
denied1: ”His adage contains an unconsidered irony, given Gladstone’s various leadership positions
and appointments within the government of the largest colonizer and dealer of injustice to nonEuropean nations and indigenous peoples world-wide. If his declaration has merit, those who are
committed to the re-dress of wrongs done to citizens under the auspices of colonialism have a difficult
undertaking ahead.
For centuries, indigenous populations have been ‘denied’ justice. The task of addressing wrongs done
during the height of colonization, and its still noxious after-effects, is complex. Hundreds of years have
passed since powerful European nations like Britain, Holland, Spain and France first recognized the
vast wealth of raw materials – people and their knowledge included – untouched and unrecognized for
1
http://en.wikipedia.org/wiki/Justice_delayed_is_justice_denied
1
Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
their economic potential beginning in the 16th century; from their own perspective of Western,
enlightened privilege, those European governments asserted authority, subjugating the “’backward’
and immature” subordinates (Kant, in Dussel, 2000, p. 473), replacing their culture, language,
traditions and right to self-determination with the hegemony of the ‘west’ (Dussel, 2000; Eppert,
2000; Kelbassa, 2008; Smith, 2007).
Post-colonialism theory asks for justice: it seeks to speak to the vast and horrific social and
psychological suffering, exploitation, violence and enslavement done to the powerless victims of
colonization around the world. It challenges the superiority of the dominant Western perspective and
seeks to re-position and empower the marginalized and subordinated “Other” (Smith, p. 12). It
pushes back to resist paternalistic and patriarchal foreign practices that dismiss local thought, culture
and practice as uniformed, “barbarian” and irrational (Dussel, p. 472). It identifies the complicated
process of establishing an identity that is both different from, yet influenced by, the colonist who has
left.
Similar in its goal to eradicate oppression, “powerlessness and worthlessness” (Greenwood and Levin,
2007, p. 31) created by the inequities prevalent during colonization, Action Research, particularly
‘Southern’ Participatory Action Research (PAR), is committed “to affirm solidarity with the oppressed”,
to assist moving the “stakeholders from passive to active” (p. 30) and the “fundamental alteration in
the distribution of power and money” (p. 154). Action research positions the insider or oppressed in
an ethic of efficacy; it values community, relationships, communication and equality, and through its
commitment to “reciprocity, reflexivity and reflection” action research has the potential to help
construct the conditions for a more democratic and just society (Roberson, 2000, p. 309).
The areas of the world most impacted by colonization, Africa, Latin America, Asia, are “miserably
poor”(Greenwood and Levin, 2007, p. 154), and, though they are no longer controlled politically by
foreign powers, the influence of ‘Western’ ideas of ‘how things should be done, for example, Reagan’s
marriage of capitalism, materialism and democracy in the 1980s called "Free Market Democracy,"
were still the 'official' guiding ideological ethos of the United States - at least through the Bush years
(Banks, 2008, p. 57). Greenwood and Levin (2007) note that, “existing public institutions are
distrusted and generally viewed as protectors of an unjust order. The suspect institutions include
schools and universities, churches, governments and governmental agencies, most intergovernmental
development programs, and businesses” (p. 154). Given the role these institutions played
implementing the policies of the colonizer, the distrust is not without merit. Where then does this
leave a nation or nations within nations of people trying to move forward? How impossible and
contested even is the concept “forward” within such hegemony?
Action research, at its core, holds the promise of problematizing uncontested ‘colonial’ hegemonies of
any form. Action research, implemented through the lens of post-colonial theory, offers an answer: as
noted by Susan Noffke, “the local and communitarian processes often embodied in action research
may be enhanced through the use of a wider body of social theory, one that has embraced a social
justice agenda that takes into account both local and global manifestations of oppression” (2009, p.
241).
In her paper “Understanding Development Education Through Action Research,” Sierra Leone born,
Western-educated researcher Yatta Kanu2 describes the research in which she worked to help “bring
about improved teaching practices among teachers from six developing countries” – former colonized
nations – struggling to address “prevalent appalling conditions of teaching and teacher education”
(1997, p. 167-8). As was the policy under colony rule, only those deemed capable of “[supporting] the
colonial administration” received an education (p. 168): the language, values, morals, ethics and
desires of the colonizer were extended to a ‘worthy’ minority, leaving the rest of the population
ignorant, and thus more easily managed (Smith, 2007).
2
Professor, University of Manitoba. BA., Dip.Ed., M. Ed. (Sierra Leone)., Cert. in Curr. Dev.Soc. St. (Leeds, UK), B. Litt.
(Birmingham, UK), Ph.D. (Alberta, Canada)
2
Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
Understandably then, following their liberation, many nations “embarked upon educational expansion
policies” in the hopes that a more educated, literate majority would be better positioned to expedite
their development (Kanu, 1997, p. 168); however, producing a well-trained and effective educator
work-force has been slow to keep up to the demands of an ever-expanding population and an evergrowing awareness of “a complex and changing society” (p. 168). Thus, Kanu and her team, through
the Institute for Educational Development (IED) developed, ran and assessed a teacher education
program. The eighteen-month in-service project sought to work with teachers already considered
qualified and fluent in English. After their teaching practice had been improved, it was expected they
would act as mentors to disseminate the skills, values and knowledge they gained during the project
to their colleagues back home.
Kanu provides three reasons for choosing action research to enable the project, and shares the team’s
post-colonialist aversion to emulating the superior or elite over-lord by mandating or directing the
research process:
“First, the project team members were all educated in the Western tradition and were conscious of
the prevailing disillusionment with development education delivered by outside educators (usually
from the West or educated in the West). The IED itself, resourced by Western-educated reformers,
located amidst the educational context described above and established to institute reform through
educational development, seemed to epitomize the position of expert. Being conscious about this
position of the IED, the team members were cautious with regard to providing prescriptions for
educational problems or posing questions to which they had predetermined answers. It was
thought that through action research the project team could pose initial questions about
development education and then reinterpret and reconstruct these questions where necessary in
order to arrive at the understandings which they were seeking. Second, the team wanted the
project to be run on the basis of collaboration with the teachers and the local community and third,
the team wanted to make the project a learning opportunity for themselves and for the teachers
involved, so that each party could emerge from the action-research process with a deeper selfunderstanding and transformation” (p. 169-70).
Greenwood and Levin (2007) identify a core value of Southern PAR – its “value and [reliance] on the
knowledge, analysis and efforts of local people” (p. 155). The respect shown to the local population’s
knowledge and capabilities may hold the key to creating an empowered identity: as the authors
reveal, a “co-generative dialogue begins that can transform the views of” the researcher and the local
people (p. 155). Already leery of the “unquestionable truths and realities” (p. 170) imposed by the
West, and aware of the “neocolonial 3 tradition” (p. 175), Kanu hoped for the project to create a
“fusion of horizons” where teachers and researchers in the group could co-create new understandings
about effective, quality teaching and student learning (Gadamer, in Kanu, p. 171). Through the
project, she became more aware of her own Western biases – even though she acknowledges herself
as “both a female and African whose country had been subjugated to colonial rule for over a century”
(p. 180) – she struggled with frustration and anger at the participants’ struggles with English
proficiency, ‘rational’ problem solving or producing a critical eye when offered action plans, and their
entrenched socio-cultural way of doing things (1997).
Kanu’s experience exposed her own as-of-yet-unknown cultural conflicts and “ambiguities” (p. 182).
She describes how her doctoral studies introduced her to a vast array of ideas and theories through
which to interpret her liberation and freedom - which she then attempted to use in the IED program.
As she explains, “these [resulting] tensions made me realize that these discourses were ‘working
through’ me in repressive ways to reproduce the same repressive colonial conditions I was trying to
address through development education” (p. 181). Her realization highlights the complicated nature of
individuals and nations attempting to create a new identity once the colonizer has left. What was
original, authentic and ‘true’; and, what is adopted, constructed and ‘false’? And, once the co-opting
3
Neocolonialism: a term used by post-colonial critics of developed countries' involvement in the developing world. Writings
within the theoretical framework of neocolonialism argue that existing or past international economic arrangements created by
former colonial powers were or are used to maintain control of their former colonies and dependencies. The term
neocolonialism can combine a critique of current actual colonialism (where some states continue administrating foreign
territories and their populations in violation of United Nations resolutions) and a critique of the involvement of modern capitalist
businesses in nations which were former colonies.
3
Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
of the foreign identity has occurred, how does one un-learn and reclaim the real self? These are
essential questions Canadian educators confront when working to engage First Nation, Métis and Inuit
(FNMI) peoples; the atrocities4 done to indigenous populations – including forced attendance at
Residential Schools in order to “kill the Indian in the child” 5 – has created a third world legacy within
Canada’s First Nation population:
“The incidence of tuberculosis and diabetes among First Nations is three times that of the broader
population. First Nations housing conditions are below acceptable standards for 65% of on-reserve
households and 49% of off-reserve households. The figure for the non-First Nations population is
30%. Incarceration rates in federal and provincial jails in 1995-96 were at least five times greater
for First Nation versus non-First Nations individuals. Suicide rates are 2.5 times higher among First
Nations than the broader population. Homicide rates are six times higher than in the broader
population” (The Cost of Doing Nothing: A Call to Action, 1997).
Post-colonial theory and action research ethics demand we work to excavate all that was lost ancestral traditions, languages, history, culture and religion - and restore honor and status to that
which was stolen in order to address what must be regained and re-learned, and how that will occur.
Education holds a key to lifting FNMI peoples out of poverty (& thus improving prosperity for all
Canadians) by providing access to further education 6 and training – as well as creating a future
society that recognizes and esteems the diversity created by inclusion; however, this means inclusive
education, relevant and meaningful to FNMI learners, which acknowledges the different kinds of
knowledge, knowing traditions and ways of being that are part of indigenous cultures.
In the past two decades, leading post-colonial theorists Edward Said7, Homi K. Bhabha8 and Gayatri
Chakravorty Spivak9 have sought to detangle these complicated questions in the hopes of ‘decolonizing’ the future. Their various contributions to this discourse compel educators to listen and
critically reflect on the ongoing, often innocuous acts of inequity, stereotypes, oppression and
exclusion we still carry out in classrooms. How, through our selection of texts, through our
recollections of history, through our viewing of other cultures, through the ways we esteem, privilege
and construct certain kinds of knowledge are we continuing the myth of inferior worlds, inferior races
and inferior ways of being? How do we honor the wisdom and knowledge of oppressed peoples
without further exploitation?
Following his study of the Oromo oral traditions in Ethiopia, researcher Workineh Kelbessa (2008)
concludes, “the critical appropriation and implementation of indigenous values and practices is a
necessary condition for solving [all] environmental, social, economic, and political problems” (p. 304).
4
There were over 2.5 million First Nations people prior to colonization. Now there are about 800,000 according to 2009 census
figures.
5
Residential and Industrial Schools were established in locations across Canada, predominantly in Western Canada for the
purpose of “killing the Indian in the child.” Over 150,000 children attended these residential schools up to 1973.
http://www.afn.ca/article.asp?id=2586
6
The cost of incarcerating and individual for one year: $100,000.00 VS post-secondary education, roughly $13,200.00 per
student (funded through the Federal Post Secondary Education program for First Nation students).
http://www.afn.ca/cmslib/general/mfnps.pd
7
Palestinian born, Said is most famous for describing and critiquing "Orientalism", which he perceived as a constellation of false
assumptions underlying Western attitudes toward the East. Said concluded that Western writings about the Orient depict it as
an irrational, weak, feminized "Other", contrasted with the rational, strong, masculine West, a contrast he suggests derives
from the need to create "difference" between West and East that can be attributed to immutable "essences" in the Oriental
make-up.
8
Bhabha is an Indian critical theorist. One of Bhabha’s central ideas is that of "hybridization," which, taking up from Edward
Said's work, describes the emergence of new cultural forms from multiculturalism. Instead of seeing colonialism as something
locked in the past, Bhabha shows how its histories and cultures constantly intrude on the present, demanding that we
transform our understanding of cross-cultural relations. His work transformed the study of colonialism by applying poststructuralist methodologies to colonial texts.
9
Self-described "practical Marxist-feminist-deconstructionist," she is best known for the article "Can the Subaltern Speak?",
considered a founding text of post-colonialism, and for her translation of Jacques Derrida's Of Grammatology. Spivak is perhaps
best known for political use of contemporary cultural and critical theories to challenge the legacy of colonialism on the way
readers engage with literature and culture. She often focuses on the cultural texts of those who are marginalized by dominant
western culture: the new immigrant, the working class, women and the "postcolonial subject."
4
Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
There is an Italian proverb: Once the game is over, the king and the pawn go back in the same box.
For too long, subjugated peoples have been used as pawns in ambitions of the powerful and elite. As
our global fates become more entwined, we will be challenged to address increasingly complex global
issues.
Educational institutions, teachers, and educational researchers play pivotal roles in addressing those
issues. The dominance of the Western perspective has deeply entrenched hierarchical structures and
power positions. But these have little relevance in schools whose goals are to create collaborative,
equalitarian, and thoughtful world citizens able to embrace diversity, challenge injustice, think
globally, and value a variety of way of being and knowing. Kurt Lewin, considered the father of ‘action
research,’ emigrated with his wife and children to the U.S. in 1933, in response to growing AntiSemitism in Germany. Sadly, his mother and other family members remained behind, and were
murdered by the Nazis. Shaped by his own experiences with a powerful nation’s goals of empire,
Lewin offers this insight from the past that may provide a perspective for the future:
“[I]t is not similarity or dissimilarity of individuals that constitutes a group, but rather
interdependence of fate. Any normal group, and certainly any development and organized one
contains and should contain individuals of very different character…What is more, a person who
has learned to see how much his own fate depends upon the fate of his entire group will be ready
and even eager to take over a fair share of responsibility for its welfare.” (1948, p. 165-6).
Post-colonial theory – committed to addressing the plague of colonialism - coupled with the dialogic,
critically reflective, and collaborative values of action research offers a portal to “the full range of
human wisdom [essential for] the health of our planet and its inhabitants” (Kelbessa, p. 305). For too
long, the voices of those whose lives were, and continue to be, impacted by colonialism have not been
attended to well enough in schools. Educators, more than any other professional, must be positioned
to address, reflect, and create spaces where action research processes, focused through a postcolonial lens, can illuminate lingering biases and stereotypes, and where racism and ignorance can be
analyzed challenged, and ultimately eliminated.
References
Assembly of First Nations – Residential Schools – A Chronology. Retrieved January 15, 2011, from
http://www.afn.ca/article.asp?id=2586
Banks, R. (2008) Dreaming up America. New York: Seven Stories Press.
Dussel, E. (2000). Europe, modernity, and eurocentrism. Nepantla: View from South, 1(3), 465-478.
Duke University Press.
Eagleton, T. (1996). Literary theory: An Introduction (2nd ed.). Minneapolis: The University of
Minnesota Press.
Edward Wadie Said. Retrieved November 9, 2010, from http://en.wikipedia.org/wiki/Edward_Said
Eppert, C. (2000). Relearning questions: Responding to the ethical address of past and present
others. In R. Simon, S, Rosenberg, & C. Eppert (Eds.), Between hope and despair: Pedagogy
and the remembrance of historical trauma. Lanham, MD: Rowman and Littlefield.
Gayatri Chakravorty Spivak. Retrieved October 28, 2010, from
http://en.wikipedia.org/wiki/Gayatri_Spivak
Greenwood, D.,& Levin, M. (2007). Introduction to action research (2nd ed.). Thousand Oaks, CA:
Sage.
Homi Bhabha. Retrieved October 26, 2010, from http://en.wikipedia.org/wiki/Homi_K._Bhabha
5
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Kanu, Y. (1997). Understanding development education through action research: Cross-cultural
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Peter Lang.
Kelbessa, W. (2008). Oral traditions, African philosophical methods, and their contributions to
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purposes: A conversations among cultures. University of Hawaii Press.
Lewin, K. (1948) Resolving social conflicts; selected papers on group dynamics. In G. W. Lewin (Ed.).
New York: Harper & Row.
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Education: Access, opportunity and outcomes. The First Nations Post-Secondary Education:
Access, Opportunity and Outcomes Panel. Assembly of First Nations. Retrieved October 11,
2010, from http://www.afn.ca/cmslib/general/mfnps.pdf
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Noffke, S. (2009). Revisiting the professional, personal, and political dimensions of action research. In
S. Noffke, & B. Somekh (Eds.), The SAGE handbook of educational action research, 6-23,
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from http://www.afn.ca/cmslib/general/mfnps.pdf
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Collaborative Action Research: Teaching of Multiplication and
Division in the Second Grade
Eda Vula
University of Prishtina, Kosovo
[email protected]
Lirika Berdynaj
Mileniumi i Tretë Primary School, Kosovo
[email protected]
Abstract
This paper discusses the impact of action research methodology used in the teaching and learning
process and professional teacher development. In this study are including 58 students of three
second grade classes, 3 teachers of those classes and a university professor. Aiming at using a
different approach in their teaching of multiplication and division in the second grade, all three
teachers agreed to cooperate and jointly plan the learning activities, to observe systematically their
students and to reflect on the outcomes. This way of research doing in their classes enabled them
to ‘act’ effectively in designing an action plan appropriate to students’ achievement level. This
research was carried out in the period of February 18 to May 31 incorporating several different
methods, such as classroom observation, interviewing and worksheets.
Keywords: Action research; multiplication; division; sharing/partitive; grouping/quotative
Introduction
The four fundamental operations – addition, subtraction, multiplication and division, and their
relations are basic mathematical concepts to be taught at primary education level. Acquisition of those
four concepts and their relations enables students to develop their understanding for ‘numbers and
calculating strategies’ as well as associating them with daily life problems. In the curriculum of
Kosova’s primary education (MASHT, 2004), multiplication and division are presented for the first time
in the second grade. According to this curriculum, second graders learn the meaning of multiplication
as repeated addition, and division as an inverse operation of multiplication ( finding a factor, when the
product and the other factor are known). As in most traditionally programs, these concepts taught
separately with multiplication preceding division. The teaching is very similar in most classes. Each
teacher is quite rigorously based on school math textbooks. They use them for preparing the lesson,
class organization and as resource for students work. Traditionally, for the first 10 weeks of the
second term, in all schools, students learn the ‘multiplication table’ and after that they start with
division (as inverse of multiplication).
Lirika, is a primary school teacher at “Mileniumi i Tretë”, which was listed by an external evaluation as
achieving the best results in mathematics, compared to other schools within the same municipality.
This evaluation was carried out in all fifth grade 10 classes. The evaluation also concluded that there
are still some obstacles related to the application of multiplication and division operations by students.
Lirika was concerned with these results and had her dilemmas: Should multiplication and division be
taught separately and does memorizing the table of multiplication help children understand division
concepts? Are the examples in the textbook related with different division situations? Is it possible for
students to understand the division concepts only as the inverse of multiplication? How can I better
teach these concepts? Thus, Lirika carefully analyzed the existing curriculum and relevant practices in
other countries, including the literature related to math teaching at primary education levels. She
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MASHT (NjVS-Testi i kl.V - 2009)
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found that, there are many arguments that multiplication and division are closely connected to the
lesson plan, and they should be taught jointly (Greer, 1992; Carpenter et.al., 1999; Van de Wale,
2004). Mulligan and Michelmore (1997), in a longitudinal study of Grade 2 and 3 students, found that
students possessed several intuitive models for division when faced with word problems. They defined
these models as “internal mental structures corresponding to a class of calculation strategies” (p.
325). So, students should solve problems using their strategies and should be able to explain what
they did with numbers, words or drawings.
Firstly, Lirika decided to consult two of her teacher colleagues (Miranda and Shqiponja), who work at
the same school as she does, then the school principal, and afterwards she invited the instructor
(author) from the Faculty of Education to discuss her dilemmas. After some meetings, an action plan
was designed, and a decision was made to carry out an action research related to the teaching of
multiplication and division concepts.
The aim of this study is the assessing of the student’s ways of experiencing word problems in different
situations. Also, this study assesses how students make a conceptual connection between
multiplication and division and develop the reasoning skills. The study was carried out within the
action research methodology.
Literature review
What is Action Research?
“Action research is any systematic inquiry conducted by teacher researchers to gather information
about the ways that their particular school operates how they teach, and how well their students
learn. The information is gathered with the goals of gaining insight, developing reflective practice,
effecting positive changes in the school environment and on educational practices in general, and
improving student outcomes" (Mills, 2003, p.4). Often an action research is considered as a
collaborative activity and focuses on the co-creation of knowledge about practices. It is an appropriate
methodology since it enables teachers to get involved in joint practical activities, to make changes to
their practice and to examine their own teaching and students’ learning through descriptive reporting,
purposeful conversation, colleagual sharing, and critical reflection for the purpose of improving
classroom practice (Miller and Pine, 1990; Wilson, 2009; Mcniff and Whitehead (2010); Koshy, 2010).
According to Kemmis and Taggart (2000), action research is represented through spiral cycles, which
are repeated. Every cycle is constituted of four stages as following: Planning- planning a change;
Acting and observing the process and consequences of the change, reflecting on those processes and
consequences and then re-planning the change. Action research is considered as a form of “applied”
research, which not only serves for the professional teacher development, but also for increasing the
performance of the school and education in general.
The collaborative action research is the joint research between two or more teachers or between
universities and teachers. They collaborate and influence in changing the curricular approach, and
their main focus is on practical problems of individual teachers or schools. This collaboration between
universities and schools may foster communication and mutual respect (Raymond, 2004).
At the very beginning of this research, we introduced the issue of using different approaches related
to teaching of multiplication and division in the second grade of primary school. Collaborative action
research has directly influenced the application of these new approaches in classroom. This
methodology enabled us to find out more appropriate ways of teaching aimed at acquisition of basic
mathematical concepts through the spiral cycles of collaborative planning, acting and reflecting.
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Research Related to Early Teaching and Learning of Multiplication and Division
Several researchers have studied how young students multiply and divide. Nunes and Bryant (1996)
indicated that a general point of view about multiplication and division is that they simply “are inverse
arithmetical operations ... that are taught after addition and subtraction” (p. 144). However, they
stress that such a viewpoint is incomplete knowing the fact that “multiplication and division represent
a significant qualitative change in children’s thinking” (p. 144).
The first confrontation of students with multiplication is usually accompanied with situations that
include sets with equal number of objects Greer (1992). Although there are other models available
that represent multiplication, the model of equal sets (repeated addition) is known as a basic intuitive
model for multiplication. A challenge in this situation is the child’s reflection on the ‘set’ as a unit and
the addition of those ‘units’. In such a case, different expressions are used, such as ‘3 times 5’, 3
multiplied with 5’ or ‘3 with 5 each’. In their study, Gray and Tall (1994) noted that some children are
not able to apply repeated addition to find out the product of two numbers. Thus, for instance, they
can add 5+5=10, but then they continue to count 11, 12,..15 in order to get to know how much is
3x5. Consequently, a precondition to teach children how to multiply is to teach them first to do
repeated addition. Since multiplication is the addition of ‘many times’ of equal sets, the initial thinking
of children related to division is connected to the division of a set of objects in equal portions.
Fischbein, et al (1985) discussed two models of division used when either number of portions or the
number of items in each portion is known. These are generally known as … division through
partitioning (sharing out), partitive division and division by ‘chunking’ (grouping), quotitive division.
According to the model through ‘partitioning’, the general number of objects represents the dividend,
while the divisor represents the total of partitioned parts. For instance, three children should share 6
apples; how many apples each of them will receive? (6:3). Apples are related to the dividend, while
the divisor is related to the children. According the model through grouping, the problem is
formulated as following: How many children will receive 3 apples if there are 6 apples in total? (6:3)
(in this case both the dividend and the divisor are the apples). According to the research, the initial
intuitive model used to develop the concept of division is that of ‘partitioning’, while as a result of
teaching the other mode is developed, i.e. through ‘grouping’ (Fischbein, et al.(1985); Mulligan
(1992); Murray, et al. (1992); Kouba (1989)). However, there is often misunderstanding when these
two models are discussed. In the first model, the dividend (3) represents the number of ‘children’;
while in the second model the number (3) represents the ‘apples’. From the child’s perspective,
division situations are often related to the division expression (6:3) rather than the situation itself.
Therefore, it is important to pay particular attention if the child is experiencing such differences, i.e. if
they understand that number 3 has a different meaning in the division through grouping and another
one in the division by partitioning. From research related to these two concepts, we come to the idea
that considering multiplication as (always) increasing numbers, while division as inverse operations
that (always) decrease numbers and that a smaller number cannot be divided with a big number are
wrong ideas (Kouba (1989); Arighileri (1989)). Therefore, understanding multiplication and division as
a repeated addition and subtraction represents a future challenge. On the other hand, word problems
not only serve as a basis for understanding children’s strategies for solving addition, subtraction,
multiplication, and division problems, they also can provide a unifying framework for thinking about
problem solving in their daily life (Carpenter et.al., 1999). Children’s thinking and their reasoning are
important parts of the problem solving process (Barmby, (2009). Using practical experiences of
children themselves and linking those with informal calculation strategies helps children count easier
and clearly see the connections between the concepts and their application in problems solving.
Method
Aim and Research Questions
The aim of this study was to investigate the ways of teaching and learning activities which enable
students to use their experiences, consider different ways of calculation and justify word problem
solving related to multiplication and division.
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The main research question was formulated:
What is the effect of using the word problem solving in the understanding of division, through
sharing/partitive situations and grouping/quotitive situations and their relations to
multiplication?
So this research contributes to the understanding of how action research may serve as a ‘tool’ for
teaching activity and assessing the impact of word problem solving to ensure a better understanding
of basic mathematical concepts and their application in problem solving.
School Context and Participants
This research is carried out in a non-public funded school called “Third Millennium” which has a
student population of 527 and 55 teachers. There are three second grade classrooms with 58 students
were the teacher are, Lirika, Miranda and Shqiponja. Lirika graduated as a primary teacher in the
Faculty of Education three years ago. Miranda graduated in the same faculty, five years ago and she
is working in her Master Theses on school management. Shqiponja graduated in the Higher
Pedagogical School and she has a six year experience in teaching. She also finished some in-service
teacher courses. This school closely cooperates with the staff of Faculty of Education - University of
Prishtina. Thus, Lirika invited me (author) as a staff member of the Faculty of Education to discuss her
dilemmas about teaching of multiplication and division in her class. Together, I and Lirika, engaged in
this joint effort as co-researchers. The data collection and all activities were carried out in Lirika’s
classroom during the second term with twenty students (7-8 years old). In that school, the teaching
and learning process , from first to fifth grade develops mostly according to the philosophy of the
‘Step by step’ program11. According to this philosophy, interactive teaching and the integration of
different subjects have a primary role. At the beginning of the day, known as the morning meeting,
usually teachers work with the entire classroom where the daily plan is presented. Then, the work is
carried out in different learning centers. I took part three times per week, usually when children were
learning in the mathematics center. Teacher Miranda and Shqiponja also took part in this research.
They collaborated with us and carried out the same activities in their classrooms. Also, the school
vice-principal and parents were informed about this study.
Research Design
Action research was used in this study. At the beginning, we carried out a plan for action research in
order to explore the word problem as part of ‘curriculum’ during the teaching and learning of
multiplication and division. First, it was compared with the learning outcomes for multiplication and
division in the Mathematics Curriculum 12 with the math textbook’s content for second grade. Then we
designed the action stages:
First, planning and selecting appropriate teaching/learning materials, examples and methods for
representing mathematical ideas related to multiplication and division were developed. The
mathematics learning center was designed to be an activity-based center providing the students with
many opportunities to solve different problem situations. Secondly , interpreting and evaluating the
students’ mathematical solutions, their arguments or representations (verbal or written, drawing or
modeling), including misconceptions. Also, in this stage, we diagnosed the students achievements,
strengths and weaknesses. Because it was a practical research, after reflecting we reassessed the
activities and adapted the tasks for different student needs. Different assessment instruments were
used to collect data, including: classroom observation, interviewing, and worksheets. The research
took place during the second term, three times per week.
In the beginning, I was a passive observer during Lirika’s teaching. I observed how she interacted
with students, discussed with them and how students discussed among themselves. But when
students were working in groups or individually, we both interacted with them. In these cases we
used the interviewing which was videotaped or registered as notes in our notebooks. Transcribed
11
12
The ‘Step by step’ program, http://www.kec-ks.org.
MASHT (2004)
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materials were then analyzed by us. Worksheets were used as data in order to analyze and assess the
students reasoning in their problem solutions.
The triangulation technique was used for the validation of this study (Mcniff, at al, 2010). There were
different gathering data methods, and the analyses were done from both of us, sometimes together
and sometimes separately. Two other teachers and the vice-principal helped us validate our work
through the whole process. They were our ‘critical friends’ and we established trusting relationships
which became the grounds for giving and receiving critique (Mcniff and Whitehead, 2010).
Findings and Interpretations
The presentation of the results is divided into three sections. First, we were interested to observe and
analyze how students experienced the computation with multiplication and formal division. Formal
division here means ‘division as the inverse of multiplication’ as it is in the existing mathematics
curriculum13. We analyzed the teacher’s instruction and students work in their student’s textbook. The
second section is related with different strategies that students use to explain their reasoning on word
problem solving related with multiplication, and the third section concerns the division through
sharing/partitive situations and grouping/quotitive situations. The findings of the above sections are
included as cases. They are based on classroom observations and student work during the different
periods.
Case 1
This is a whole class situation in the ‘Morning meeting’ where teacher Lirika, expands the daily
objectives. She starts with a problem that she takes from math textbook for secondary grade (p.109).
Afterwards, she picks out 12 counters from a box and asks three children to come to the board. The
teacher than shares out the counters in a ‘one for each of them’ order and when the counters are
shared out, the three children count their counters and then saw that they have four each. She writes
in the table, 12:3=4 and explains how it relates with multiplication 4x3=12. She presented another
example from the textbook: Four friends equally share 24 candies. How many candies each of them
have? The students discussed that the answer is related with multiplication and in that case, answer is
6 because 4x6=24.
Thus, it was supposed that students understand the division as ‘sharing equally’ and as the inverse
operation of multiplication. After this situation, the teacher invited children to work in their learning
centers, where they have to solve problems in their student’s textbook (p.80).
We observed students how they ‘filled’ their worksheet. Most of them just memorized the
multiplication table …and used the calculation (in their mind or using the counters or other things that
they had in their learning centers).
Case 2
Here the teacher prepared the supplement worksheet, with three word problems. The reason was: did
the students know to relate the ‘situations’ with multiplication? In this context, students were required
to solve the three problems related to daily life and afterwards we analyzed their solutions and
reasoning. Below we present one of the analyzed problems.
It is shown in the Figure 1, that a student has used a drawing to solve the problem: On the table
there are 5 plates with 7 biscuits each. How many biscuits are altogether? A student explaining his
correct answer based in his ‘drawing’.
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MASHT 2004
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Figure 1. Using Drawing to Solve Problem
Not always students relate their ‘modeling’ with the context in the correct way. A student, used the
same presentation, but he didn’t show correctly the relation between the context and the drawing
(Figure 2). For this student it is unclear what does the number 5 means. He just draws some circles
(biscuits) and plates without numbering them.
Figure 2. Uncorrected Relation between ‘Drawing’ and ‘Context’
In this example, we found that all students wrote the correct answer, except one. Nine students had
correct results without reasoning, 5 of them used drawings, 2 of them had correct answers but they
presented their drawing incorrect, 2 students used arraying and 2 students used repeated addition (by
7).
Case 3
As in the above example, we found that most of the second grade students relate their drawing with
the context. To find the solution of the problem: Four girls eat 8 apples equally. How many apples
each of them eat? Most students draw the girls and apples (Figure 3).
Figure 3. A Student’s Solution Using Drawing Related with Context.
In this problem, the dividend concerns apples and the divisor girls. So it is related with partitive
division, so ‘sharing equally’ and drawing was used from most of students. There were 7 of them, who
wrote only the correct answer.
It seemed that it was difficult for some of second graders to write the correct reasoning of problem
solving. Not always students relate their solution with correct representations. Below, in the Figure 4
is shown a student’s solution of this problem: In the second grade there are 48 students. If they have
to divide in 6 clubs, how many students are in each club? Even though the result is correct, the
student misunderstands what ‘sharing equally’means. The student considered the procedure ‘ finding a
factor, when the product and the other factor are known’ ( she memorized) and fund the correct
solution, but it wasn’t important for her if there are 8 or more circles in each set (which in this case
represent the students and clubs).
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
Figure 4. A Student’s Solution with Not Correct Reasoning
From the analysis of the student’s solutions, we see that the reasoning of most of them were the
same (48:6=8 because 6x8=48). Some of them just memorized the multiplication table, and the
others used the ‘drawing’ model in the correct way.
During the textbooks analysis, we didn’t find any problem related with measurement or quotative
problems. Thus we prepared some additional problems to understand how children think and use their
strategy to solve division problems (by grouping). Here is an example:
Era has 28 balls and some boxes. She places four balls in each box. How many boxes did Era
fill?
This problem seems to be harder. It was not a ‘routine-problem’, so there was some uncertainty. We
understood from analyses that some students didn’t understand yet how to connect the situations
with the dividend, divisor and multiplier (Figure 5). They do the computations, whenever they find
numbers and don’t worry about the ‘context. However, from our observing, them who relate the
counting and adding strategy with ‘drawing’ seem to have no problem to connect ‘situations’ with
division (Figure 6).
Figure 5. A student’s Wrong Representation
Figure 6. A student who uses the
counting and adding strategy and then
presents it with a drawing
Adapted Plan
After analyzing the students work, we decided to prepare the ‘treatment plan’ for students who had
difficulties understanding the relation between the ‘concepts’ and the problem situations. This plan
was discussed with the two other teachers too. It was decided to use student interviewing during the
problem solving process. So, the supplement worksheets with more illustrations and figures were
prepared. They were considered as necessary material for students. For two weeks, teachers worked
after regular classes with the identified students in need using individual interviews. All interviews
started with similar initial questions, but the follow-up questions depended on the answers that were
given. During this process, cubes, counters, and other objects available in the classroom were used,
including paper and pencil to take notes. Students were encouraged to freely talk, write and draw. It
was required to explain their way of thinking in their solutions. In the same way, teacher Miranda and
teacher Shqiponja interviewed their students. Everything that students said and did was registered
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and then discussed with me in order to analyses and evaluate two aspects of the use of multiplication
and division – as operations for calculation and, as operations to solve problems in different situations.
Discussion
The first steps toward engaging in collaborative action research in the mathematics classroom are vital
in establishing quality research projects, designed and implemented jointly by classroom teachers and
universities (Raymond (2004). This collaborative research helps us not only to engage in the
classroom inquiry, but as practical research it contributes to improve teaching and student
achievements. The variation of ways in which young students experience word problems has been the
focus of this research. The findings illustrate that even students of the same age, have different
experiences and capabilities in solving mathematical problems. The drawings and notations made by
children in this study illustrate the process of gradual generalisation, from concrete details to
abstraction. Van de Wale, suggested that multiplication and division activities should begin with
models before word problems (Van de Wale, 2004). So, in Case 1,‘sharing equally‘ shown by the
teacher’s demonstration was the first confrontation of students with division and the basis for the
development of initial concepts related to multiplications and divisions (Greer , 1992; Carpenter at.al,
1999). Also, other intuitive strategies were used, as repeated addition of equal sets, or ‘modeling’.
‘Modeling’ here means, using concrete materials to help the problem solving. Thus, during this case,
we concluded that the demonstration of repeated addition with two, with five, with six,… and so on,
does not present difficulties if addition operations are excellently acquired. Because, textbooks 14 have
most of the examples with ‘calculation’ it was a routine for students to solve most of them in the same
way, using only memorization. However, using only calculation skills and ‘routine models’ isn’t
sufficient to understand what the factor and product mean. Even though there were no perceiveable
mistakes in the textbook pages ‘filled’ by students, it doesn’t mean that they understand what each of
the ‘numbers’ represents in the problems that were presented in the Case 2.
“Today, mathematics is not about computation, especially pencil-and-paper computation.
Mathematics is about reasoning and patterns and making sense of things. Mathematics is problem
solving” (Van de Walle, 2004, p.176). Using practical examples and word problems enables children
not only to improve their calculation skills, but also to understand the meaning of ‘size’ presented
through those problems, which is very important for the development of the division concept in
children (Fischbein at al., 1985; Mulligan, 1992; Gray and Tall, 1994). However, Vergnaud (1983)
stated that multiplication, multipliers and product present different links of the ‘factors’ to the
problems of division. According to this research, initial intuitive models were used to develop the
concept of division as ‘sharing equally’, while as a result of teaching, other models were developed,
i.e. through ‘grouping’ (Fischbein, et al.,1985; Mulligan, 1992; Murray, et al., 1992; Kouba, 1989).
“Teaching activities for multiplication and division need to give young learners the opportunity to
explore different representations of multiplications and division and to reason about connections
between these” (Barmby, 2009, p.60). In Case 3, additional problems were presented, regarding
quotative division problems. In general, connecting the situations with the dividend, divisor and
multiplier may cause problems in most cases (Neuman, 1999). But, providing children the opportunity
to solve not only routine problems is the best way to help them construct the procedures for
calculations.
Undoubtedly, individual interviews with students significantly contributed to the analysis of their
knowledge and identification of their obstacles in the learning process. Children develop their
understanding by constructing relationships, and in order to understand they must speak something
and be able to comprehend the relationships (Carpenter et.al., 1999, p.53). So, the ‘treatment
process’ as part of action research methodology impacted directly the improvement of the student’s
ability to understand multiplication and division as inverse concepts and to solve different problems.
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Conclusion
The process of collaboratively working toward the problems solving not only provides a wide range of
expertise, but also generates positive working relationships. So, using collaborative research in this
study is considered as a very useful educational resource. The planning, interpretation, evaluation,
and afterwards the adapted plan can provide useful resources for the improvement of student’s
abilities and skills. This collaborative research suggest that using different teaching and learning
resources, appropriate activities and managing individual interventions in math learning centers
/classes helps students construct and develop the basic concepts. Also, this study suggests teachers
to teach multiplication and division not as separate concepts but jointly. Also, it suggests teachers to
use word problems as tools for concept understanding. They should engage their students in solving
and explaining their problem solving strategies, and not to get them textbook ‘to do pages’. Teachers
should look on the textbook as a teaching resource and not as object of instruction.
Limitations of the Study
Because the research was carried out in a private school where in each classrom there is an avaregae
of twenty students, and students stay at school during the whole day, the major limitation of the
study is the generalization of its conclusions for other schools, where the student number in
classrooms is larger than 30 and math classes run for 40 -45 minutes.
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
Preservice Secondary Mathematics Teachers’
Knowledge of Students
Hülya Kılıç
Yeditepe University, Turkey
[email protected]
Abstract
The aim of this paper is to present the nature of preservice secondary mathematics teachers’
knowledge of students as emerged from a study investigating the development of their pedagogical
content knowledge in a methods course and its associated field experience. Six preservice teachers
participated in the study and the data were collected in the forms of observations, interviews and
written documents. Knowledge of students is defined as teachers’ knowledge of what mathematical
concepts are difficult for students to grasp, which concepts students typically have misconceptions
about, possible sources of students’ errors, and how to eliminate those difficulties and
misconceptions. The findings revealed that preservice teachers had difficulty in both identifying the
source of students’ misconceptions, and errors and generating effective ways different than telling
the rules or procedures to eliminate such misconceptions. Furthermore, preservice teachers’
knowledge of students was intertwined with their knowledge of subject matter and knowledge of
pedagogy. They neither had strong conceptual knowledge of mathematics nor rich repertoire of
teaching strategies. Therefore, they frequently failed to recognize what conceptual knowledge the
students were lacking and inclined to address students’ errors by telling how to carry out the
procedure or apply the rule to solve the given problem correctly.
Keywords: Knowledge of students; pedagogical content knowledge; mathematics; preservice
teachers
Introduction
Preservice secondary mathematics teachers deal with different aspects of learning, teaching, and
curricular issues in their teacher education programs. Teacher education programs provide several
content, general pedagogy, and content-specific methods courses to support the development of
professional knowledge for teaching. In these courses, preservice teachers are expected to construct
and improve different knowledge domains for effective teaching.
Unquestionably, having strong subject matter knowledge is essential to becoming a teacher but it is
not sufficient for effective teaching (Ball & Bass, 2000; Borko & Putnam, 1996). Teachers should know
how to teach a particular mathematical concept to particular students, how to represent a particular
mathematical idea, how to respond to students’ questions, and what curriculum materials and tasks to
use to engage students in a new topic. Shulman (1986) used the term pedagogical content knowledge
to name a special knowledge base that involves interweaving such various knowledge and skills. He
stated that pedagogical content knowledge (PCK) includes teachers’ knowledge of representations,
analogies, examples, and demonstrations to make a subject matter comprehensible to students. It
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
involves knowledge of specific topics that might be easy or difficult for students and possible
conceptions or misconceptions that student might have related to the topic.
Although many scholars agree upon the existence of PCK as a distinct knowledge domain (Brown &
Borko, 1992), there are different views about what constitutes it (e.g., Gess-Newsome, 1999;
Grossman, 1990; Hill, Ball, & Schilling, 2008; Marks, 1990). Because PCK is perceived as knowledge of
how to teach a particular subject matter (An, Kulm, & Wu, 2004), knowledge of subject matter and
knowledge of pedagogy is not enough to achieve effective teaching practices without knowing the
students, curriculum, educational goals, and instructional materials. In most studies, knowledge of
subject matter, knowledge of pedagogy, knowledge of students, and knowledge of curriculum are
accepted to be the components of PCK (e.g., An, Kulm, & Wu, 2004; Marks, 1990; Morine-Dershimer
& Kent, 1999). Teachers need to know personal and intellectual characteristics of a particular group of
students, and their conceptions and misconceptions about a particular topic that will be taught. Then
teachers should tailor their lesson in a way that address students’ needs and their difficulties in
understanding the subject matter and eliminate their misconceptions effectively. They also need to
know the arrangement of the topics within a particular grade level and between grade levels, and how
to use curriculum materials to achieve the learning goals identified in the written curriculum.
Therefore, not only knowledge of subject matter and knowledge of pedagogy but also knowledge of
students and knowledge of curriculum are essential components of PCK (Ball, Thames, & Phelps,
2008; Park & Oliver, 2008).
Pedagogical content knowledge is assumed to be developed as teachers gain more experience in
teaching because it is directly related to act of teaching (Borko & Putnam, 1996). However, studies of
preservice mathematics teachers’ knowledge and skills related to teaching have revealed that methods
courses and field experiences are likely to contribute to the development of PCK to some extent (Ball,
1991; Ebby, 2000; Graeber, 1999; Grossman, 1990; Tirosh, 2000; van der Valk & Broekman, 1999;
van Driel, de Jong, & Verloop, 2002). Although there is no widely accepted standardized instrument
specifically developed to measure teachers’ PCK or the development of their PCK, researchers could
learn about the nature of teachers’ PCK by using different methods such as classroom observations,
structured interviews, questionnaires, and journals (e.g., An, Kulm, & Wu, 2004; Even & Tirosh, 1995;
Foss & Kleinsasser, 1996; Grossman, 1990; Marks, 1990). In other cases, workshops for inservice
teachers could be designed with an intention of raising their awareness about the level of their PCK
and improving their PCK through various practice (e.g., Barnett, 1991; Clermont, Krajcik, & Borko,
1993; Hill & Ball, 2004; van Driel, Verloop, & de Vos, 1998) or a methods course for mathematics
teachers could be designed in a way that preservice teachers would have various opportunities such
as analyzing students’ error, developing a task, and microteaching to improve their PCK (e.g., Ball,
1988; Ebby, 2000; Graeber, 1999; Kinach, 2002; Tirosh, 2000). Therefore, I aimed to investigate
what components of preservice secondary mathematics teachers’ PCK developed in a secondary
mathematics methods course and its associated field experiences. However, in this paper, I will
discuss the findings about the nature of one of the components, namely knowledge of students and
how it was influenced by the other components of PCK. Because of the space limitation, I will only
discuss the findings obtained from interview data.
Knowledge of Students
Knowledge of students is generally defined as knowing about the characteristics of a certain group of
students and establishing a classroom environment and planning instruction accordingly to meet the
needs of these students (Fennema & Franke, 1992). Shulman (1987) stated that teachers should
know their subject matter thoroughly and be aware of the process of learning in order to understand
what a student understands and what is difficult for them to grasp. Then, they need to develop a
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
repertoire of effective ways of teaching a particular subject, assessing students’ understanding, and
addressing their difficulties. Furthermore, An, Kulm, and Wu (2004) identified four aspects of PCK of
students’ thinking. These aspects are 1) building on student ideas in mathematics, 2) addressing
students’ misconceptions, 3) engaging students in mathematics learning, and 4) promoting student
thinking about mathematics. They noted that teachers need to relate students’ prior knowledge with
new knowledge through various representations, examples, and manipulatives and focus on students’
conceptual understanding rather than procedures or rules. Teachers also need to identify students’
misconceptions correctly and eliminate such misconceptions by probing questions or using appropriate
tasks.
In fact, teachers not only need to be able to help students when mistakes arise but also need to craft
their lesson plans to either avoid or deliberately elicit common student errors. Moreover, teachers
need to be able to determine the source of students’ difficulties and errors in order to correct them
effectively. For instance, a student’s difficulty in solving a geometry problem might not necessarily be
due to not knowing the geometric concept but may be due to a lack of arithmetic or algebraic skills.
The studies on teachers’ knowledge of students have shown that beginning teachers lack knowledge
of students’ mathematical thinking (Fennema & Franke, 1992; Morris, Hiebert, & Spitzer, 2009; van
Dooren, Verschaffel, & Onghena, 2002). They do not know much about what problems students may
encounter when learning a specific topic. Moreover, they do not have a rich repertoire of strategies for
presenting the material in a way that facilitates students’ understanding or for eliminating students’
misconceptions effectively.
Furthermore, teachers’ own knowledge influences their efforts to help students learn (e.g., Ball &
McDiarmid, 1990; Even & Tirosh, 1995; Grossman, 1990; Morris, Hiebert, & Spitzer, 2009; van
Dooren, Verschaffel, & Onghena, 2002). Teaching is not just delivering procedural information but
helping students improve their conceptual understanding. For instance, Even and Tirosh (1995)
examined teachers’ presentations of certain content in terms of their knowledge of subject matter and
students. Their study was premised on the idea that to generate appropriate representations and
explanations for a concept, teachers should not only know the facts, rules, and procedures but also
know why they are true. For instance, one participant knew that 4 divided by 0 is undefined but did
not know why. Therefore, this participant would tell students that it is one of the mathematical axioms
that should be memorized. Additionally, Even and Tirosh noted that the preservice teachers were
unable to address students’ misconceptions effectively. Given two cases of incorrect solutions for 4
divided by 0 (e.g., 4  0  0 and 4  0  4 ), they preferred to suggest their own answers rather
than attempting to understand the students’ reasoning. Thus, Even and Tirosh concluded that
teachers’ knowledge of subject matter and students’ thinking had a strong influence on their
pedagogical decisions.
Theoretical Framework
Based on the literature about teacher knowledge, I accepted that PCK includes knowledge of subject
matter, knowledge of pedagogy, knowledge of students, and knowledge of curriculum. Furthermore, I
adopted Shulman’s (1986, 1987) ideas about PCK and defined it as the ways of knowing how to
represent a topic effectively to promote students’ understanding and learning and being able to
diagnose and eliminate students’ misconceptions and difficulties about that topic.
In my definition of PCK, knowledge of subject matter refers to knowledge of mathematical facts and
concepts and the relationships among them. I define strong mathematical knowledge as knowing how
mathematical concepts are related and why the mathematical procedures work. Subject matter
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
knowledge also influences teachers’ instruction and students’ learning (e.g., Ball, 1990; Ball & Bass,
2000; Borko & Putnam, 1996; Ma, 1999; Thompson, 1992). Therefore, subject matter knowledge
includes being able to relate a particular mathematical concept with others and explain or justify the
reasons behind the mathematical procedures explicitly to promote students’ understanding.
Knowledge of pedagogy covers knowledge of planning and organization of a lesson and teaching
strategies. Teachers who have strong pedagogical knowledge have rich repertoires of teaching
activities and are able to choose tasks, examples, representations, and teaching strategies that are
appropriate for their students (Borko & Putnam, 1996). In addition, they know how to facilitate
classroom discourse and manage time for classroom activities effectively.
Knowledge of students refers to knowing students’ common difficulties, errors, and misconceptions.
Teachers who posses a strong knowledge base in this domain know what mathematical concepts are
difficult for students to grasp, which concepts students typically have misconceptions about, possible
sources of students’ errors, and how to eliminate those difficulties and misconceptions (An, Kulm, &
Wu, 2004; Even & Tirosh, 1995; Tirosh, 2000).
Finally, knowledge of curriculum includes knowledge of learning goals for different grade levels and
knowledge of instructional materials. Teachers with strong knowledge in this area know the state’s or
national standards for teaching mathematics identified for different grade levels and plan their
teaching activities accordingly (Grossman, 1990; Marks, 1990). They choose appropriate materials
(e.g., textbooks, technology, and manipulatives) to meet the goals of the curriculum and use them
effectively.
Methodology
This study was designed to investigate the nature of PCK developed in a methods course and its
associated field experience in a group of preservice secondary mathematics teachers. I observed the
methods course and its associated field experience course in fall 2008 at a large public university in
the southeastern part of the United States. I wanted to understand the variety and the extent of the
issues discussed in these courses and how preservice teachers could benefit from those discussions
and field experiences. I decided to conduct a qualitative study because I was “concerned with process
rather than simply with outcomes or products” (Bogdan & Biklen, 1998, p. 6).
I used multiple sources for collecting data, including interviews, observations, a questionnaire, and
written documents. I was a participant-observer in all class sessions in both classes and took field
notes. I conducted three interviews with each participant throughout the semester and collected all
artifacts distributed in the courses and looked at the students’ assignments to gain a better
understanding of the course topics and students’ thoughts and reflections about those topics. The
methods course and its associated field experiences were not designed with an intention of developing
preservice teachers’ PCK. Therefore, at the beginning of the semester I interviewed the instructor of
each course to learn about their goals for the course. Then, I attempted to triangulate all data to
reduce the risk of the biases and the limitations of a specific data source (Bogdan & Biklen, 1998;
Cohen, Manion, & Morrison, 2007).
Participant Selection
From the 29 preservice teachers taking both courses, I chose 6 representative students as my
participants based on a questionnaire administered at the beginning of the semester. The
questionnaire consisted of 13 items; 8 of them were multiple-choice, 1 was Likert-type and 4 were
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
short-answer question. Through multiple choice and Likert-type items I aimed to learn how preservice
teachers perceive their level of knowledge for each component of PCK. Short-answer type questions
were context-specific and were similar to the questions that I would ask during the interviews.
Therefore, they not only helped me learn more about my participants but also decide probing
questions that I could ask during the interviews.
The questionnaire items were written to address the components of PCK that I identified in my
theoretical framework. Each multiple-choice item was aligned to one knowledge type. For instance,
Items 1 and 6 were aligned with knowledge of subject matter, Items 2 and 5 were aligned with
knowledge of pedagogy, Items 3 and 7 were aligned with knowledge of curriculum, and Items 4 and 8
were aligned with knowledge of students. The short-answer questions involved multiple knowledge
types. For instance, Item 10 entailed knowledge of subject matter, pedagogy, and students. The
alignment of each questionnaire item with aspects of PCK was discussed with two faculties from the
mathematics education department and reached an agreement on all items. The questionnaire with
alignment and the rubric for the items are illustrated in Appendix.
Because I wanted the participants to be a representative group of preservice teachers taking the both
courses, I assigned points to each questionnaire item to categorize preservice teachers in terms of
their perceived knowledge level of PCK as having low, medium or high level of PCK and then choose
two preservice teachers from each category. Such categorization not allowed me to work with a
representative group of preservice teachers taking the both courses but also learn about whether their
perceptions about their knowledge level of PCK had changed by the end of the semester. For shortanswer type questions I discussed the ratings for each answer with a peer and we had .90 inter-rater
reliability (Cohen, Manion, & Morrison, 2007) on the scores. In cases where we disagreed on a rating,
we discussed what points to assign those answers and agreed on the final scores.
The total scores ranged between 29 and 43 (out of a total possible of 52 points). Because the
categorization was mostly based on preservice teachers’ perceptions about themselves, I did not
specify the PCK levels in terms of scores. Instead, I ranked all scores from the smallest to highest and
divided them into three groups having the same size. Therefore, 10 students with scores between 29
and 35 were categorized as perceiving themselves having a low level of knowledge; the next 10
students with scores between 36 and 38 were categorized as perceiving themselves having a medium
level of knowledge; and the last 9 students with scores between 39 and 43 were categorized as
perceiving themselves having a high level of knowledge. Then, I asked two volunteers from each
group to be the participants of this study.
Based on the analysis of questionnaire data, 2 male and 4 female students agreed being the
participants of the study. Laura and Linda (pseudonyms) were categorized as perceiving themselves
having a low level of PCK with overall scores of 29 and 34, respectively. Laura was 21 years old,
White, and a senior. Linda was 21 years old, White, and a senior. Monica and Mandy (pseudonyms)
were categorized as perceiving themselves having a medium level of PCK with overall scores of 36 and
37, respectively. Monica was 20 years old, African American, and a senior; she was pursuing a double
major in mathematics and mathematics education. Mandy was 34 years old, White, and a senior.
Henry and Harris (pseudonyms) were categorized as perceiving themselves having a high level of PCK
with overall scores of 42 and 43, respectively. Henry was 26 years old, White, and a graduate student.
Harris was 22 years old, White, and a senior. The choice of pseudonyms of the participants was
purposeful such that the initial letter of the pseudonym represents the participant’s perceived level of
PCK (L for low, M for medium, and H for high).
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
Data collection
In the methods course the preservice teachers usually worked in groups to discuss given tasks, and
then they shared their ideas with the rest of the class. I took extensive notes about their performance
on the given tasks and what the 6 participants said during whole class discussions. Furthermore, I
collected any artifacts (e.g., handouts, and multimedia presentations) discussed in the class in order
to make inferences about the goals of that particular lesson and make a list of major topics discussed
in the methods course and the field experience course. In the field experience course, the preservice
teachers were required to write field reports during their time in schools. I examined all assignments
and field reports completed by the participants to gain a better understanding of their experiences in
the methods course and in the field.
I conducted three interviews with each participant. The first interview was held during the third week
of the semester, the second one was held during the eighth week of the semester just after their
second field experience, and the third one was held during the last week of the semester. At the
beginning of the interviews, I asked them to reflect on the issues discussed in the methods and the
field experience courses and how they contributed to each aspect of their PCK. Then I gave them
some content-specific questions to understand the nature of their PCK. I also wanted them to reflect
on their field experiences. During the last interview, I gave them a shortened version of questionnaire
including multiple-choice and Likert-type items to see how they perceived their knowledge levels at
the end of the semester. Furthermore, I asked them to make an overall evaluation of the methods
and field experience course in terms of their gains from these courses.
Data analysis
I used the PCK framework developed for this study to analyze the interview transcripts, field notes,
and students’ written work. I read through each students’ work, transcripts, and daily field notes to
get familiar with the content. I read each transcript to code each participant’s answers in terms of the
type of knowledge demonstrated in the questions, and then I compared the answers to similar types
of questions to determine the similarities and differences between the explanations and also to detect
any change, if there was, in their knowledge level of that particular knowledge domain. I discussed
my decisions about each participant’s responses to the interview questions with a faculty from the
mathematics education department and we agreed on almost all of them.
The preservice teachers’ answers to given mathematical problems and the validity of their
explanations were counted as the indicators of their knowledge of subject matter. When their answers
and explanations were mathematically valid, I categorized their responses as 1) procedural without
reasoning (e.g., flipping the inequality sign when multiplying or dividing both sides of the inequality by
a negative integer because it is the rule), 2) procedural with reasoning (e.g., using the FOIL method
when multiplying binomials because FOIL method is based on the distributive property), and 3)
conceptual (e.g., in Cartesian coordinate system, if a system of equations has no solution it means
there is no common point satisfies the both equations, that is, the lines represented by those
equations are parallel.) When their answers or explanations were mathematically invalid I noted them
as the indicator of deficiencies in their knowledge of subject matter.
The variety and the reasonableness of preservice teachers’ choice of teaching activities, tasks,
examples, and representations and comprehensiveness of their lesson plans were accepted as their
pedagogical knowledge. For instance, using the example of “finding the number of all possible
arrangements of five different books on a shelf” is valid to explain permutation concept but the
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
example of “finding all possible two-letter words from the word BOOT” is not valid to explain
combination concept.
The preservice teachers’ repertoire of students’ possible difficulties and misconceptions in
mathematics and their ability to identify and eliminate such difficulties and misconceptions was coded
as their knowledge of students. I gave some tasks such as error analysis to the preservice teachers
and I categorized their responses in terms of their ability to identify all possible sources of difficulties
or errors and their ability to suggest various ways to eliminate such errors. Therefore, they either 1a)
diagnosed all possible difficulties or misconceptions correctly, or 1b) diagnosed some of the possible
difficulties or misconceptions (in the case of there were more than one) correctly, or 1c) could not
diagnose the possible difficulties or misconceptions. Then, they either 2a) suggested telling the rules
and procedures to solve the given problem correctly, or 2a) suggested a reasonable way different
than telling the rules or procedures to eliminate them. Finally, the preservice teachers’ ability to
identify a reasonable order of mathematical concepts to be taught in a semester, to differentiate
learning goals for different grade levels, and to choose appropriate instructional materials such as
textbooks, technology, and manipulatives to meet those goals were identified as their curriculum
knowledge. For instance, linear equations are placed before quadratic equations in a typical secondary
mathematics curriculum. Therefore, given a list of topics (including linear and quadratic equations) to
be taught in a semester, linear equations should precede quadratic equations. Furthermore, a teacher
may prefer to discuss the similarities and differences between linear functions and quadratic functions
through the graphs of each type of functions by using graphing calculator or similar computer applets.
Findings
In this study, knowledge of students is defined as teachers’ knowledge of students’ common
difficulties and errors in different contexts and teachers’ ability to diagnose and eliminate them. The
preservice teachers’ knowledge of students’ common difficulties and errors is limited by their
classroom observations during their field experiences. They noted that they did not know much about
them. To understand the nature of how they would address and eliminate students’ errors and
misconceptions, I gave some content-specific cases to them during the interviews. I gave some
student work involving errors and asked them how to address those errors and I also asked them how
they could help students who are struggling with understanding some mathematical concepts. When
given examples of students’ errors and asked how to address them, the preservice teachers tended to
repeat how to carry out the procedures or explain how to apply a rule or mathematical fact to solve
the problem. That is, their responses mostly fell into categories of “diagnosed some of the possible
difficulties or misconceptions correctly” and “suggested telling the rules and procedures to solve the
given problem correctly.” They had limited repertoire of teaching strategies to help students
understand mathematics. Although, in some cases, the preservice teachers noted that they would first
ask students to explain their solutions to help students assess their own understanding and realize
their mistakes, they usually preferred to tell how to solve the given problem rather than using various
visual aids such as tables, schemas, computer applets to help students solve the problem. Moreover,
when they explained the solution of the given problem they rarely mentioned the reasoning
underlying the procedures. That is, in terms of their knowledge of subject matter, their explanations
mostly fell into category of “procedural without reasoning.”
The most salient finding about the nature of preservice teachers’ knowledge of student was the
weakness in analyzing the reasons behind students’ errors or difficulties which was emerged as a
result of the nature of their subject matter knowledge. The preservice teachers usually came up with a
reason, which was apparent and procedural. However, they did not state how flaws in students’
conceptual understanding would likely lead to failure in generating a correct solution. For example,
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
during the first interview, I asked them how they could help a student who was having difficulty in
multiplying binomials. Most of them said they would explain the procedure for using the “FOIL
method” to multiply binomials. FOIL is a mnemonic used for multiplying the terms of two binomials in
an order such that first terms, outer terms, inner terms, and last terms are multiplied and then
simplified to find the result of the multiplication. The preservice teachers did not attempt to justify the
reasoning behind the procedure, but two of them indicated that they were applying the distributive
law when multiplying binomials. They assumed that applying the distributive law after separating the
terms would help students understand the multiplication of the binomials. However, the students
might not understand why the distributive law works and just try to memorize the procedure. The
preservice teachers did not consider that students might know how to apply the distributive law but
fail to multiply variables or negative integers correctly. For instance, students might think that
2x  5x  10x
or
 2( x  3)  2 x  6 . Laura and Henry did point out that students might struggle
with multiplying variables and adding similar terms, but they did not explain how they would clarify
those issues for the students.
In another task, I asked the preservice teachers how to help a student who simplified a rational
expression inappropriately by using “canceling” as shown in Figure 1. All of them started by saying
they would explain the procedure of simplifying rational expressions.
Simplifying rational expressions
Look at the student work given below. How can you explain to the student that his or her solution is
incorrect?
Figure 1. The Simplifying Rational Expressions Task
Mandy and Henry were unsure how to clarify the student’s misconception. Mandy said that she would
tell the student that the numerator and denominator are a unit, and therefore she cannot randomly
cancel out the terms. She stated that the rules for multiplication of exponents are different from the
rules for addition; however, she did not give examples of such rules or explicitly relate them to this
task. She suggested using the idea of a complex conjugate to get rid of the denominator, but then
she realized that she could not use a complex conjugate in the context of real numbers. Although she
was aware of that the student’s solution was incorrect, she could not recognize that the numerator
and denominator should be written in factored form before simplifying the terms. Hence, she failed to
generate an effective way to approach the student’s misconception and help her to understand how to
simplify rational expressions.
Similarly, Henry said he would tell the student that a term cannot be simplified when it is associated
with another term through addition or subtraction. However, he did not explain what he would do to
clarify such misconception. Instead, he said that explaining why the solution is incorrect is harder than
solving the problem.
In contrast, some participants mentioned that they would show the student how to factor the given
expressions and then simplify them. Laura and Linda said they would explain how to factor the
numerator and denominator and then cancel out common terms. Laura would tell the student that
“when we want to cancel out we need to remember that we are taking away every term in our
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
numerator and every term in our denominator.” Then she would show how to factor the numerator
and denominator and then simplify them. She also said, “Being able to explain is tricky.” She noted
that she would emphasize the idea of factoring and try to make sure that the student understood it.
Similarly Linda would show how to factor the terms step by step, first working on the x terms and
then the y terms. She said that she did not know whether there is an easier way to explain it.
Although Laura and Linda, explained how to factor, this might not be convincing for the student
because it does not include a rationale for why it is necessary to find common terms in the numerator
and denominator and then cancel them. They did not clarify the reasoning behind writing the
numerator and the denominator in factored form rather than leaving them as they are. Furthermore,
Linda used the term “taking away” to explain how to simplify the common terms in the numerator and
denominator. Because “taking away” is used to indicate subtraction operation students may confuse
about whether simplification refers to division or subtraction.
Harris also would explain how to factor the numerator and the denominator. However, first, he would
try to convince the student that his or her reasoning was invalid by rewriting the given expression as
the sum of two fractions, that is,
a
b

and then applying the student’s method to the
cd cd
fractions such that for each fraction, he would simplify the single term in the numerator with one of
the terms in the denominator. Thus, he would show that the answer obtained in this way was
different from the student’s answer in the example. While Harris’ explanation would help the student
realize her mistake, it would not necessarily help her to understand why she needs to factor the
expressions.
During the second interview I showed preservice teachers student work where the student found the
2 x 4  18 x 2  0 to be ± 3 by taking 18x 2 to the other side of equation and
2
then dividing both sides by 2x (see Figure 2). I asked them how they could explain that the solution
solution of the equation
is invalid.
Solving polynomial equations:
Look at the student work given below. How can you convince your student that his/her answer is
invalid?
2 x 4  18 x 2  0
2 x 4  18 x 2
2 x 4 18 x 2

2x 2
2x 2
2
x 9
x  3
Figure 2. The Solving Polynomial Equations Task
With the exception of Henry, the preservice teachers did not recognize the student’s error. They
stated that they would tell the student that factoring is a better way to solve that equation because it
will help you find all of the solutions, including zero. For instance, Monica said “you just have to
remind them that there are other ways of solving the problem, and this is one way she didn’t
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necessarily get every solution.” It was evident that she did not notice the student’s error and therefore
did not recognize that her explanation would not help the student understand why her method was
incorrect. Henry also said he would explain how to factor the given equation; however, he would first
tell the student that when dividing by x she needs to make sure that x is not zero. Thus, he was
able to identify and clarify the student’s confusion about why her method did not work. The preservice
teachers’ approaches to this problem revealed that they were unable to recognize the gap in students’
understanding of solving polynomial equations. Instead, they merely focused on the procedural steps
and suggested another method that they were sure would yield all solutions.
2
During the third interview, I gave an example of student work in which the student forgot to change
the direction of the inequality sign when dividing both sides of the inequality by a negative number
(see Figure 3). With the exception of Linda, the preservice teachers failed to remember the reason
behind this procedure. They noted that there exists a mathematical explanation for it, but they were
unable to recall it.
Solving inequalities
Look at each of the student work given below. How can you explain to the student that his or her
solution is incorrect?
 2x  5  x  1
 2 x  x  1  5
 3 x  6
x2
Figure 3. The Solving Inequalities Task
Linda explained that if a number is less than a negative number, then it is itself a negative number.
Therefore, -3x has to be a negative number. Then she used the fact that the product of two numbers
is negative if and only if one of the numbers is negative and the other is positive. Thus, x would be a
positive number. Henry attempted to explain it by using the idea of solving systems of inequalities. He
suggested setting up
y  3 x and y  6 to investigate the common solution as if they were
inequalities. However his reasoning was vague because he did not identify the inequalities clearly.
Based on his explanations, I concluded that he assumed that
thought
y  6 , but it was not clear whether he
y  3 x or y  3 x because he did not solve the problem completely. To obtain the answer
as “x is greater than or equal to 2” he probably considered the latter inequality, but he did not state it
explicitly.
On the other hand, when preservice teachers had a deeper understanding of a particular topic, they
attempted to justify the reasoning behind mathematical procedures and facts by using visual or
concrete representations or by making connections with other concepts. For instance, during the first
interview, I asked the preservice teachers how they could help a student who was confused about
getting
2  0 as the solution of a
system of linear equations, namely
2 x  y  1 and 2 y  4 x (see
Figure 4).
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
Solving systems of linear equations
Assume that one of your students got confused when he or she found 2  0 as the result of the
solution of a system of linear equations. How do you explain to him or her the meaning of this result?
Sample student work:
2 x  y  1
2x  1  y
2 y  4x
2 y  4x
2  (2 x  1)  4 x
4x  2  4x
2  4x  4x
20
Figure 4. The Solving Systems of Linear Equations Task
Although Henry and Mandy did not recognize that the solution 2 = 0 meant that there was no solution
of the system or that the lines did not have a point of intersection, the others did recognize and
suggest sketching the graphs of each to show that they are parallel. Henry thought that “it means you
divided by zero or did some kind of illegal maneuver.” He suggested writing the equations in the
slope-intercept form to find the wrong step, but he did not explain further how it would help him to
detect the error. Likewise, Mandy said “Whenever you get something like 2  0 or 7  3 , somewhere
along the line here you didn’t follow the mathematical rule.” She rewrote the second equation as
y  2 x but did not continue working on this question. Mandy failed to realize that the lines have the
same slope and are therefore parallel, even though she wrote the equations of the lines in slopeintercept form. It is unclear whether she did not know that the slopes of lines provide information
about the relationship between (i.e., parallel lines have the same slope) or whether she was simply
unable to recall and apply this knowledge at the time of the interview. However, neither preservice
teacher was able to reason about the task by thinking about what a solution to a system of linear
equations represents (a point of intersection of the lines). Neither one suggested using visual aids
such as graphs to investigate the given case and help students understand the context better; rather
these participants said they would explain the procedural steps for solving the system of equations to
students.
In contrast, the other participants said they would graph the lines to show students that they would
not intersect. Linda noted that getting such an answer would indicate that there is no x value that
satisfies both equations for any y value. Then she said, “Graphing it would be the easiest way
because…if you give them a picture they can understand a lot better.” Linda said she would graph the
equations to support her explanations and foster students’ understanding.
Laura stated that she would ask the student to check the calculations first. If the student got the
same answer, then she would tell her that “this x in the first equation is probably not equal to this x in
the second equation.” Then, she would graph both equations to show that the graphs would not
intersect. She suggested using graph paper or a graphing calculator to sketch the graphs. She would
also talk about parallel lines because “when lines do not intersect that means they have the same
slope and further they are parallel.” Thus, her reason for graphing the equations was twofold: to
address the student’s difficulty in understanding systems of linear functions and to make connections
with other concepts such as parallelism and slope.
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
Harris also said he would suggest checking the answer for accuracy and then he would talk about
what it means to get no solution as the result of systems of linear equations. He would relate that
discussion to the idea of independent lines, and then he would graph the lines to show that getting
20
means that there is no solution and the lines are independent; that is, they are not
intersecting. It was evident that he would graph the lines to support his explanations and help
students understand the given case better.
Monica said she would prefer to talk about all possible cases of the solution of systems of linear
equations. She would rewrite the given equations in the slope-intercept form and then graph them to
show that the graphs are not intersecting. Then she would give examples of the other two cases and
graph them to show how the solution of the system relates to the graphs of the lines on the
coordinate plane. It seemed that Monica’s goal was to put this particular example in a larger context
by providing examples of each case: A unique solution means the lines intersect, no solution means
the lines are parallel, and infinitely many solutions means the lines coincide. By approaching the
problem in this manner, Monica was trying to help the student make sense of systems of linear
equations more generally rather than just in the given case.
Discussion
The interview data revealed that the preservice teachers’ knowledge of students was intertwined with
their knowledge of subject matter and pedagogy such that they sometimes had difficulty in identifying
the source of students’ difficulties and errors correctly, and in finding effective ways to eliminate
them. The preservice teachers thought that students fail in mathematics because they do not know
the procedures or rules to be applied or they apply them incorrectly. Therefore, they were inclined to
address students’ errors by repeating how to carry out the procedures or explaining how to apply a
rule. Such approach of the preservice teachers could be counted as an indicator of the weakness of
their repertoire of appropriate examples, representations, and teaching strategies could be used when
teaching mathematics, that is, it was the indicator of the weakness in their knowledge of pedagogy.
Although there are a number of more conceptual approaches to address students’ difficulties and
errors, the preservice teachers did not mention during the interviews. For instance, in the case of
multiplying binomials, a teacher could work with small numbers to show how the distributive law
works. For instance, one could create a simple word problem to show that
3  7  3  (2  5)  3  2  3  5 . Similarly, it is possible to use an area model to explain the
multiplication of binomials in the form of ax  b . Given two binomials ax  b and cx  d , draw a
rectangle having these binomials as the dimensions and then construct four small rectangles with
dimensions
(ax)  (cx) , ( ax )  d , (cx )  b , and b d . The sum of the areas of all of the rectangles
gives the area of the original rectangle, which is a visual illustration of the multiplication of binomials.
Also, using algebra tiles would allow students to find the area of a rectangle as the sum of partial
areas in a manner similar to the area model just described. The teacher could also use more
conceptual approach to help students even if the distributive property is not the cause of the problem
but lack of prior knowledge such as operations with variable expressions.
In the case of simplifying variable expressions, the preservice teachers might use particular numerical
examples to show that the student’s reasoning was invalid. For example, if the 2s are canceled in
24
4
, the answer is
, but the correct answer is 2. The order of operations could be used to
52
5
explain this task as well, noting that when the numerator or denominator of a fraction involves more
than one term, they are assumed to be inside parentheses. Because the division operation does not
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
precede parentheses, simplification cannot be applied randomly over the single terms. In addition, the
idea of equivalent fractions and simplification could be applied in this situation. For instance, showing
that
6 23 3


and then extending the analogy to examples with variables would show how
8 24 4
these concepts are related to the given problem. Furthermore, the preservice teachers said they
would explain to students how to factor the numerator and denominator before canceling out the
common terms. They noted that the student failed to simplify the given expression because she did
not know how to factor variable expressions. However, another reason underlying the error might be
weakness in the student’s knowledge of exponents and operations with them. Although Monica stated
x3
that she would review the properties of exponents, such as showing that x  x  x  x or 2  x ,
x
3
she did not state explicitly how she would relate these properties to the idea of simplifying the terms
or writing the expressions in factored form. Therefore, not only the weakness in preservice teachers’
knowledge of pedagogy might the cause of incomplete responses but also their knowledge of subject
matter. For the simplifying variable expressions tasks, the preservice teachers could not recognize all
possible sources of the student’s error. Thus, they did not suggest alternative ways of helping the
student.
Similarly, in the case of solving polynomial equations the preservice teachers could not recognize the
student’s error. They confused with the student’s answer because her solution was seemingly correct
but they knew that zero is also in the solution set of the given equation. Although they realized that
something had to be wrong with student’s solution they preferred to explain the solution in their
minds, that is, factoring the equation first and then solving for x. Such an attempt not only revealed
deficiencies in preservice teachers’ knowledge of subject matter but also nature of such knowledge,
which is procedural. The preservice teachers came up with two methods to solve polynomial
equations: either factorize the equation or simplify. They thought that both methods have to yield the
same answers. However, it was not the fact because they overlooked a special case that one of the
values of the unknown was zero. Although some of them recalled the fact that the degree of a
polynomial function determines how many roots the function would have, they could not justify this
fact to address the student’s error more effectively. They preferred to tell the student that she might
check the accuracy of her answer by using this rule. Another example of the preservice teachers’
procedural knowledge of mathematics was “solving inequalities task.” Except one participant, the
preservice teachers did not explain why the inequality sign should be flipped when multiplying or
dividing both sides of inequality by a negative number. Seemingly, they just memorized it as a
mathematical rule and did not reason why it works. On the other hand, in the case of solving systems
of linear equations the preservice teachers attempted to use representations to explain the underlying
concept. Except two of the participants, the preservice teachers had solid understanding of solving
systems of equations and they suggested using the geometric meaning of such solution by graphing
the given linear equations.
Briefly, the examples discussed here and above revealed that the preservice teachers’ knowledge of
subject matter and pedagogy had an impact on their knowledge of students. If they knew the concept
in depth, then they were able to detect the flaws in students’ understanding. If they had rich
repertoire of teaching strategies, representations and examples then they could address students’
errors and misconceptions effectively.
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
Conclusion and Implications
The aim of this paper was to present the findings about preservice teachers’ knowledge of students as
emerged from a study designed to investigate the development of preservice teachers’ PCK in a
methods course and its associated field experiences. The findings support the earlier studies on
teachers’ knowledge of students (e.g., Ball, Thames, & Phelps, 2008; Even & Tirosh, 1995; Kagan,
1992) that the preservice teachers lacked knowledge of students’ mathematical thinking. They neither
knew much about what problems students might encounter when learning a specific topic nor how to
help students overcome their difficulties and correct their misconceptions.
To improve preservice teachers’ knowledge of students, they should be given opportunities to work
with individual students to develop their repertoire of students’ misconceptions and also improve their
ability to help address students’ difficulties effectively. Graeber (1999) suggested that preservice
teachers should be given different examples of students’ misconceptions and asked to analyze
students’ thinking and generate a way of eliminating such misconceptions in the methods course to
improve their knowledge of students’ thinking. Although the preservice teachers in this study were
given such examples a few times during the methods course, it seemed that the number of those
activities should be increased to help preservice teachers improve their knowledge of students.
Furthermore, the preservice teachers should be given opportunities to work with individual students or
a group of students to experience how to help students understand mathematics. Thus, they could
improve their repertoire of different ways of addressing students’ difficulties and misconceptions such
that they may need to use representations, manipulatives, or real-life examples rather than merely
telling of the rules or procedures.
Acknowledgement
The study reported in this article was conducted as part of the author’s doctoral dissertation
completed at the University of Georgia under the direction of Denise S. Mewborn. I would like to
express my gratitude to Denise S. Mewborn for her helpful comments on an earlier draft of the article.
I also want to thank to my committee members Dr. Sybilla Beckmann-Kazez and Dr. Jeremy Kilpatrick
for their encouragement and valuable comments to make this work better.
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Appendix
Questionnaire15
Instruction: For each of the following items choose the response that best fits you.
1. At the end of my degree program I will have taken enough content courses to be an effective
mathematics teacher in grades 6-12. (KSM)
a. Agree
b. Somewhat agree
c. Disagree
2. At the end of my degree program I will have taken enough courses about teaching
mathematics to be an effective mathematics teacher in grades 6-12. (KP)
a. Agree
b. Somewhat agree
c. Disagree
3. I know what mathematics content is to be addressed in each year of the 6-12 mathematics
curriculum. (KC)
a. Agree
b. Somewhat agree
c. Disagree
4. I know possible difficulties or misconceptions that students might have in mathematics in
grades 6-12. (KS)
a. Agree
b. Somewhat agree
c. Disagree
5. I have a sufficient repertoire of strategies for teaching mathematics. (KP)
a. Agree
b. Somewhat agree
c. Disagree
6. I know how mathematical concepts are related. (KSM)
a. Agree
b. Somewhat agree
c. Disagree
7. I know how to integrate technology in mathematics lessons. (KC)
a. Agree
b. Somewhat agree
c. Disagree
8. I know how to diagnose and eliminate students’ mathematical difficulties and misconceptions.
(KS)
a. Agree
b. Somewhat agree
c. Disagree
15
Alignment of the questions are given in the parentheses with abbreviations. KSM: Knowledge of subject-matter, KP: Knowledge of
pedagogy, KS: Knowledge of students, KC: Knowledge of curriculum
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9. Read the definitions of the following Knowledge Bases:
Knowledge of subject-matter: To know mathematical concepts, facts, and procedures, the reasons
underlying mathematical procedures and the relationships between mathematical concepts.
Knowledge of pedagogy: To know how to plan a lesson and use different teaching strategies.
Knowledge of students: To know possible difficulties, errors, and misconceptions that students might
have in mathematics lessons.
Knowledge of curriculum: To know learning goals for different grade levels and how to use different
instructional materials (e.g., textbook, technology, manipulatives) in mathematics lessons.
How do you perceive your knowledge level in each knowledge base identified above? Use the
following scale: 1-not adequate
2-adequate
3-competent
4-very good
Knowledge of subject-matter: ……
Knowledge of pedagogy: ……
Knowledge of students: ……
Knowledge of curriculum: ……
10. Look at the student work given below. How can you explain to the student that his or her
solution is incorrect? (KSM, KP, KS)
9 x 2  25 y 4  3x  5 y 2
11. Assume that you will introduce “inverse functions”. Make a concept map for inverse functions
showing which mathematical concepts or facts relate to inverse of functions. ( KSM, KC)
Inverse
functions
12. If you were introducing how to factor trinomials, which of the following trinomials would you
use first? Explain your reasoning. (KSM, KP, KS)
2 x 2  5x  3 ,
x 2  5x  6 ,
2 x 2  6 x  20
13. Assume that you will teach the following topics in a semester. In which order would you
teach them to build on students’ existing knowledge? Explain your reasoning. ( KSM, KC)
Polynomials, trigonometry, factorization, quadratic equations
Rubric
Scale for Items 1 through 8. Disagree: 1 pt., Somewhat Agree: 2 pts., Agree: 3 pts.
Scale for Item 9. Not Adequate: 1 pt., Adequate: 2 pts., Competent: 3 pts., Very Good: 4 pts.
Scale for Items 10 through 13. 0: No answer, 1: Vague answers or answers without explanations,
2: Answers without justifications or answers with minor mathematical errors, 3: Valid explanations or
justification.
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Turkish Online Journal of Qualitative Inquiry, April 2011, 2(2)
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Acting and Teacher Education:
The BEING Model for Identity Development
Kemal Sinan Özmen
Gazi University, Turkey
[email protected]
Abstract
This study follows three pre-service teachers during three academic semesters in which they took
an acting course for teachers and participated in practicum with a special focus on rehearsing and
developing their teacher identities. In order to create the necessary context for them, an acting
course for pre-service teacher education was designed in parallel with a model which is based on
an influential acting theory. This model, namely the BEING (Believe, Experiment, Invent, Navigate,
Generate), was also designed by the researcher. The incentive behind designing a model grounded
on acting literature was that the relevant literature does not provide trainers with a universal model
which can be referred as a manual for running and monitoring acting courses for teachers. In this
case study, this model was also tested in terms of its applicability and functionality in practice.
Based on analyses of audio taped interviews, session journals and reflections, the five stages of the
BEING Model was found to be highly applicable and functional in terms of reflecting the natural
development process of teacher identity development. Pre-service teachers displayed a significant
development in communication skills and professional identities. Therefore, the BEING model
provides a perspective and a philosophy of benefiting from acting literature for teacher educators
with little or no knowledge on acting and theatre.
Keywords: Pre-service teachers; professional identity; acting
Introduction
The task of integrating actor preparation methods into teacher education has been going on for at
least four decades, but these studies have never been a central debate in teacher education.
Fortunately, the efforts of a few scholars enable us to conduct more specific research studies. Among
these scholars, there is a general accord with the idea that considering teachers as performing artists
has an influential impact on the practice and production of teacher education (DeLozier, 1979; Eisner,
1979; Griggs, 2001; Hart, 2007; Sarason, 1999; Travers, 1979; Tauber, Mester & Buckwald, 1993;
Tauber & Mester, 2007). In terms of effective teaching skills, this impact is usually defined as the
ability and consciousness in nonverbal communication (Vandivere, 2008) and nonverbal immediacy
(Hart, 2007), teacher enthusiasm (Tauber & Mester, 2007), constructing strong teacher identities
(Hart, 2007), an effective use of body language and voice (Baughman, 1979; Dennis, 1995; Freidman,
1988; Nussbaum, 1988; Tauber & Mester, 2007; Timpson & Tobin, 1982), use of humor (Baughman,
1979; Tauber & Mester, 2007), and effective communication (Griggs, 2001; Freidman, 1988; Javidi,
Downs and Nussbaum, 1988). Many more variables can be studied so as to reveal and unravel the
contributions of acting methods to teacher education on the grounds that this is not only a pursuit of
developing communication skills of teachers, but also a philosophy of the teaching profession that can
radically change the way we approach teacher education and accordingly shape professional identities
of trainers. It is quite surprising that this issue has been mostly neglected in teacher education
(Sanford, 1967; Nussbaum, 1992).
Scholars carrying out studies on professional identity, or teacher identity, claim that teachers need to
develop an identity, preferably beginning by pre-service, so as to perform their professions effectively
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(Danielewicz, 2001; Hanning, 1984; Hart, 2007; Palmer, 2003; Rodgers & Scott, 2008). Travers
(1979) accentuates that teacher educators should benefit from acting theories, specifically from the
theory of Stanislavski, so as to construct consistent and influential teacher identities. He claims that
Stanislavski provides teacher educators with a theory of identity construction in pre-service years
(1979).
The available studies present various theoretical discussions on similarities of acting and teaching
professions (Burns, 1999; Dennis, 1995; Eisner, 1979; Freidman, 1988; Hanning, 1984; Van Hoose
and Hult, 1979; Jarudi, 2000; Lessinger & Gillis, 1976; Rives Jr., 1979; Sarason, 1999), acting
activities designed for teacher education (Griggs, 2001; Hart, 2007; Tauber & Mester, 2007), some
acting materials for teacher training (Lessinger & Gillis, 1976) and a course design with a syllabus and
materials (Hart, 2007). Among these studies, we cannot come across abundant number of studies
which suggests a model that may lead us to shape our practice in using acting techniques, activities
and materials (Özmen, 2010). On the other hand, the syllabi and course designs may shed light on
our curricular choices in teacher training practice, but as is known, syllabus and course design studies
have an aspect which heavily addresses local and institutional needs. We may need a model based on
a widely-accepted theory of actor training or preparation for teacher education so that we can
facilitate and monitor the acting courses designed for teachers more consciously and effectively.
Moreover, such practice-oriented models may help trainers with a limited knowledge of acting feel
more confident in using acting tasks in their context. In this respect, this study aims at suggesting a
universal model of teacher identity development which is based on the acting theory of Stanislavski
(1949). The proposed framework, The BEING Model (Believe, Experiment, Invent, Navigate and
Generate) was designed by the author in a case study completed in a fifteen months in pre-service
English teacher education.
Teachers as Actors
A persuasive argument of the idea of “teacher as actors” can be constructed by addressing the study
of Hanning (1984). Hanning reflected on his early years as an advisor when he encouraged the
novices who were anxious about their teaching attempts by saying: “Just go there and be yourselves!”
Hanning (1984) then admitted this advice was not valid, mentioning that pre-service teachers are to
develop a teacher identity, and that they may do it by shaping their teacher identities in parallel with
the needs of the learners just like actors do in theatre performances.
The burden on the shoulders of teacher education programs may get even heavier with these
propositions. However, a slight change in our understanding and practice may result in amazing
improvements in pre-service teachers’ experience of preparation to become a teacher. No matter how
talented a teacher is in terms of using acting techniques, it takes time to construct the whole teacher
identity. What we also know is that the construction period should start by the first course hour of a
teacher education program. In this sense, creation of a teacher role is quite different from that of an
actor in that actors are trained to perform different roles during their professional career. They are
trained to use their cognitive, affective and biological resources to embody someone else. As for the
teachers, they are just finding a new way of expressing and embodying themselves, but in a more
alert, conscious and professional way and for using the resources of this new self for getting learners
to a level where they may enhance their learning process. “The teacher does not want to create a role
that is a ‘false front’ but rather wants to create a way of the BEING that maintains her personal
integrity and allows her to interact with her students most effectively” (Hart, 2007, p. 36).
Hart (2007) acknowledges that “While the actor’s lines remain constant from performance to
performance, the teacher varies her text each time she performs a lesson” (p. 62). This is a very
important distinction between the dynamics and functions of both performance-based professions.
The most important aspect of this distinction is that actors need to stick to the play-script and the
instructions of the director so that all the components of a show, such as music, setting and so on,
can function harmoniously. However, in this sense, teachers are like actors, producers and directors of
the whole play. “Teachers are in much greater control of their own scripts – they write, direct, and
produce them” (Timpson & Tobin, 1982, p. 28). I may not agree with Timpson and Tobin (1982) on
the idea that teachers write their plays in that teachers are already given a play script, which is the
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syllabus of the course and all the materials to be utilized for the completion of the course program.
However, it is certain that teachers are both actors and directors of their own plays, and even
sometimes they can do many manipulations on the syllabus and materials, which means they can
interfere in the authors business to a certain extent.
Theory of Stanislavski and Development of Teacher Identity
The contributions of Stanislavski to a contemporary understanding of theatre acting are invaluable
(Bilgrave & Deluty, 2004) in that he constructed a theory which has had a great impact on all actors,
directors and theoreticians of this field. His universal methodology is known as ‘The Method’ and is
referred to unequivocally as one of the major theories of acting in theatre and cinema arts. Mainly,
the theory of Stanislavski is a way of rehearsing and embodying an identity for theatre performance.
“The focus of the method approach is to develop self-awareness for the purpose of broadening one’s
self-identity, one’s capacity to play a range of characters credibly” (Griggs, 2001, p. 30). As an
educator, Travers (1979, p. 16) notes that “Stanislavski had essentially a complete theory of how a
personality can be created in the adult.” This process is materialized through analyzing the emotional
and cognitive schemata of the target identity and discovering ways of performing them so that an
authentic version of the role can be created. Thus, what Stanislavski proposed is not an insincere
imitation of the role to be performed, but the actualization of a possible and believable version of the
role. In this sense, Stanislavski does not offer pretending, but becoming and “being.” Pointing out the
limitations of competency-based teacher education three decades ago, Travers (1979) refers to
Stanislavski’s work by claiming that “Superficial features of a role do not have to be learned, for they
appear automatically once the deeper structures have been developed” (p. 17). As for teachers in a
pre-service program, these deeper structures represent their objectives, motivations, their personal
and professional resources, all of which form the characteristics of their ideal teacher identities. In this
respect, the proposal of this study is that the acquisition and internalization of the teacher identity,
which Griggs (2001) defines as a transformational period, can be enhanced by the theory of
Stanislavski.
In Stanislavski’s theory, creating a role starts with an emotional journey to the life and heart of the
actor who is working on the role. Actors are the people who are aware of their emotional and physical
resources, possibilities and limitations. This ability is also crucially important for the teachers. This
emotional journey is accompanied by the emotions, dispositions and personality of the target role.
Actors simply find certain ways of embodying the target role by basing it on their personal resources
so that an authentic version of the role can be created. In other words, this emotional preparation
process is highly important because the only way of creating a believable identity depends on a
careful analysis of the self and the target identity. Imitation or copying the role is a threat for the
process of creating a version of the role. “An attempt to copy a role produces disastrous effects, for
the role then lacks the authenticity that it must have to be effective” (Travers, 1979, p.17). This
emotional preparation process offered by Stanislavski is also quite important in that pre-service
teachers should be aware of the development process of their professional identities. Therefore, a
model based on Stanislavski’s theory will require much attention on the observation and analysis of
the personalities of the pre-service teachers. The first step is to lead pre-service teachers to ponder
over the qualities which can make them effective teachers. Therefore, in addition to thinking about
their ideal teacher identities, pre-service teachers should also analyze themselves carefully so as to
find out which of their personal resources are critical and necessary to embody their ideal teaching
identity. When this process is completed, the rest is based on practice and a discovery process.
Actors need to find out the right codes of voice and body language, all of which represent the
emotional characteristics of the target role. As for the pre-service teachers, this process can be a
discovery process of using body language, voice, communication strategies in the classroom, use of
classroom space, observing and manipulating the classroom atmosphere and so on.
In order to apply the theory of Stanislavski in pre-service teacher education, the BEING Model is
developed based on the remarks of Stanislavski on creating a role. In this case study, I have observed
the identity development process of three pre-service teachers to find out whether this model works in
practice. The trainer of the course shaped the course content and methodology in parallel with this
model.
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Research Method
Aim, Research Questions and Design
The incentive behind this research study is to test the applicability and functionality of “the BEING
Model” as a framework based on Stanislavski’s acting theory. I aimed to answer the following research
questions:
1. Can we apply Stanislavski’s ‘The Method’ to teacher education as a model for constructing
teacher identity?
2. Are the stages that the BEING model presents in parallel with the actual development process
of teacher identity development?
3. Can the BEING Model provide a basis for acting courses designed for development of teacher
identity?
A case study was conducted in an English language teaching department on three pre-service
teachers who took the course “Acting for Teachers”. Ceren (Female, 23), Ece (Female, 22) and Cem
(Male, 22) were the subjects and selected randomly from the class. Development process of teacher
identities of these pre-service teachers was observed in terms of the designed model. The case study
includes three stages that were completed in two years. The first stage was the 14-week acting
course in the fall semester, 2008, in which pre-service teachers practiced acting techniques in terms
of Stanislavski’s approach. The second stage was the following semester (spring, 2009) during which
the pre-service teachers took typical language teaching methodology courses, and they performed
many teaching demonstrations in these courses. During this semester, pre-service teachers were
asked to report the possible impact of the acting course on their teaching strategies and beliefs. The
third stage began in the fall semester of 2009, when the pre-service teachers started to teach in the
practicum to real students. Throughout these three stages, the following data collection tools were
utilized.
Data Collection
The following instruments were used for data collection:
1. Pre-service teachers kept a weekly session journal in which they wrote down the details of
their experiences in their acting course.
2. They were asked to write reflections on the contributions of the acting course to their
methodology courses and their beliefs on teaching and learning. They began to write these
reflections in September, 2008, and completed in November, 2009. The pre-service teachers
were free to decide how many reflections to write. The collected reflections varied from 7 to
12.
3. Three interviews were conducted with the pre-service teachers. Duration of the interviews
was between 30 minutes to 50 minutes. The first one was completed at the first weeks of the
acting course in September, 2008. The second interview was made at the end of the course in
January, 2009. The third was carried out at the end of the teaching practicum in December,
2009. All interviews were audio taped and transcribed verbatim.
4. The researcher observed the acting course regularly and took notes for his research journal.
During the study, the researcher interacted with the participants in the interviews.
Data Analysis
Data analysis started from the first interviews so that the possible problems that pre-service teachers
might encounter could be anticipated before the course begun. Then the reflections and session
journals of each week were analyzed so as to observe whether the presumed stages of the BEING
model were applicable and feasible in terms of the natural professional identity development of the
pre-service teachers. Constant-comparative method, which is derived from grounded theory (Glaser
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and Strauss, 1967), was used in analyzing the data. Also another researcher analyzed the data in
terms of the proposed thematic categorization (The BEING model) and confirmed the reliability with a
97%.
The identified categories which are based on the theory of Stanislavski were: believe, experiment,
invent, navigate and generate (Tables 1 and 2). While all categories were highly parallel with the actor
preparation stages of Stanislavski (1949), “navigate” was added by the researcher to place the data
that relates to the problem solving strategies of the pre-service teachers during the process of
rehearsing their professional identities.
Results and Discussion
The Designed Categories
The first category, Believe, refers to the data that was collected when three pre-service teachers
carried out “emotional preparation” activities in which they were simply asked to analyze themselves
and to identify an ideal professional identity that they want to become and accordingly rehearse in the
acting course and other methodology courses. The second category, Experiment, refers to the data
that was collected during the acting activities that were conducted in the course. These activities
aimed to strengthen the body language, voice control and sensory awareness of the pre-service
teachers. In the third category, Invent, the participants were asked to find out their way of teaching
which they were to display with various gestures, mimics and nonverbal communication patterns that
are unique to them. In addition to the written data that were gathered from reflections and session
journals, the observation of the researcher and the trainer were also used to verify the self-reporting
of the pre-service teachers in this stage. The fourth category, Navigate, refers to the problem-solving
strategies that pre-service teachers employed during the acting course. They were asked to identify
the actual obstacle in their pursuit of constructing their professional identity and to overcome it
through various actions that were decided by peers and the trainer. While these four categorizations
were mostly constructed during the first phase of the research, which was the 14-week course period,
the data that relate to the last category, Generate, was analyzed and categorized during the other
methodology courses and teaching practicum between the January and December, 2009. The
category generate refers to the core of the identity and to the repertoire of certain verbal, nonverbal
communication strategies, inner and outer observation skills, gestures, mimics and improvisation
techniques that reflect the unique identity of each pre-service teachers and were created during the
acting course and aftermath. The following sections discuss the findings in terms of the categories of
the BEING Model in parallel. In these sections, the categories are addressed as stages.
Experiences of the Three Pre-service Teachers during and after Acting Course
All of the pre-service teachers reported that the idea of rehearsing their ideal teacher identities and
working on them provided new and uncharted thinking territories for them. According to Ceren, the
idea of distinction between personal and professional identity was a revolutionary one. She reported
that:
“I had never thought about developing a teacher identity, nor had I known something like that.
However, judging by the teaching of our professors, I can see that they are actually acting out a
professional self. For instance, Dr. […] is very active and funny in young learners course, but when
lecturing a theoretical course, he adopts a different role” (Reflection).
Developing a professional identity is a natural and expected process for all fields. However, this
process can be more successful if pre-service teachers are given opportunities to ponder over and
study on it. In this respect, three pre-service teachers were quite excited and interested in the idea of
identifying the territory and dynamics of their own teacher identities from the first hour of the acting
course. During the first three weeks of the course, emotional preparation activities, which were
designed to help pre-service teachers decide on their identities, enabled them to set up achievable
goals for the following acting activities in the course. Cem told that:
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“The first weeks of the course was quite important for me since I was more conscious in acting and
improvisation activities. I mean I knew what I was doing, why I was performing all that activities. It
was all kind of experiments to reach my ideal teacher self” (Second interview).
In the following weeks of the course, the pre-service teachers were introduced to various aspects of
acting, such as body language, voice control, the use of setting and atmosphere control, and
manipulation. After they had completed these fundamentals of acting, the pre-service teachers
focused on certain rehearsals of their teacher identities in various tasks and activities. The last step of
these tasks and activities were completed after the course when the pre-service teachers began to
teach in their teaching practicum, which is categorized in the stage ‘generate’. The objectives of these
activities are presented in Table 1.
During these activities, the pre-service teachers noted that they were able to see how much of their
objectives were achievable and doable throughout these activities. They also accentuated that during
the course, they discovered many aspects of their both personal and professional identities. Remarks
of Ece on this issue are quite important, as follows:
“At first, I really felt nervous about the course, but the emotional activities helped a lot to
overcome my anxiety. It is interesting that the teacher identity I identified was quite a modest and
honestly an ordinary one. Of course I realized it after I saw that I was actually better in observing
myself and others so as to change the atmosphere in the classroom, or in finding gestures and
mimics that are unique to me” (Second Interview).
Table 1. Course Content of the BEING Model
STAGES OF
THE BEING
MODEL
BELIEVE
TYPE OF ACTING
ACTIVITIES
OBJECTIVES OF ACTING ACTIVITIES
Emotional preparation.
Analyzing the personal
resources.
Stating or finding out why to become a teacher:
what is my mission as a teacher?
Observing and analyzing emotions that relate to
teaching performance.
Finding out personal concerns concerning becoming
a teacher.
Identifying the characteristics of the professional
identity.
Finding out personal resources, skills and
knowledge to support the construction of the
professional identity.
EXPERIMENT
Body language, Voice,
Sensory awareness
Acting tasks and activities on using body language,
voice and sensory awareness.
Improvisations on using space, setting and
communication.
Analyzing nonverbal communication patterns of the
self and others.
Practicing nonverbal immediate behavior.
INVENT
Body language, Voice,
Sensory awareness
Observing the existing atmosphere of the classroom
and giving some attempts to manipulate it to create
the target atmosphere.
Practicing personal gestures, mimics and postures
as well as nonverbal communication patterns that
are unique to oneself.
Doing general acting exercises to construct
automatic and habitual reactions deliberately.
NAVIGATE
Establishing new thinking
dispositions, Problem solving,
Rethinking the objectives
Overcoming the problems that emerge in the
previous stages.
Pondering over the missing links of the professional
identity and referring to the previous stages to find
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STAGES OF
THE BEING
MODEL
TYPE OF ACTING
ACTIVITIES
OBJECTIVES OF ACTING ACTIVITIES
a solution.
Evaluating constructed teacher identity in terms of
the first stage.
Discovering the uncharted territories of the teacher
identity: is it really like what it was planned before?
GENERATE
Construction of teacher
identity
Performing the teacher identity in micro and macro
teaching demonstrations.
Performing the teacher identity in the practicum,
the real classroom context.
Creating further ways of interactional expression.
Observing the change in teacher identity in different
classes and teaching contexts.
Deciding on what to do next to invest in the
development process of the teacher identity.
Believe: Exploring the Territories and Borders of Teacher Identity
In the beginning of the course, the pre-service teachers were curious about the content. As the weeks
pass, they began to understand that the course was not a kind of ‘show-like’ course in which they will
learn how to act, but truly an actor/teacher preparation course through which they were expected to
question their missions, their ideals, thoughts and emotions about becoming a teacher. Only then the
regular acting activities were presented to them so that these pre-service teachers had a real purpose
for putting forth their efforts and energy wholeheartedly. Besides construction of an identity, whether
in theatre for artistic purposes or in teacher education, requires a lot of thinking about personal
resources, abilities, motivations and feelings in order that the constructed identity could be a
believable and an authentic one. Stanislavski (1949) advocates that no verbal and nonverbal
messages will be convincing and believable if they are not accompanied by corresponding feelings.
Therefore, the first three weeks were mainly designated for materializing this purpose, which is also
the first stage of the model (Believe).
Ceren was an open-minded person. She could easily find creative and innovative ways of expressing
herself. Her process of emotional preparation was mostly based on shaping her ideals that relate to
becoming an effective teacher. She repeatedly noted in her reflections that her ideal teacher identity
was such an influential one that it was hardly possible to reach that level. However, she was told that
the aim of the course was not to construct perfect teacher identities in couple of years, but to
construct the core and the thinking dispositions of a flexible teacher identity which can be developed
in some years and updated autonomously by her. Ceren responded positively to this feedback and
presented an objective of teacher identity which is close to her way of thinking and life. Her reactions
were actually inspiring for the rest of the classroom because she unconsciously led her peers to
ponder over their teacher identities, instead of offering some objectives which are quickly decided and
quite artificial.
On the other hand, Ece was an introverted person who is quite and composed in the classroom.
Selfless and naïve as a young woman, Ece displayed a lot of doubts and concerns about studying her
teacher identity. Ece used to believe that it was impossible to stand in front of students and teach
them English. We decided to give her extra out-side-the-class tasks which aided her to think about the
source of her fear. She cooperated with us and shared some of her experiences of presentations and
demonstrations in secondary school, where she had been scolded by the teacher quite harshly. I
offered a drama activity for her in which the same case would be dramatized by her and later she
would share what she felt. In her reflection, Ece reported that “I have never talked to a teacher that
way before, but this time I warned a professor!” (Reflection).
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Cem has always presented a social but controlled character in the course. His process of deciding on a
teacher identity was also a pursuit of finding out his reason to become a teacher and the meaning of
this profession in his life. His dream was to be an influential and a respected teacher who is
knowledgeable and consistent. Cem also reflected a lot about the differences between his personal
and professional identities. He even prepared a list, which he called “Me Versus Me” list, in which he
stated the similarities and differences between his teacher identity and personal identity. His remarks
on his professional identity and acting are quite interesting:
“The BEING a respected and a consistent teacher is not only a matter of the BEING able to use
my voice and body language effectively. However, when I taught in the practicum, I was amazed
to see that it was the acting skills that helped me perform my methodology knowledge” (Third
interview).
Experiment: Finding out Unique Ways of Oral and Bodily Expression
The second stage, Experiment, was literally the stage in which participants learned about main tenets
of acting and practiced many different acting tasks, activities and improvisations. The first acting
exercises were mostly detached from English language teaching (ELT) methodology and their teacher
identity. Following acting activities were related with ELT context so that participants were able to do
a lot of experiments on their professional identities. Some of the activities focused on nonverbal
communication and nonverbal immediacy. Others provided a context in which the participants were
able to analyze and practice their teaching styles and strategies in parallel with acting techniques. In
addition to classroom work, many pair and group tasks were assigned to them so that they were able
to do more acting exercises outside the classroom. They were told to ground their performances on
an argument when doing all the activities. Our argument was the idea of doing a lot of experiments
on the construction of their teacher identity.
The experiments of Ceren were successful. She discovered various nonverbal devices and patterns
that were practical and helpful in her teaching attempts. In addition to these patterns, she displayed a
significant improvement in her observation skills. In one of her session journals, she gave us a
valuable reflection, “When someone teaches, I can observe them successfully. But it is not that easy
to observe myself when doing a performance. As I do practices, I can see that I can observe myself in
my demos [micro teachings] more effectively.” Ceren simply mentioned the differences between
regular observation and ‘observation in-action’. Actually this is not a problem that only Ceren
experienced, but a natural process of learning to act.
Ece also went through a successful experimental stage, in which she was able to try a lot of dramatic
devices in both acting course and methodology courses. In her words, “It was like trying many
different clothes and finding the best dresses in a nice department store” (Second interview). In this
stage, Ece repeatedly wrote about her ideas on self-observation. She believed that her success as a
teacher depended on her ability to observe her mood and nonverbal communication style. As an
introverted person who most probably has a high intrapersonal intelligence, she diagnosed herself
quite carefully and reflected on her experience. “Learning acting has become even more exciting for
me since I can see that I observe myself consciously, not only in classroom but everywhere, even
when I talk with someone at the bus stop” (Reflection).
In this stage, Cem reflected on his experience in terms of the discoveries he made concerning his
body language and voice. “Each and every acting task has made me reveal a different way of figuring
out the nature of my communication. I think these discoveries will help me make right choices of body
language and voice in teaching” (Reflection). He also reported the impact of acting course in his daily
life. Cem believed that learning to act is not only doing a lot of tasks and improvisations but also to
pondering over it and doing experiments wherever and whenever possible. “I sometimes change my
mood and behave differently in different places, like in shopping, to see whether I am convincing or,
or just acting naturally” (Second interview).
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INVENT: Discovering the Instruments of Expressing Themselves through Dramatic
Devices
The third stage was a transitional one, in which participants were expected to associate their acting
knowledge and skills with general teaching skills and teaching English. During this stage, regular
acting activities were conducted in parallel with more complicated assignments such as performing
short plays, analyzing micro teachings on video and doing certain rehearsals of personal teaching
styles. In addition to these assignments, pre-service teachers were also expected to perform more
practices on observing, analyzing and manipulating classroom atmosphere. The BEING able to analyze
and manipulate classroom atmosphere was central to the studies in the phase invent because the preservice teachers could only display their performance skills by creating a strong bonds of
communication and interaction with the students they teach. Otherwise, the acting course provided
for these per-service teachers may turn into a drama course in which pre-service teachers could
possibly focus on their own performance without thinking about any interaction with the students.
Therefore, the idea of analyzing and manipulating classroom atmosphere was our focus throughout
this phase (Figure 1). This idea also enriched the experiences of the pre-service teachers in that it
provided a context, and a purpose, for doing certain rehearsals on general acting skills and on their
unique teacher identities.
EXISTING
ATMOSPHERE
•Shaped by general
and daily variables
TEACHER'S
OBSERVATION AND
MANIPULATION
•Making right
choices of context
and dramatic
devices
TARGET ATMOSPHERE
• The result of
teacher's
manipulation via
dramatic devices
Figure 1. Phases of Classroom Atmosphere Control by an Acting Teacher
The third phase enabled Ceren to expand her horizons in terms of teaching and acting beyond her
recognition. She even reflected on the first phase, Believe, and made some adjustments in her
teacher identity by adding more specific objectives. Most of her inventions in terms of nonverbal
communication devices, gestures, mimics and so on were quite creative and unique to her. In this
stage, she also tried hard to make discriminations between her teacher identity and other influences
such as her primary and secondary school teachers, even professors. Although the trainer advised her
that she did not have to make such a distinction if the models were beneficial for her. However, Ceren
noted that she wanted to do it so that she could control her verbal and nonverbal communication
skills more consciously.
After taking active part in many acting activities, Ece begun to create her own way of communicating
nonverbally and show some evidence of her control over her body language and voice. While she did
not develop her voice significantly in the last five weeks, which is quite acceptable, Ece was able to
make creative inventions of dramatic devices which made her feel comfortable in both acting activities
and other demonstrations that they performed in methodology courses. “I feel safer when I know
where to put my hand, or simply how to walk in the classroom and monitor students. The feeling
confident enabled me to focus on methodological aspect of my teaching performance” (Second
interview). Although she kept complaining about weakness of her voice, Ece provided us with a
valuable feedback on her development by reporting that “I still need lots of practice for strengthening
my voice. However, I realized that even if my voice is not that strong, I can still control the classroom
by teaching at a high level of energy, with an enthusiasm” (Reflection). Her observation reminds us of
the studies of Tauber and Mester (2007), who claimed that use of dramatic devices and knowledge of
acting contributes to teaching performance in terms of enthusiasm.
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The success and applicability of a theoretical model is surely based on whether its stages are in
parallel with the natural development of the phenomena. In our case, the BEING model should be
offering a set of phases that reflects and fits to the actual reality. In this respect, Cem’s reflections in
the Invent stage are very significant. Cem believed that finding out some personal dramatic devices or
creating a way of acting the professional self is nothing but a natural process. “For me, this process
[referring to invent stage] was full of discoveries and creations of my acting self. It is like learning to
swim or ride bicycle; you never forgot them (Third interview).
Cem’s insights and reflections as a novice were impressing because he gave us adequate feedback on
not only the applicability of the BEING model but also on the structure and content of the syllabus
that had been prepared in parallel with the five phases of our model. In his reflections, he also noted
that “I think my body has a memory, too, because once I acquire a dramatic device, or any technique
of using my body language, I never forget them. And during a teaching performance, they all activate
the moment I need them.”
NAVIGATE: Breaking through the Problems and Obstacles
As was mentioned, this stage of identity construction is not directly related with the acting method of
Stanislavski. However, it is crucially important to leave room for the problems that emerge during the
preparation period and rehearsals of teacher identities and guide pre-service teachers to find solutions
for the probable obstacles. Navigate stage is also a point of meta-cognitive reflection about the
objectives of the pre-service teachers. Some of the pre-service teachers did better than they
imagined, and conversely, some did not achieve what they identified. Therefore, this stage enabled
them to think and talk about their experience to address such concerns and occurrences.
Ceren was among the few students who went through this process smoothly and rapidly. She had
already made some adjustments in her objectives that she identified in the stage believe. However,
Ceren reflected on her concerns to become a teacher quite frequently in her written reflections and in
the classroom tasks and discussions. “I can really see the improvement in my teaching skills in this
course. But I sometimes feel nervous when thinking about my professional career. Will I be able to
become a good teacher?” (Reflection). Her concerns were actually quite understandable because her
aim was to become an influential teacher. We interpret her concerns like the feeling of anxiety that
actors feel just before the play night. Ceren shared these concerns when the course was about to be
completed. In the following semester (2009 spring), they were observed in their other methodology
courses and they kept writing reflections on their developments. However, when they began to teach
in the real classroom setting (2009 fall), I felt a need for reminding Ceren her concern and ask her
whether she thought the same way. She responded that “No, I don’t think the same way! After some
teaching attempts, I felt better and every week I felt stronger as a teacher and tried many of my
dramatic devices and other patterns that I invented in acting course (Third interview).
Ece felt a need for overcoming her anxiety of being in front of people. While she reported that the
drama course helped her to feel more confident in her teaching demonstrations, she also believed that
her anxiety problem was an obstacle for performing her acting skills. Therefore, in the navigate stage,
Ece asked for more responsibilities in the drama activities. She took part in nearly all drama activities,
and assisted the groups who need extra participant. Later, Ece noted that “Drama activities made me
feel better. I just tried to stand in front of the classroom because sitting and watching teachers and
peers have not helped me for years” (Second interview). Ece also mentioned that she voluntarily
presented assignments with her friends in different courses.
Cem claimed he focused on his performance to such an extent that he sometimes forgot to observe
the classroom. He specifically mentioned that “When I cannot make effective observations, I cannot
manipulate the classroom atmosphere spontaneously” (Reflection). He was advised to keep doing
acting activities and not to forget this important point when teaching in the classroom. Throughout a
whole year, Cem displayed a significant improvement in his observational skills. “Well, it is all about
automaticity. Just like learning a language. When the dramatic devices became a part of me, I was
then able to give extra attention to the interaction in the classroom” (Third interview).
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GENERATE: Stretching the Boundaries of the Teacher Identity in the Real Classroom
Context
The stage ‘Generate’ is a product as well as a process. It is a product because it is what we want to
achieve. It is also a process due to the flexible and dynamic nature of the phenomena, which it is
called professional or teacher identity. It surely takes years to construct the whole dispositions and
actions of the teaching-self. However, the stage generate refers to the state in which pre-service
teachers and novices have constructed the core of their identities and major professional thinking
dispositions. Stanislavski (1949, 1972) repeatedly mentions that superficial aspects of a role do not
have to be necessarily acquired, because once the core of the character is developed, the details of
the role emerge instinctively. In this respect, this stage constitutes the core of the professional
identity.
At the end of the acting course, most of the work concerning the previous four stages was completed.
Also, the pre-service teachers practiced many tasks on the stage ‘generate’. However, after the
completion of the first phase of the research, the pre-service teachers were observed in the following
two semesters in methodology courses and in the practicum to see how they experienced the impact
of the acting course and the development process of their professional identity. I observed many
significant developments of their teacher identities specifically in the practicum phase, during which
the pre-service teachers taught in real classrooms. They unanimously reported the fact that after they
saw how useful the acting skills were in the real classroom setting, they began to feel confident.
Does the BEING Model Really Work?
On the one hand, it is quite easy to say ‘Yes!’ because we know that acting methods contribute
significantly to the education of teachers. On the other hand, that is a hard question to answer. It is a
fact that more studies, especially in different countries, should be conducted to see effectiveness and
applicability of the BEING Model in developing professional identity. We experienced many different
problems and situations that we did not even think about before the research study. I am sure any
application of this research study will bring different problems in different settings. However, it is our
conclusion that the BEING Model provides pre-service teachers with valuable stages of identity
construction. Figure 2 describes visually how these stages are interrelated in the acting course for
pre-service teachers. The first three stages are cyclical in that any problem that hinders the
generation of certain aspects of teacher identity is handled in this cyclical process. Therefore, the
stage navigate is also a meta-cognitive thinking and problem solving process, the results of which are
so step back to the previous stages and do the necessary tasks and exercises.
Figure 2. The BEING Model in Action
It is a fact that pre-service teachers go through an education which requires a transformation of their
various social identities. While it is commonly accepted that transformation is the heart of all
educational activities (Griggs, 2001), the transformation of a pre-service teacher requires more
challenging tasks in that an effective teacher is known to display a strong teacher identity. “Student
teachers must undergo a shift in identity as they move through programs of teacher education and
assume positions as teachers in today’s challenging school contexts” (Beauchamp and Thomas, 2009,
p. 175). In this respect, an acting course does not only provide pre-service teachers with the
opportunity of practicing basic acting skills but also creates a context in which pre-service teachers
see themselves as teacher candidates working on their professional identities. In doing so, The BEING
model facilitates the application of different syllabuses of acting course and enables pre-service
teachers to see where they are in this journey. The categorization of the data given in Table 2 also
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shows the stages that pre-service teachers went through and roles of the trainer during the
application of the acting course.
Table 2. Developmental Stages of the BEING Model
STAGES OF
THE BEING MODEL
EXPECTED ATTITIDES OF THE
PRE-SERVICE TEACHERS
ROLES OF THE TRAINER
BELIEVE
Identifying an identity which one
wishes to become
Giving feedback for emotional
preparation
EXPERIMENT
Creating own version of the role
Monitoring and eliciting rehearsed
identity
INVENT
Analyzing oneself carefully to discover
required qualities
Shaping the identities by reflections
and feedback
NAVIGATE
Rehearsals in a practical situation
Providing group discussions and
feedback for problem solving
GENERATE
Constructing a flexible, democratic
teacher identity that is open to
change and innovation.
Feedback for identity that is
developed, and identifying personal
dispositions.
Do teacher education programs provide a context in which teacher candidates acquire the deeper
structures of their teacher identities? Have our graduates really developed strong professional
identities so that they can carry what is academic and methodological into their teaching context? The
answers will vary depending on the country, system of education and so forth. However, one universal
answer may be found in benefiting from acting literature to help pre-service teachers develop their
core of teacher identities. In this respect, the BEING model was found to provide certain sound stages
of rehearsing teacher identity in an acting course for teachers and in the following teaching practicum.
Conclusion
This research study shows how, through the BEING Model, the development process of professional
identity in pre-service teacher education is facilitated in an acting course designed for teachers. The
BEING Model aims to assist trainers to sequence the acting activities, monitor the developmental
stages of preparation of a role in teacher education, do the correct manipulations when and where
necessary and impose the idea of rehearsing the professional identity by referring to personal
missions, resources and skills. The data analysis displayed how this model worked in the professional
development of three pre-service teachers. The stages of the model were in parallel with the
theoretical framework of Stanislavski.
In this final section, I will discuss the place of the BEING model and the acting course in a typical
English pre-service program. Is it a luxury to design yet another course and find trainers who are
able to teach acting to teacher trainers? The results of this research study show that it is not. The
ongoing debate about focusing on personal growth or competences of pre-service teachers in teacher
education (Meijer, Korthagen & Vasalos, 2009) is also a discussion of our approach to educating
young people to become teachers. There are surely certain competences that pre-service teachers
should acquire so as to become effective teachers. However, Danielewicz (2001) believes that it is not
the methodology that makes someone an effective teacher, but “it requires an engagement with
identity, the way individuals conceive of themselves so that teaching is a state of the BEING”
(Danielewicz, 2001, p.3). There are also some variables that are critical for using these competences
in classrooms. Surely these variables are based on the state of a new self and another way of the
BEING. Whether we accept or deny it, the process of becoming a teacher is also a process of personal
growth.
Therefore, incorporation of acting methods into teacher education is also a pursuit of leading preservice teachers to acquire the professional teaching competences and associate the professional
knowledge with the personal one. Meijer et al. (2009) found out that “Paying attention to the
connection of the personal and the professional in teaching and teacher education may contribute to
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educational goals that go far beyond the development of the individual teacher” (p. 308). In this
respect, in addition to the critical competences of effective teachers like awareness in nonverbal
communication and use of dramatic devices to shape classroom atmosphere, the model I proposed
also aims at integrating the professional thinking dispositions and habits with the process of personal
growth.
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