THE NOTION OF NETWORKING: THE FUSION OF THE PUBLIC AND PRIVATE COMPONENTS OF TEACHERS’ PROFESSIONAL DEVELOPMENT

   Thomas J. Cooney                                                                Konrad Krainer

University of Georgia                                                    University of Klagenfurt / IFF

tcooney@coe.uga.edu                                                  konrad.krainer@uni-klu.ac.at

 

Abstract:  Krainer’s (1999) story of Gisela depicts an individual whose early teaching experiences in the Austrian schools were marked by isolation.  Krainer’s analysis involved the notions of action, reflection, autonomy, and networking as these constructs apply to an individual working cooperatively with critical friends who discuss problems they encounter in their classrooms.  Gisela’s story is about an individual working in a community of professionals.  But the story is also about Gisela’s individual propensities that can be characterized by a scheme developed by Cooney, Shealy, and Arvold (1998).  In an effort to fold these two theoretical perspectives together, the authors introduce the notions of horizontal and vertical networking to capture socialization processes that also honor an individual’s ability to reflect and adapt.  Other research on teacher change is also considered.

 

 Perhaps at no time in the history of research in mathematics education has there been such an emphasis on the professional development of teachers.  We now see teachers as cognizing agents whose beliefs and knowledge are recognized as an essential and contributing determinant to what gets learned in classrooms.  In this paper we present the case of Gisela and analyze her professional development through various lenses in an effort to further our understanding of teachers’ professional development more generally.  We begin with a brief glimpse of Gisela’s journey. 

Gisela’s Professional Journey

Gisela entered the teaching profession in 1971 as a mathematics and geography teacher in the Austrian schools having supported her university studies by giving private lessons.  Her studies were primarily subject matter oriented with minimal attention on how to teach mathematics.  The culture of the university and its emphasis on scholarship had a significant impact on Gisela’s orientation toward teaching.  She described her early years of teaching mathematics as traditional and isolated in that teachers rarely discussed problems they encountered in their classrooms.

In 1985, Gisela became interested in a series of professional development seminars in which teachers engaged in various sorts of research activities aimed at improving their teaching.  In 1989 Gisela moved to a new high school with a small mathematics faculty but in which communication among colleagues was encouraged.  Two years later Gisela assumed administrative responsibilities in addition to her teaching responsibilities.  Since 1995 Gisela has actively promoted professional development activities among her growing mathematics faculty.  Most of the professional seminars were conducted by the second author.   (See Krainer, 1999)


Gisela’s Individuality

Gisela’s journey was influenced by several factors.  She was motivated to take advantage of the professional development programs supported by the Austrian Ministry of Education in an effort to improve the teaching of mathematics.  She welcomed the opportunity to interact with other ”critical friends” (Krainer, 1998) and to diminish the extensive isolation she had experienced in her early days of teaching.   Krainer’s (1999) analysis of the case of Gisela is predicated on four dimensions: action, reflection, autonomy, and networking.  These dimensions are defined in the following way.

Action:  The attitude towards, and competence in, experimental, constructive and goal-directed work.

Reflection: The attitude towards, and competence in, self-analysis and one’s ability to reflect on his/her actions.

Autonomy:  The attitude towards, and competence in, self-initiating, self-organized and self-determined work.

Networking:  The attitude towards, and competence in, communicative and co-operative work with increasing public relevance.  (Krainer, 1994)

These four dimensions provide a basis for describing ways that teachers develop within a group setting in which critical friends assist in analyzing and reflecting on each other’s lessons (Krainer & Goffree, 1999).  Imagine a teacher who works in isolation to realize his/her individual goals.  But then imagine that the teacher is challenged to reflect on his/her actions and to share his/her individual experiences and beliefs with other colleagues in an effort to explore alternative methods of teaching.  That transition is indicative of Gisela’s professional experience.  Reflecting and networking are fundamental precepts of Krainer’s professional development programs but they are not necessarily part and parcel of teachers’ experiences.  The notion of autonomy can be conceived in two different ways. On the one hand, autonomy can be a limiting factor in a teacher’s ability to reflect and network if the teacher insists on ”going it alone” rather than working in concert with colleagues.  On the other hand, the individual’s efforts to reform must necessarily be self-initiated and self-sustained. Gisela’s early teaching experience could be described as almost completely autonomous in an isolated way.  Although she was probably reflective in those early years, circumstances prevented her from networking with other teachers and benefiting from their insights. 

What was there about Gisela that enabled her to develop professionally when other teachers in the Austrian system were much more inclined to isolate themselves?  To account for Gisela’s individual propensity to reflect, adapt, and grow professionally, we can turn to the scheme developed by Cooney, Shealy, and Arvold (1998).  This scheme consists of four positions that describe a teacher’s way of knowing. Fundamental to this scheme is an individual’s orientation toward seeing authority as the ultimate determiner of truth. 

Isolationist:  An individual who tends to have beliefs structured in such a way that beliefs remain separated or clustered.  Evidence exists of closed-mindedness.

Naïve idealist: An individual who tends to be a received knower in that he/she absorbs what others believe to be the case but without critical analysis.

Naïve Connectionist:  An individual who realizes conflict or differences in beliefs between him/herself and others but fails to resolve or account for those differences.

Reflective Connectionist:  An individual who realizes conflict or differences among beliefs and who attempts to resolve these differences through reflection and critical analysis.

These four positions provide a means of conceptualizing the structure of teachers’ beliefs and their potential for reforming beliefs and practice.  Interestingly, Krainer keyed on Gisela’s unhappiness with being a ”lone fighter” and her sense of isolated autonomy, precepts that are fundamental to Cooney, et al.’s scheme as well.  Gisela’s propensity to reflect and to make connections with critical friends are trademarks that characterize the position of a reflective connectionist.  Had Gisela not been a reflective connectionist, perhaps she would not have overcome the isolated autonomy that characterized her early years of teaching. Thus, reflecting and networking are fundamental precepts both of Krainer’s dimensions of professional development, and of Cooney et al.’s stages of professional growth. In the following, we mainly focus on the notion of networking, differentiating between horizontal and vertical networking.

The Notion of Networking

Generally speaking, it is quite natural for people to network in the sense of forming communities.  We can envision two ways in which this networking occurs.  To use the metaphor of tree, one can conceive of networking in which the roots of the tree network in a horizontal way, perhaps spreading widely but not deeply.   The roots of a pine tree come to mind.  One can also imagine a different type of networking in which the roots develop more vertically but not necessarily as much horizontally as, for example, with a fir tree.  What seems obvious is that some kind of networking is necessary in order for the organism to survive and thrive.  We examine each of these kinds of networking.

 

 

Horizontal Networking

Horizontal networking is common among a considerable number of teachers as they strive to form relationships with like-minded peers.  The commonality may be an interest in school affairs, technology, or other facets of school life.  This is a powerful kind of networking as mutual interests are shared and individuals strive to become critical friends.  Gisela demonstrated this kind of networking when she became an administrator at her school and wanted the entire mathematics faculty to become a community as they engaged ideas of reform.  Although originally skeptical, the teachers found the seminars invigorating and profitable.  They were surprised that their colleagues could offer so many insights about teaching and learning, insights that they had not considered (Krainer, 1999).  In some cases, their horizontal networking developed into vertical networking, e.g., when they began to question their traditional approach to assessment  Some teachers, however, honored their colleagues’ views in a reflective way, but provided no strong evidence that they connected those views intensively to their own teaching. In a sense, they demonstrated a form of naïve connectionism.  The group as a whole showed a general tendency of increased reflection and networking, and a movement from naive to reflective connectionism.  There were, however, obvious differences among individuals.

Even for Gisela, there was some pain involved in the process of sharing.  In one of the seminars the group decided to investigate what their students believed about mathematics.  Subsequently, students in a class taught by Gisela were asked to draw a picture and provide a brief explanation of the picture.  One of Gisela’s 17 year-old female students drew a picture of a thick book with a locked clasp and called it the ”The Great Book of Mathematics.” She added the caption:  Where is the key?  She provided the following explanation (translated from German):  ”The sealed, closed book is not accessible to all.  It is only possible to open the book with the key.  But even when the book is open one may not understand the content.  You either understand it or not!  In order to understand it, you have to read it from beginning to end.”  Gisela appreciated the student’s creativity yet was upset that a student in her class held such a view.  It was a rather painful experience for Gisela but, nonetheless, it opened her eyes as to what her students were thinking about mathematics.  In this case it would have been easy for Gisela, who doubled as a school administrator as well as a mathematics teacher, to withdraw from the community and resort to a kind of vertical networking void of sharing experiences with others. Individuals who share their challenges with others not only increase their own capacity for dealing with these challenges but also contribute to the learning of others. Thus, horizontal networking is an important characteristic of a reflective connectionist and a good starting point for vertical networking.

Vertical Networking

Vertical networking involves accommodation and a certain willingness to change and adapt one’s teaching.  It is the second defining characteristic of the reflective connectionist.  Vertical networking can be difficult and tension-filled.  The fact that Gisela dwelled on the student’s drawing suggests that she reflected on the significance of the girl’s response and found that reflection to be somewhat painful.  It would have been easier for her to reject the girl’s view as idiosyncratic.  Rather, Gisela probed her own consciousness for how she might have contributed to that girl’s meaning.  The act of reflecting is not always a pleasant experience if it brings to the forefront the essence and consequences of what one believes. It is obvious that someone who seriously reflects on his/her own practice has a better starting point for learning from reflections of other people and to contribute to their learning. Thus, horizontal and vertical networking are closely interconnected, in sum being the characteristic of a reflective connectionist.

The case of Sue (Cooney, 1994) illustrates vertical networking quite dramatically.  Her view of teaching mathematics was shaken and then reconstructed during her graduate program.  She then attempted through horizontal networking to influence her fellow teachers the year following her graduate study.  But they would have none of it, at least initially.  But Sue was committed, stayed the course, and eventually began to influence her colleagues to adopt a more reform-oriented approach to teaching.  For Sue, her propensity to be reflective invigorated her own vertical networking which then lead, eventually, to horizontal networking.

Reflecting on the Notion of Teacher Change

We often wonder how it is that preservice teachers seem so enthusiastic in our methods classes yet demonstrate so little of what they learned during their student teaching.  See, for example, Cooney, Wilson, Chauvot, and Albright (1998). Cooney and Wilson (1995) described two preservice teachers’ beliefs as they progressed through their reform-oriented teacher education program.  Harriet showed evidence of isolationist thinking as it appeared that she did not attend to much of what was emphasized in her teacher education program.  Kyle, on the other hand, did attend to the inquiry orientation of his program but failed to resolve differences between his beliefs and his experiences as a first year teacher.  The analysis provided by Cooney, Shealy, and Arvold (1998) provides a theoretically descriptive account for how teachers like Harriet and Kyle make sense of their individual worlds.  What is perhaps missing from this analysis is attention to the powerful horizontal networking that the teachers experienced during their teacher education program.  Even an isolationist like Harriet defined her being in terms of the group:  She knew how to teach, the others did not. 

The situation with preservice teachers is often mirrored with inservice teachers.  For example, Mr. Burt (Wilson and Goldenberg, 1998), a middle school teacher, accepted certain tenets of reform but only in rather transparent ways.  He was interested in networking with others in the sense of sharing ideas about reform but failed to incorporate them in fundamental ways into his teaching. Jaworski’s (1998) research on the development of teaching which that involves teachers in cycles of reflective activity suggests that teachers can engage in vertical networking but, perhaps, only when accompanied with substantial horizontal networking with critical friends. However, we also have cases of teachers who show deep reflections on their own teaching, being convinced of their personal approach, but who have tremendous problems in making their approach understandable to other colleagues.  Consequently, they often remain isolated and have little or no impact on the professional development of others.

Could it be that horizontal networking is a precondition for vertical networking?  Or is it the case that vertical networking is a precondition for horizontal networking?  Or is each a precondition for the other?  The strength of Gisela’s reflective connectionist orientation seems to confirm the latter hypothesis.  What is clear is that teachers need some kind of networking.  Unlike trees, people can consciously select and promote both kinds of networking.  The problem occurs when people rely too much on only one kind of networking.  Horizontal networking provides the community that is so vital yet so often missing with teachers.  Yet, like pine trees, when the brutal winds of public opinion or controversy over reform occur, the pines usually fall from want of deeper roots.  Gisela had deep roots.  Consequently, she had the strength to persevere even in the face of disinterest or when faced with the unpleasant evidence that her students had not perceived mathematics in the way she had hoped.  Fir trees usually remain standing tall in stormy times. But this characteristic, applied to people, can be limiting if the result is a certain intransigence in which the individual chooses to isolate him/herself from the system as a whole.  Let us find ways to promote the kind of networking that allows teachers to develop the strength to stand tall with their own philosophy of teaching rooted in the evidence of student learning, but at the same time to share their actions and reflections with others in order to learn from them, and, equally important, to give others the chance to learn from them.  Teacher educators and researchers play an important role in this process. On the one hand, we have to foster teachers’ struggle for reflection and (horizontal and vertical) networking.  On the other hand, we have to increase our own reflection and networking on teacher education, as a field of both practice and inquiry.

References

Cooney, T. (1994).  Inservice programs in mathematics education.  In S. Fitzsimmons & L. Kerpelman (Eds.), Teacher enhancement for elementary and secondary science and mathematics:  Status, issues, and problems. (pp. 8.1-8.33).  Cambridge, MA:  Center for Science and Technology Policy Studies.

Cooney, T., Shealy, B., & Arvold, B. (1998). Conceptualizing belief structures of preservice secondary mathematics teachers. Journal for Research in Mathematics Education, 29, 306-333.

Cooney, T. & Wilson, P. (1995). On the notion of secondary preservice teachers’ ways of knowing mathematics. In Owens, Reed, & Millsaps (Eds.), Proceedings of the 17th PME-NA Annual Meeting (pp. 291-296).   ERIC, Columbus, Ohio: ERIC, pp. 2.91-2.96.

Cooney, T., Wilson, P., Albright, M. & Chauvot, J. (1998). Conceptualizing the professional development of secondary preservice teachers.  Paper presented at the annual meeting of the American Educational Research Association, April 1998, San Diego, CA.

Jaworski, B. (1998).  Mathematics teacher research: Process, practice, and the development of teaching.  Journal of Mathematics Teacher Education,1, 3-31.

Krainer, K. (1994). PFL-Mathematics:  A teacher inservice education course as a contribution to the improvement of professional practice in mathematics instruction. In J. Ponte , J.  & J. Matos, J.  (Eds.), : Proceedings of the 18th PME Annual Meeting, ngVol. 3 (pp. 104-111).. University of Lisboa: Lisboa, Portugal: University of Lisboa. V. 3, 104-111. 

Krainer, K. (1998). Some considerations on problems and perspectives of inservice mathematics teacher education.  In Alsina, et al. (Eds.), 8th ICME:  Selected lectures (pp. 303-321)..  S.A.E.M. Thales; Sevilla, Spain, 303-321: S.A.E.M. Thales.

Krainer, K. (1999). Learning for Gisela: Finding a bridge between classroom development, school development and the development of education systems. In Lin (Ed.), Proceedings of the 1999 International Conference on Mathematics Teacher Education. National Research Council (pp. 76-109)., Taiwan, 76-109.

Krainer, K. & Goffree, G. (Eds.) (1999). Investigations into Teacher Education: Trends, Future Research and Collaboration. On Research in Mathematics Teacher Education. From a Study of Teaching Practices to Issues in Teacher Education (pp. , 223-242). Forschungsinstitut für Mathematikdidaktik, Osnabrücckk, 199.9. Internet: http://www.fmd.uni-osnabrueck.de/ebooks/erme/cerme1-proceedings/cerme1-group3.pdf

Wilson, M. & Goldenberg, M. (1998).  Some conceptions are difficult to  change:   One middle school mathematics teacher’s struggle.  Journal of Mathematics Teacher Education,1, 269-293.