Angela Fatima Guzon
Ateneo de Manila University Debbie Marie Verzosa
Ateneo de Davao University Maria Theresa Fernando Ateneo de Manila University
Abstract. Despite limitations associated with short-term sporadic professional development programs, this kind of training is the dominant model of professional development or in-service training (INSET) in the Philippines.
This paper provides an in-depth account of our experiences as teacher educators as we participated in one three- day INSET program. The objective of this program was to promote pedagogical principles hinged on relational understanding by allowing teachers to reflect on their own practice. This paper aims to investigate the extent to which we were able to communicate pedagogical principles during the INSET, in a way that has potential impact in classrooms. The analysis was framed by Vygotsky’s Zone of Proximal Development (ZPD), in relation to the professional growth of teachers. The data suggests that the design of the INSET training was not aligned with the teacher’s ZPD, thereby limiting the impact of the INSET in the classroom. Instead, focusing on actual classroom needs may actually be more relevant for teachers within a short time frame. Pursuing the more lofty goals of developing content knowledge and transforming pedagogical principles to actual practice can be better realized in more long-term professional development settings.
Keywords: INSET, professional development, zone of proximal development, Valsiner’s zone theory INTRODUCTION
Despite criticisms of short-term in-service training (INSET) programs, it has been the dominant model in the Philippines for at least the past 30 years (Nebres, 2006), and the current infrastructure makes any significant change unlikely. It is thus important to investigate how to facilitate the practical implementation of pedagogical strategies introduced during an INSET program. Consequently, this study aims to determine the extent to which a short-term INSET program can communicate pedagogical principles and transform teaching practice.
This article provides a rich first-hand account of our experiences as teacher educators who participated in such a program. As the authors grappled with the reasons why teachers seemed to find it difficult to relate the INSET to their classroom practice, Vygotsky’s notion of the zone of proximal development (ZPD) emerged.
This realization prompted us to review the literature on ZPD in relation to the growth of teachers. We now describe a “learning-through-teaching process supported by reflective practice” (Llinares & Krainer, p. 447) whereby zone theory was used a framework for interpreting our INSET experience.
ZONE THEORY
Vygotsky emphasized the sociocultural influences on cognitive development. He developed the concept of the Zone of Proximal Development (ZPD) as the region representing the tasks that a learner can perform only through the guidance of a more knowing other. While this framework has traditionally applied to students as learners, more recent work has applied Zone Theory for describing the professional development of teachers (Blanton, Westbrook, & Carter, 2005; Goos, 2008; Warren, Cooper, & Lamb, 2006). These researchers also strengthened the role of social interactions in learning by drawing on Valsiner’s (1997) extension of Vygotsky’s concept of the ZPD.
Valsiner (1997) proposed the Zone of Free Movement (ZFM) and the Zone of Promoted Action (ZPA) as zones representing a learner’s interaction with the environment. The ZFM defines actions that learners are allowed to take while the ZPA represents actions being promoted in order to influence a learner’s actions.
Theoretically, the ZPA must be within the ZFM, and maximum learning occurs when the learner’s ZPD lies within the ZPA.
Researchers contend that an understanding of teachers’ ZFM/ZPA complex can reveal teachers’
capacity for professional development within their ZPD (Blanton et al., 2005; Warren et al., 2006). Using this approach, Blanton and her colleagues observed that a teacher may appear to promote something that they do not actually allow, in which case the ZPA is not within the ZFM. For example, one teacher appeared to promote sense-making but the dominance of procedural short-answer questions she presented left little room for students to do their own thinking. To explain this discrepancy, Blanton et al. propose an Illusionary Zone of Promoted Action (IZ) to represent promoted actions that are in fact not allowed.
A different view is espoused by Warren et al. (2006). In their study, they observed a teacher whose lesson seemed to be conducted primarily in the IZ, prompting them to propose a further zone, the Zone of Survival, present within the IZ. This zone may emerge when a teacher feels unprepared to present and organize the lesson. In this case, the dominance of the IZ places teachers on the spot—their main focus is shifted to
“getting out alive”. They may be able to verbalize desirable teaching practices even when they cannot transform these theories to practice. In this case, the dominance of the IZ is not seen as a potential for development but as an indication that certain aspects of professional development programs may not be within a teacher’s ZPD.
RESEARCH METHODOLOGY
This study was conducted in the context of a three-day INSET program. This INSET program forms part of the annual week-long INSET mandated across all government schools. Such INSET programs are often school-wide. It is not unusual to have teachers across all grade levels and all subjects to participate one general INSET program. However, in this study, funds from a civic organization made it possible to organize a separate INSET for 30 mathematics teachers of Grades 7-10. One author was approached by the organization to provide the training, and the two other authors were invited to help design and implement the program.
The context itself presented several constraints. There was no time for needs assessment, and the program had to cater to participants who were teaching varied mathematics courses. As such, it was not possible to focus on just a single content area or a specific teaching need. Instead, it was decided to offer an INSET with a framework of developing relational understanding (Skemp, 1976) where teachers can be provided with opportunities to reflect on their own practice. The plan was to present general pedagogical principles that can promote relational understanding in the classroom.
The first general principle was the importance of cognitive analysis as a pedagogical tool (Cobb &
Wheatley, 1988). Such a perspective presumes that learners are always rational as they solve problems based on their current level of understanding. Errors then become more than just symptoms of gaps in learning but are also indicators of how learners construct meaning.
The second general principle involved the interrelation of conceptual and procedural knowledge. This has often been a source of conflict among educators. A consensus is that both types of knowledge form important strands of mathematical learning (National Research Council, 2001). In connection, the affordances of multiple representations to communicate conceptual and procedural aspects of mathematics were emphasized.
The structure of the INSET program involved cycles of introductory activities, lectures, and small and whole group discussions of the practical implications of the general principles.
Data Collection
The authors collected a range of data sources, as described below.
Pre- and Post-assessments. The teachers were asked to respond to an assessment of mathematical pedagogical content knowledge (MPCK). The majority of the test items were piloted during a MPCK workshop (Tulao- Fernando, 2010).
Work Samples. Small-group discussions often included a writing component where the teachers synthesized their views on manila paper. These responses, as well as individual reflections on common student errors, were included in the data.
Evaluation Forms. At the end of each day, teachers were asked what they have learned and what questions they might still have. They were also asked to complete an evaluation form at the end of the INSET. This evaluation form included Likert items on the logistics, the INSET facilitators, and the particular activities. Open-ended questions (e.g., which part was most/least useful?) were also included.
Field notes. Immediately after each day of the INSET, the authors discussed and recorded the INSET as it was experienced. The field notes were both descriptive and reflective (Howard, 1995). It contained personal observations and feelings about the INSET.
Audio recordings. Whole-group discussions were audio-recorded and transcribed.
Data Analysis
Responses to the assessments and evaluation forms as well as the work samples were typed and organized on a worksheet. These, together with the field notes and audio recordings made it possible to cross-reference findings and establish triangulation. Using a process of theoretical coding (Auerbach, 2003), each data source was initially scanned to get a sense of the data. During the second reading, the three authors individually identified codes by noting repeating ideas within the data corpus. They met over a series of six months to discuss these repeating ideas, with the goal of identifying a small number of themes and produce a coherent account of the INSET program. Three themes emerged from the data, and have been presented in the results. Supporting evidence from the set of repeating ideas have also been provided, forming a basis for how each theme was generated.
RESULTS AND DISCUSSION
This study aimed to investigate the extent to which a short-term INSET program can communicate pedagogical principles and transform teaching practice. Three themes emerged from the analysis: (1) the difficulty in extending the range of teaching strategies, (2) the incongruence of conceptual and practical tools, and (3) the importance placed on non-cognitive aspects of teaching and learning.
Difficulty in Extending the Range of Teaching Strategies
Most teachers predominantly ascribed to teaching mathematics as a set of rules or procedures. For example, 16 of the 39 responses in the group analysis of student errors and 40 of the 49 responses in the individual analysis indicated that the primary strategy for rectifying errors was to help students recall rules.
Common responses include:
“[I will] explain to the students that when we divide both sides of the inequality by a negative number, the inequality symbol will be changed.”
“I will let the student recall the meaning of the given expression: if there are 2 terms in the denominator, then the denominators should be distributed, applying the simplification, another form of the expression will come up, which is also equivalent to the given expression.”
One of the pre-test items required teachers to discuss how they will correct a common algebraic misconception of adding dissimilar terms. The majority of teachers adhered to the rule of adding similar terms as shown by the following response.
"I will convince the student that 2 and 3x are dissimilar terms and they are not supposed to be added since it violates certain rules in algebra. Explain the rule in adding terms and let him find the correct answer."
Reliance on rules and procedures persisted even after the extensive discussion on instrumental and relational understanding (Skemp, 1986). For example, one teacher shared her strategy for explaining why √20 2√5 and not 4√5 as follows:
“If they are not unique, they’re left inside the house. Four is a perfect square, and if I move it out, it becomes a different person. Something like that.”
Twelve of the thirty teachers utilized rules in correcting students’ misconceptions of certain mathematical concepts. Additionally, giving students many repetitive examples and exercises of the same concept is a common strategy shared by the majority of the teachers.
Teachers valued traditional tasks that can be solved using routine procedures. For example, many teachers found it difficult to modify textbook tasks to make them more open-ended and open for investigation.
During the INSET evaluation, three teachers expressed that “tweaking” textbook questions was not interesting or useful because of the difficulty in doing so and because it was not seen as an urgent need for improving instruction.
By contrast, it was observed that teachers were very engaged as they played a Bingo game that involved solving linear equations. Although the plan was just to show the teachers how the game is played through a few examples, the teachers requested to proceed and actively solved the equations.
The continued reliance on traditional teaching approaches may also be due to certain weaknesses in content knowledge. This was evident in the discussion of the properties of the logarithms, where several teachers expressed confusion among the expressions log ∙ log , log and log . Not surprisingly, these teachers said they would give additional drills and recall rules to assist students who found logarithms confusing.
Gaps Between Conceptual and Practical Knowledge
As mentioned in the methodology, the decision to focus on pedagogical principles rather than specific content stemmed from the fact that the participating teachers were teaching different year levels. The data suggests that the principles discussed during the INSET were well received by the teachers. When teachers were asked to write what they have learned in the end-of-day slips, 16 teachers in Day 1 and 10 teachers in Day 2 clearly identified aspects that were emphasized during the INSET. Several teachers also indicated that they wanted to extend the seminar to at least five days, and stated their appreciation for the knowledge shared by the authors.
However, there are some doubts as to whether the impact can be translated to the classroom. First, many teachers found it difficult to reflect on the principles in relation to their own practice. Their focus was on the topics and the activities rather than the teaching and learning principles. Several teachers mentioned in the evaluation that the topics used in the activities were not suitable to the level they were teaching:
“The examples do not fit the year level I am teaching.”
“There is no focus on only one topic or concept.”
They also expected to be given some kind of “cookbook” consisting of teaching strategies and activities instead of being given principles and opportunities to reflect on their practice. In the comments section of the evaluation, several teachers requested for more sample materials, activities and handouts. One teacher stated that the discussions involved very broad topics and that their thoughts should have been evaluated as right or wrong.
It was also evident that there was lack of appreciation of the principles and ideas that were shared in the INSET, as revealed in this comment from one teacher:
“From my point of observation, the speakers are all good but the focus of the seminar is not as interesting as expected. Probably what I want to get from the seminar is to be more informed about the strategies applied by their university that can be applied to public schools so that at least we can increase our level of mastery.”
While teachers appeared to agree with the general principles presented in the INSET, they only provided vague statements about what they learned from the INSET. Of 28 teachers who completed the evaluation form, 15 cited the title of an activity and 7 indicated that all activities are useful:
“Working with algebra tiles, because it has the least computation.”
“All the part of the seminar, because I need all of them.”
Some teachers even interpreted the pedagogical principles as statements to be parroted inside the classroom:
“Our students should not only hear symbols/rules but they should also hear about concepts.”
“When our students commit this error, we will teach them that not only the symbols should be learned but also the concepts. We will also tell them that I will give them concrete examples for them to understand the lesson.”
Importance Placed on Non-cognitive Aspects of Teaching and Learning
The data suggest that non-cognitive factors play an essential role in framing teachers’ decisions. Fifteen responses showed evidence of these non-cognitive elements that teachers consider affecting their decisions and actions in the classroom. One teacher shared that she found the activity on analyzing student errors the least useful because “if possible I don't like to find errors in the work of others.” Another teacher expressed reluctance in correcting a student who gives an incorrect answer because it may humiliate them; instead, she suggests that another student may be asked to give another answer.
Many teachers also cited non-cognitive reasons for student misconceptions. A couple of teachers blamed the lack of study habits compounded by media-related distractions while another teacher stated that students hesitate to answer because they “are afraid they will be scolded” if they fail to give the correct answer.
Discussion
Carrying the dual role of researcher and INSET facilitator, we clearly knew what we intended to communicate. Based on the results, however, these ideas were interpreted in various ways. This analysis is an attempt to explain the difficulties in communicating pedagogical ideas during the INSET program through the framework of zone theory.
The data suggests that teaching for relational or conceptual understanding is largely within the teachers’
IZ. Although teachers agreed that mathematical learning involved an understanding of concepts, gaps in content knowledge and the reliance on rules and procedures may actually prevent such understanding to surface in classrooms. Relational understanding is then a good thing to be strived for. However, implementation may be limited to informing students that they should understand concepts instead of constructing a learning environment wherein students can discuss and negotiate mathematical meanings.
The teachers were less accepting of a cognitive analysis of errors. Some even indicated a reluctance to directly address errors. Thus, the data suggests that a cognitive analysis of errors is outside the teachers’ ZFM, and thus also outside the ZPA. The focus seems to shift from developing conceptual understanding to ensuring that a student does not feel hurt or humiliated.
There were clearly different expectations between the researchers and teachers. Whereas the facilitators provided several opportunities for teachers to discuss and reflect on their own practice, the teachers desired immediate answers and more specific activities. As with Warren et al.’s (2006) study, the INSET was not presented in a form that the teachers could receive. That is, the INSET was not attuned to the teachers’ ZPD.
The incongruence between the INSET and the teachers’ ZPD makes it likely that the teachers will continue to rely on old habits, as is evident in their primarily rule-based explanations for various mathematical concepts and misconceptions. As Day (cited by Warren et al. (2006)) stated, meaningful professional development occurs when teachers’ knowledge is taken as a valuable starting point and that, “if teachers are forced to choose, they will usually revert to their secure established ways of doing things” (p. 549).
Implications
Increasing the potential impact of a short-term INSET program is not a straightforward task. Still, it is important to understand how to increase the effectiveness of INSET because for practical reasons, it will continue to be the strategy for training teachers to be equipped to teach challenging curricula (Nebres, 2006).
This study presents a significant obstacle that short-term INSET programs need to address. Teachers have developed their own ZFM and ZPA over a period of several years, and expecting a significant shift within a period of three days is a little too much. One potential avenue for developing pedagogical theories is through teaching materials, which teachers often value and appreciate. The teachers in this study requested more materials, time, and specific strategies to accompany the discussion, then the development of materials that describe classroom activities that are directly aligned with the official learning competencies. Attention to the teachers’ day-to-day needs has to be an important focus of a short-term INSET program.
The question remains on how to address teachers’ IZ. Bernardo and Limjap (2012) offer a bleak prognosis that short-term programs may, in fact, contribute to the missing link between teacher beliefs and practices.
It seems that teachers think they are doing something progressive when they are actually simply doing the same old stuff with some new trimmings. All this may be [an] unintended product of sporadic, intermittent, and rudimentary in-service education programs (Implications, par. 4).
Thus, it is not realistic, within a relatively short time, for INSET providers to stretch teachers beyond their ZPD.
Within such a context, focusing on actual classroom needs may actually be more relevant for teachers. Pursuing more lofty goals of developing content knowledge and transforming pedagogical principles to actual practice may be realized in more long-term professional development settings.
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