In this chapter I define the research question for the main project of my thesis. I consider the ‘main project’ to be the period following the Reconnaissance Period (RP), see Chapter 2. As mentioned before, the RP set some boundaries related to the possibilities for the study and also helped me to develop some initial hypothesis about the influences on teachers trying an innovation in practice in the context of my investigation. Additionally, the RP helped me to familiarise and acclimatise to the setting where my study would take place.
In the next sections, before presenting the research question, I summarize relevant literature focused on justifying my choices, and state the results already known in the field that have influenced my decisions during this period. Research results that support my conclusions are presented in the final chapters of this thesis along with the discussion of the findings (Chapter 8 and Chapter 9).
Following the RP, the approach during the main project was still exploratory in nature, meaning that the initial goal of the study was refined during the research process (Hammersley, 2018). My initial general goal with the PhD study was to investigate the phenomena of teachers changing their practices with low-set groups as openly as I could, allowing unforeseen issues to emerge.
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3.1. Change in teaching
Teaching demands teachers be adaptable to change in many situations, to adopt new curricula, to use new technology, to accommodate new textbooks, new cohorts of students, and different examination boards, etc (Jaworski, 1989; Lampert, 2010). Although some of these changes are a natural part of a teacher’s job, others might not be as natural, such as change in teachers’ practices that do not seem to come easily (Hiebert, 2013; Wood et al., 1990).
Teaching is a complex task, which is highly influenced by different types of knowledge and beliefs (Ball et al., 2008; Shulman, 1986; Wilson and Cooney, 2002), has a constant need for instant decisions while interacting with a group of children (Ball, 1993), and has pressures from different sources (Hargreaves, 1994). This all increases the difficulty of understanding the barriers to the changes that are not integrated into the job description, such as changes in classroom practices.
Additionally, in many situations in the school context, the actions taken to improve students’ learning are directly related to improving the quality of teaching (Hiebert, 2013). This is the case for the majority of aspects of the changes in schools’ curriculum, or reform. Research in teacher development has paid a lot of attention to the reform context. The scenario in mathematics education is the same, with the focus on teacher change in practice largely dominated by the context of reform (Adler et al., 2005).
Richardson (1990) argued that the focus of the literature on teacher change in practice is mainly on whether teachers are able or not to implement the new program under investigation. She showed that the studies moved from the acceptance of the new program or not by the teachers to examining features influencing implementation of the new program, but at least one similarity persisted: the fact that the innovation was brought from an outsider and was not under the control of the teachers who had to change their practices. Studies looking at changes
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imposed upon teachers are the norm, this approach leaves a gap related to issues of teacher change in a non-imposing situation. This issue is known for some time now, and Richardson (1990) suggested that teacher personal attributes and autonomy should be considered when research is undertaken in a context of teacher change.
Therefore, instead of focusing on a reform context, my particular focus on this issue of changing teaching practice is towards providing teachers with more agency in terms of approaches to use in the classroom, enabling them to develop a large repertoire of teaching strategies to choose from when they are teaching.
One reason for the need of this large repertoire of practices comes from Lambert’s (1985) and Ball’s (1993) examples of daily dilemmas that mathematics teachers face in the classroom: deciding what and how to teach in their classrooms, and finding a balance between pressures of time, performance, their own teaching skills and the outcomes for students’ learning, etc. Lambert and Ball both portray the teaching job as one of constantly making decisions to cope with challenges. Coping and managing dilemmas in the classroom, they argue, is and always will be, a major part of the job for teachers (Ball, 1993; Lampert, 1985). If teachers have more options to use while teaching, they will be better prepared to face these daily choices in their classrooms.
A teacher who tries a new strategy in the classroom is testing it, and possibly incorporating it to her repertoire of strategies to use in the classroom. Beyond that, as Clarke and Peter (1993) suggest:
Teacher experimentation is the principal operationalized consequence of the changes in knowledge and beliefs, as well as being a principal stimulus for reflection. From this perspective the role of teacher classroom experimentation within professional growth is a central one (Clarke and Peter, 1993, p.173).
This conclusion is aligned with the results I obtained in the RP. Considering addition and subtraction of fractions, Julia chose to teach her Year 9 the mnemonics of the procedures, which in her opinion, would be
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sufficient for her students to do well in the examination questions about this topic. On the other hand, the project during the RP created the opportunity for Julia to plan and teach different lessons from the ones she taught her Year 9. During these different lessons she perceived that students had learnt more about fractions than just the mnemonics for adding and subtracting. This experience led her to rethink her own teaching for that low-set group, as discussed in Sections 2.3 and 2.4.
Some research suggests that space to take risks is one of the ingredients to foundational change, which “involves a change in orientation of self (identity) and practice (actions)” (Chapman and Heater, 2010, p.456). Anthony, Hunter and Thompson (2014) investigated one teacher’s self-reported experience of participating in a professional development initiative and the authors concluded that:
the provision of both space for collective and individual learning, the provision of a space to take risks, and the prompts and support for him to experience and attend to tensions involving self and practice have enabled [...] ‘foundational change’ (Anthony et al., 2014, p.288)
But experimenting with different practices in the classroom can be too great a risk (Penteado and Skovsmose, 2009; Smith et al., 2005) and teachers can suffer from diverse emotional and professional setbacks (Nolder, 1990; Reio, 2005). To deal with these issues, many studies of professional development initiatives mention the importance of support and collegiality as means to foster teachers engagement with new practices (Goldsmith et al., 2014, p.15). For instance, Penteado (2001) found that collaboration among her participants was enhancing their use of new technologies. Penteado (2001) used an analogy with risk when teachers were implementing novelty, and with comfort when teachers kept using old practices and did not create opportunities for developing their pedagogical strategies.
My approach to this issue is the Innovation Zone. As I discussed in Section 2.4.2, Julia’s experimentation of an innovation in her classroom balanced novel and old practices, facilitating the expansion of Julia’s
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repertoire of strategies and placing her in a privileged position when making choices for future lessons (Ball, 1993; Borko et al., 1990).
This claim was limited to the specific context and to only one teacher during the RP. The main project investigated three teachers over one academic year in the same context who were involved in a profession development initiative (PDI) similar to Julia’s, and focused on features influencing the teachers to teach in their Innovation Zone. The details of the main project are presented in Chapter 4.
In summary, I agree with Zaslavsky and Sullivan (2011) that teacher development includes facilitating teacher change from:
novice possibly uncritical perspectives on teaching and learning to more knowledgeable, adaptable, judicious, insightful, resourceful, reflective and competent professionals ready to address the challenges of teaching (Zaslavsky and Sullivan, 2011, p.1)
The initial aim of this project was to investigate change in practice, considering it to be beneficial mainly for improving teachers’ adaptability and resourcefulness in the classroom. The results, discussed in Chapter 8 and Chapter 9, suggest that the focus on trying an innovation in practice also encouraged the participant teachers to develop their knowledge (about teaching fractions and about low-set students) and their decision- making skills for planning and teaching lessons.
The next section focuses on positioning this study as considering teacher change as learning. I also explain why I chose to study change in teacher practice, and after that I turn to review some PDIs that also focus on the adoption of innovations in practice.
3.2. Teacher change as learning
In educational research it is common to come across studies about:
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1) students’ learning, most commonly referring to children in the school in relation to a subject;
2) teachers’ perceptions of students’ learning, as studies about teachers’ beliefs regarding students and about the subjects they teach;
3) teachers’ learning about teaching, which is more commonly known as teacher development (initial or continuing), but in general people learning about the job of teaching.
My study focused on the third area, more specifically on teachers’ learning about teaching practices. The statement “teachers learning about teaching” is already a widely accepted assumption and a declaration of a belief that teaching can be learned (Goldsmith et al., 2014; Hiebert, 2013; Lampert, 2010; Shulman, 1986).
Shulman (1986) proposed different types of knowledge that teachers need in their jobs, implying that it is possible to learn the job of teaching. Another example of learning the job of teaching is the discussion about teacher development and teaching practice in Lampert (2010). Lampert’s article is a discussion of this topic, and assuming that “learning [to teach] is whatever one does to get better at that work” (p.21), she suggested the use of the term ‘learning teaching’ as a way to allow the possibility that teachers also learn while they are teaching. Lampert’s approach also indicates that she agrees that teaching can be learned. These are only two examples, but as I said earlier, the assumption that teaching is not a “gift” one is born with, but rather a profession that can be learnt, is well accepted.
Although the two studies mentioned above do not have the same specific topic, Shulman’s and Lambert’s views on teacher development suggest that there are different approaches to the issue of learning to teach. While Shulman’s ideas suggest an emphasis on the processes by which teachers might get to know things (understand, explain, representations, analogies, demonstrations) that will supposedly help
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them teach, Lampert’s emphasis is on teacher-student relationships, on the possibility of learning about teaching while teaching, and on the context where teachers might learn.
As these two examples suggest, different theoretical approaches to teacher learning reflect different views on what learning is and how it occurs, and there is no clear consensus about which view would be more appropriate for investigating different issues (Cobb and Bowers, 1999; Greeno, 1997).
The theory I consider from now on has helped to establish my definition of what might be considered learning in the context of teacher development. This definition is relevant because it has informed decisions about the format of the PDI in the project and the choices I made regarding data collection methods and focus for data analysis.
It is important to highlight that my PhD project was not focused on developing the philosophical aspect of what learning is for teachers, rather my contributions are related to the influences on how learning can occur.
My study considered that the context, the interactions and the communities teachers were engaged in are relevant when investigating teacher development, coherently with Wenger’s (1998) views. Below, I discuss other studies that supported my view of how teacher learning can be seen as teacher change.
Putnam and Borko (2000) presented a discussion of recent research on teacher learning and after considering research on staff development in which learning experiences were situated in practices, they concluded that:
the most appropriate staff development site depends on the specific goals for teachers' learning. […] Experiences situated in the teachers' own classrooms may be better suited to facilitating teachers' enactment of specific instructional practices (Putnam and Borko, 2000, p.7)
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“Enactment of specific instructional practices” is a learning experience that can be seen as change in teachers’ classroom practices.
Since teacher practice in the classroom and learning are apparently intertwined, I come back to the arguments from Clarke and Peter (1993). They claimed that “classroom experimentation should be seen as the contextual catalyst for professional growth, and the outward evidence of teacher change” (Clarke and Peter, 1993, p.174).
As suggested by the excerpt above, the terms change,
development, growth and learning are frequently used interchangeably in
research literature about teachers’ practice. Clarke and Hollingsworth (1994) offered a differentiation of the three first in relation to learning:
“development” when referring to in-service programs […] “change” when referring to a process, an observable phenomenon, or a set of behaviours; and, “growth” where the intention is to encompass both a change process and to invoke a notion of learning. (Clarke and Hollingsworth, 1994, p.154, emphasis added)
Clarke and Hollingsworth (1994) continued the discussion of different perspectives on changes. They argued for a need to reconceptualize teacher change in order to have clarity on the aims of in- service programs for teachers. They advocated for the education research community to focus on the perspective of growth and they criticise the “professional development programs based on deficit-training-mastery models” (p.160), where teachers are seen as lacking skills or implementing inefficient practices.
Although I agree with Clarke and Hollingsworth’s (1994) distinction, I have not talked about growth in this thesis. Instead, my focus will be on change in teachers’ practices. This choice was made to emphasize my interest on observable phenomenon as main data sources for my study. Therefore, not only is my research focus on what fostered or constrained changes in practice, but the PDI from which my data collection took place was focused on teachers experimenting in their classrooms.
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Clarke and Hollingsworth (2002) also developed a model of teacher change (see Figure 3.1), or of teacher growth networks, as they called a change sequence that is not momentary and leads the teacher to professional growth (Clarke and Hollingsworth, 2002, p.958). Their model contains previous suggestions, such as the model of teacher change from Guskey (1986), who argued that change in teacher practice came before change in beliefs. But Clarke and Hollingsworth included important differences, such as the cyclic possibility of changes (not having a fixed order of occurrence) and the complexity that a growth network can have, travelling through the different domains (see Figure 3.1) in any order, even repeatedly, to build an accurate description of the change (Clarke and Hollingsworth, 2002, p.951).
Their model has also been highly accepted by the research in mathematics education community, being used in different studies to investigate teacher change, (Golding, 2017; Hartnett, 2011; Justi and van Driel, 2006; Voogt et al., 2011) and even to categorize studies in a synthesis of recent research about mathematics teacher learning from Goldsmith, Doerr and Lewis (2014). But the model does not contribute to explaining the reasons and the influences behind the changes it describes.
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Based on the ideas of Clarke and Hollingsworth (2002), it is consistent to consider change in the domain of practice as professional experimentation can lead, through enactment or reflection, to change in the personal domain, where one of the options is change in knowledge. Therefore, according to the authors, it is consistent to consider change in practice as one of the ways to foster teacher learning and I am adopting this view in this study.
Lampert (2010) suggests that there is a gap in the relationship between teaching strategies (component practices) and experimenting in the classroom (practising):
A strong congruence seems to exist between the notions that teaching is made of component practices and that teaching can be learned by practicing, though there are several aspects of this link that could be clarified. (Lampert, 2010, p.31, emphasis in the original)
The aspects I investigated were factors that might affect teachers’ willingness to experiment with a new strategy in their classroom. This change in practice can be seen as learning, as Lampert defined learning
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Figure 3.1: Clarke and Hollingsworth (2002, p.951) the Interconnected Model of professional growth.
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as “whatever one does to get better at [their] work” (Lampert, 2010, p.21).
In a systematic review of the literature focused on professional development for teachers, Vangrieken, Meredith, Packer and Kyndt (2017) investigated results from empirical research on learning communities (LC) and communities of practice (CoP), which they argue are not always clearly differentiable in the literature. They used “teacher communities” as a general term to address the shared results of the studies with either theoretical approaches, LC or CoP.
The concept of teacher community considers that teacher learning happens through collaboration, which includes discussion, sharing practices and support. According to Wenger (1998), a community of practice is continually learning, and one of the ways to account for learning is change in practice, “what they [participants in the CoP] learn
is their practice” (p.95).
However, even if one assumes teachers form a Community of Practice, this may not be enough for the demands of the profession. As Jaworski (2008) pointed out, in a community of practice
participants align themselves with the normal desirable state. However, the normal desirable state does not necessarily foster the kinds of mathematical achievement didacticians, and society more broadly, would like to see (p.313)
Jaworski (2008, 2005) suggests the concept of inquiry community in order to “challenge the normal (desirable) state and question what it is achieving” (p.313). Her argument is that for teachers seeking to improve education, it is necessary a community that questions and re-thinks its practices as an integral part of their activity.
Vangrieken et al. (2017) found that in order to be successful members of the teacher community, teachers have to be in a safe environment to experiment with new ideas, being able to share failures and discuss uncertainties (Vangrieken et al. 2017, p.55). The authors concluded that successful teacher communities need trust and respect;
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alignment of goals and a balance of the following aspects: leadership and participants’ agency; top-down and bottom-up influences; safety and challenge.
This section revisited research results on the topic of teacher change in practice. It seems widely accepted that teacher change in practice can be seen as learning and that one way to promote teacher learning about teaching is experimenting with innovations. My study is based on these findings, and claims the importance of understanding what influences teachers to experiment with innovation in their practices: in other words, what influences teachers to move to their Innovation Zone.
3.2.1. Why I am not talking about beliefs?
The focus on the practice and beliefs of mathematics teachers is a common combination in educational research (e.g. Clarke and Hollingsworth, 2002; Smith et al., 2005). Due to my interest in low-set groups, the issue of teachers’ beliefs in relation to many aspects of teaching and learning mathematics involving low-achieving students emerged as a potentially relevant aspect. However, I consciously decided not to focus on beliefs and I explain the reasons for this decision in this section.
As a teacher myself, and considering all of the choices teachers have to make daily in their lessons (Ball, 1993; Lampert, 1985), I