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Author Names
Author 1:
Dr Aoibhinn Ni Shuilleabhain (corresponding author)
University College Dublin, School of Mathematics & Statistics, Dublin 4, Ireland
Author 2:
Dr Aidan Seery
Trinity College Dublin, School of Education, Dublin 2, Ireland
Title
Enacting curriculum reform through lesson study: a case study of mathematics teacher
learning
Acknowledgements
The National Council for Curriculum and Assessment (NCCA), responsible for the design of
curricula at primary and secondary level in the Republic of Ireland, provided a monetary
grant to the participating school to be used for a fixed amount of teacher substitution during
this research.
1
Abstract
Based in a time of major curriculum reform, this paper reports on a qualitative case study of
teacher professional development (PD) in the Republic of Ireland (ROI). Five mathematics
teachers in an Irish secondary school were introduced to and participated in successive cycles
of school-based lesson study (LS) over the course of one academic year. The research
investigated how teachers’ pedagogical practices and beliefs on student learning, specifically
related to a revised curriculum, were impacted as a result of their participation in this model
of PD. Data were generated through audio and field recording of teacher LS meetings,
individual teacher interviews, teacher notes, samples of student work, observation of research
lessons, and researcher field notes. Analysis suggests that due to their collaborative planning,
teaching, observation and reflection of research lessons teachers began to incorporate and
develop new pedagogical practices both inside and outside of LS. This study suggests that in
the introduction of centralised curriculum reform, LS can act as a powerful model of
professional development which can encourage the introduction of new pedagogical
practices. This research also provides evidence of the introduction of LS as a viable form of
professional development in secondary schools in the ROI.
Keywords
Lesson study; teacher collaboration; curriculum reform; mathematics education
2
Introduction
In this paper, we explore the particular opportunities for teacher learning in Lesson Study
(LS) resulting in changes to teachers’ pedagogical practices and beliefs related to student
learning. The context of this paper is the challenge of curriculum reform in mathematics
education at the classroom level in the Republic of Ireland (ROI), where there is an explicit
focus on incorporating constructivist approaches to teaching and learning in the classroom
(Lynch, 2011). Focusing on a typical, urban, secondary school, a case study was designed to
reveal the evolution and development of constructivist practices in teachers’ classrooms as a
result of participation in successive cycles of LS during one academic year (2012-2013).
Utilising a framework of constructivist pedagogical practices highlighted in curriculum
documents (NCCA 2012, 2013), and incorporating a professional development (PD)
framework of teacher learning from King (2014), this research suggests that participating in
successive cycles of school-based LS supported these teachers in incorporating new,
constructivist, pedagogical practices in their classrooms and impacted their values and
conceptions of teaching and learning.
Teacher learning and professional development (PD) is key to educational reform (Edwards
2011). However, research has repeatedly pointed to the ineffectiveness of top-down mandates
of PD in implementing educational change (Fung 2000) and studies have often evidenced the
challenges of introducing reform approaches in the complex environment of teaching (e.g.
O’Shea and Leavy 2013). Generating sustainable educational change cannot merely refer to
supplying new materials and procedures to teachers, but rather involves developing teachers’
epistemological perspectives of what it means to learn, as well as their conceptions of
learning (Franke et al. 1998). Participation in PD should therefore impact teachers’ personal,
professional and cultural beliefs and practices in order to enact sustainable reform (King,
2014).
Fullan and Hargreaves (1992) argue that in order for any fundamental change to occur in
classrooms, teachers must be encouraged to collaborate with their peers as part of a learning
community. Teacher collaboration in community can provide a powerful structure within
which individual teachers can attempt and reflect on new approaches to teaching and learning
relevant to their own school context, students and culture (Dogan et al. 2016; Vescio et al.,
2008). Furthermore, contextual, school-based, communities can assist teachers in reinventing
3
their professional norms and identities (Lieberman 2009) important factors in the
implementation of new curricula (Wallace and Priestly 2011).
In this research, LS was introduced as a new, collaborative, school-based model of PD where
teachers, in community, collectively planned, conducted, and reflected on research lessons
over a number of successive cycles. In LS teachers engage directly with the curriculum in
identifying an overall goal for their teaching and in planning research lessons which are
definitively linked to both the philosophy and content of the curriculum (Cajkler et al. 2014;
Takahashi & McDougal 2016). The authors chose this model of PD as a focus for this study
based on research evidencing the impact of LS on developing teachers’ understanding of
student learning and in encouraging new pedagogical practices (Cajkler et al. 2014, 2015;
Lewis & Perry 2009). We wanted to further investigate if LS would be a successful model in
implementing a new centralised mathematics curriculum, specifically impacting their
mathematics teaching practice and developing their beliefs and attitudes towards classroom
teaching and student learning (King 2014). Building specifically on the work of Takahashi
(2014), we provide further evidence of the potential of LS in implementing curriculum
reform. Furthermore, in the light of pending policy change on PD in the Republic of Ireland
(The Teaching Council 2015), this study provides empirical evidence of the successful
incorporation of LS in an Irish secondary school.
Constructivist Approaches and Curriculum Reform
Constructivism is rooted in an interpretive tradition which considers new understanding as
something constructed by the learner and is continuously tested and adjusted through further
experience and social interaction (Fung 2000). While constructivism is recognised as a theory
of learning, there are pedagogical practices associated with ‘constructivist teaching’ where a
teacher: encourages students to communicate and justify their thinking, facilitates classroom
discourse, and chooses pedagogically relevant activities to help students develop their
understanding of a particular topic (Simon 1995). Through these practices the teacher can
become aware of, and therefore interpret, student thinking and learning in order to make
ongoing instructional decisions. Focusing specifically on constructivist pedagogical practices
associated with teaching and learning in the mathematics classroom, it is important to provide
students with opportunity to articulate and justify their mathematical thinking (Schoenfeld
1992). Such facilitation of student learning can be elicited through a teacher’s use of varied
4
questioning as a facilitator of learning (Webb et al. 2009) or may be volunteered, unsolicited,
by students through the development of a classroom community (Goos 2004). In such a
constructivist environment students are encouraged to question their assumptions, locate
errors and invite comments or critique from other students (Simon 1995). Simon (1995) has
also highlighted the import of providing students with learning activities which have context
and meaning and where students can establish relevance between new content and their own
learning. Such constructivist practices contrast with “process-based” (Boaler 1998 p. 44)
teaching where classes consist of whole class expository teaching, individual seat work, and
where unsolicited student questions are not the norm (Lyons et al. 2003). In this paper, we
refer to such teaching as “traditional” (Boaler 2002) as opposed to the reform teaching
encouraged by the revised curriculum (NCCA 2012, 2013). These constructivist pedagogical
practices have been closely linked with mathematical problem solving (O’Shea and Leavy
2013) and have contributed to shaping mathematics reform efforts globally (Prusak et al.
2013).
Curriculum reform relies on teachers. However, when greeted with top-down reform of
curriculum teachers can feel daunted, challenged and uncertain of why and how they should
change their pedagogical practices (Fetters et al. 2002). Fung’s (2000) research on
introducing curriculum reform suggests that provision of decontextualized, in-service
seminars is ineffective. Without the fundamental support of teachers who understand the
objectives of a reform and are willing to trial new practices in their teaching (Fung 2000),
implementation of a new curriculum can be “fragile and transient” (Senger, 1999, p. 201). A
wide range of studies suggests that in introducing reform teachers should be invited to
participate in PD which positively impacts their norms and identities in a ‘bottom up’ as
opposed to ‘top down’ mode of implementation (Crawford et al. 2006; Wallace and Priestly
2011), thereby impacting on their professional practices and their attitudes and beliefs on
teaching and learning (King 2014).
Engaging in PD where teachers can observe and attempt to enact a curriculum in a
meaningful way has the potential to lead to changes in teachers’ values and conceptions of
teaching and learning, which impact their pedagogical practices (e.g. Dogan et al. 2016; Reys
et al. 1997; Senger 1999). Further research has shown that an effective way to influence
teacher learning is to focus on how students learn (e.g. van Es and Sherin 2008; Penuel et al.
2007). In attempting to enact sustainable curriculum reform, PD should therefore engage
teachers in observing and reflecting on student learning related to reform practices. However,
5
the classroom can often be an isolated environment – particularly in the ROI where there are
not yet established practices for collaboration and where PD is seen as an optional “add on”
(Sugrue, 2006). In overcoming this sense of the classroom as the arena of a sole teacher,
teachers can be supported in opening up their classrooms as arenas of learning (for both
student and teacher) through participation in teacher community which focuses on student
learning, incorporates observation of practices, and builds on the materials and pedagogy
underpinning a new curriculum.
Lesson Study and Teacher Learning
LS is a model of professional development where teachers collaboratively develop a research
theme, study curriculum materials and then plan, conduct, observe and reflect on a research
lessons with the aim of improving practice and impacting on student learning (Fujii 2016;
Takahashi and McDougal 2016; Lewis 2016; Lewis et al. 2009). This model originated in
Japan in the late 1800s and still pervades the educational culture of teacher learning there
(Lewis 2016). While LS is used extensively in Asia and North America, an increasing
number of recent studies have provided useful insights into LS as a vehicle for advancing
professional practice and teacher learning throughout the UK and the ROI (e.g. Cajkler et al.
2014, 2015; Corcoran 2011; Dudley 2013; Leavy 2015).
A review of the literature in an international context points to the effectiveness of LS in the
development of teacher knowledge and in encouraging a more student-centred approach to
teaching (e.g. Dudley 2013; first author, 2016; Lewis et al. 2009; Murata et al. 2012). In
Japan, LS is seen as a model which encourages problem solving approaches to teaching and
learning mathematics, which align with constructivist approaches to teaching and learning
(Fujii 2016; Takahashi 2014). While LS is becoming popular in a large number of countries
across the world, there is little reported evidence of utilising LS as a model of teacher
professional development in enacting curriculum reform and there has been no evidence of
incorporating school-based LS in secondary schools in the ROI.
Research has suggested that teacher learning in LS is due to the uncovering of teachers’
implicit pedagogical practices through their explicit planning and reflection conversations. In
these phases of the LS cycle, teacher beliefs and practices are detailed, challenged and
6
questioned through collaborative discussion (e.g. Cajkler et al. 2014; Fujii 2016). During the
conduction of a research lesson, teachers observe students’ learning and reflect on the
trialling or implementation of ideas during the post-lesson discussion. This collaboration
provides teachers with structured opportunities to take risks in their practice, trial new ideas,
focus on student thinking, and reflect on their pedagogy in a supportive and collaborative
environment (Dudley 2013; Lieberman 2009).
Evaluating teacher learning as a result of such PD, however, is complex - especially when
attempting to take into account possible changes in teacher attitudes, beliefs, classroom
practices, content knowledge and the environment in which the PD may be undertaken
(Dogan et al. 2016; Guskey 2002). In an attempt to evaluate the impact of PD, King (2014)
has proposed an extensive, evidence-based framework which encompasses systemic factors
(i.e. the context in which PD took place) and the degree and quality of change resulting from
the PD. This model makes explicit reference to the top levels of integration and renewal,
where teachers adopt and modify reforms i.e. transformative practice (Kennedy 2005). Much
LS research has evidenced changes to teachers’ practices, knowledge, and efficacy (e.g.
Dudley 2013; Author 2016), corresponding to the personal, professional, and collective
dispositions which are defined as outcomes of PD by King’s (2014) framework. Within this
study we align with King (2014) and define teachers’ professional learning as the growth of
teacher expertise leading to a change in practice which results in improved pupil learning (p.
90). Referencing King’s (2014) evaluation framework of the impact of PD, we further
contribute to the literature in providing empirical evidence of teacher learning, specifically
focusing on the use of new and improved knowledge and skills in their professional practice
and changes to teachers’ beliefs and attitudes towards student (or pupil) learning (p. 97).
Research Context
While constructivist approaches to teaching and learning have been central to the primary
mathematics curriculum in the ROI (Government of Ireland 1999), mathematics at secondary
level has often been taught in a process-based, didactic way with much ‘rote-learning’
remaining dominant in the majority of classrooms (Lyons et al. 2003). These traditional
7
practices, as described by Lyons et al. (2003) in their study of teaching and learning in
mathematics classrooms in the ROI, use a combination of exposition and practice where the
teacher lectures to the class group and students watch, listen, take notes, copy examples when
instructed, and give answers to closed questions when called upon (p. 113). In these
classrooms students rarely communicate their mathematical thinking, do not usually ask
unsolicited questions, and are not encouraged to collaborate on mathematical exercises with
their classmates. This form of passive learning contrasts with a constructivist approach where
student interactions are valued, where learners are asked to make sense of new knowledge,
and where learning activities build on both content and context for students (Fung 2000;
O’Shea and Leavy 2013). In an attempt to reform this traditional approach to teaching, a new
centralised mathematics curriculum, known as ‘Project Maths’, was introduced (Oldham and
Close 2009). This curriculum promotes students’ learning through “communicating and
reasoning” (NCCA 2013, p. 8) and emphasises “sense-making opportunities” where teachers
encourage learners to “share, explain and justify their solution strategies” (p. 10).
The implementation of this new curriculum was introduced through the provision of ten
compulsory PD in-service (or off site) workshops. However, aligning with research on other
top-down curriculum reform mandates (e.g. Fung 2000), a recent report has suggested that
these sessions have had (to-date) little sustained cumulative impact on teachers’ approaches
to teaching and learning mathematics (Jeffes et al. 2013) and classroom practices, in the
majority, remain the same. In addition to this curricular context, the Teaching Council
(professional standards body for the teaching profession in the ROI) recently published a
draft PD policy (2015) seeking to ensure that teachers engage in quality learning where
professional autonomy and flexibility related to the culture and context of teachers’ work are
maintained (p.5). The introduction of this proposed policy will mark the first accreditation of
PD in the secondary sector in the ROI. With this national backdrop, the authors of this paper
wished to investigate the impact on teachers’ pedagogical practices and beliefs, related to the
revised curriculum, as a result of their participation in successive cycles of LS.
Methodology: Qualitative Case Study
Results reported here form part of a larger qualitative study investigating mathematics
teachers’ learning in LS (first author 2016). In this paper, referring to case study data
generated in one secondary school only, we investigate how participating in LS impacted
8
teacher learning in moving from a traditional to constructivist approach to teaching and
learning. Utilising the framework outlined by the revised curriculum (NCCA 2012, 2013) and
based on pedagogical practices associated with constructivist approaches to teaching and
learning (Simon 1995), the impact of this PD was analysed through the lens of espousing
pedagogical practices where: 1) students are supported in communicating their mathematical
thinking, 2) teachers act as facilitators of student learning, and 3) students engage with
contextualised content.
Mathematics teachers in one school, referred to here as ‘Doone’ (all names used are
pseudonyms), were invited to participate in the research. Following discussion with interested
teachers around the likely impact on workload, five of the nine mathematics teachers in the
school volunteered to take part in the study. These participating teachers undertook four
cycles of LS (as defined by Lewis et al. (2006)) over the course of the academic year 2012-
2013, where they devised an over-arching research theme and planned, conducted or
observed, and reflected on each research lesson.
The first author, a former secondary school mathematics teacher, acted as participant
researcher in recording and taking part in teacher LS planning and reflection meetings
(Bogdan and Biklen 2007) and attended all but the final research lesson conducted in this
research. This participant researcher role was deemed necessary by the authors in order to
familiarise teachers with the processes of LS and to facilitate the initial collaboration of these
teachers who were unused to working together. This decision was made since the lack of a
‘knowledgeable other’ (Corcoran 2011) in initially facilitating LS has resulted in the failed
introduction of or in thwarted forms of LS (e.g. Fujii 2014). Furthermore, the introduction of
community based forms of PD can be fragile (e.g. Rousseau 2004) and we deemed the
establishment of such a group more provident with the participation of a facilitator.
In order to investigate any impact to teachers’ pedagogical practices or beliefs and attitudes
towards student learning, the research was exploratory in its form of enquiry. The data
generated consisted of transcripts of nineteen collaborative meetings, fifteen individual
teacher interviews, teacher notes from all phases of LS, written plans of four research lessons,
samples of student work (selected by teachers), field notes of all meetings and research
lessons, and a researcher log (see Table 1). In order to minimise bias of any form of ‘insider
research’, the first author was explicit in reducing her role as participant in LS meetings and,
9
by the third cycle, became more of an observer within the group (Bogdan and Biklen 2007).
Teachers had autonomy over topics taught in each research lesson and over the scheduling of
meetings. Teacher meetings were held, on average, once every two weeks and each meeting
lasted, on average, one hour. Data analysis did not commence until all data had been
generated and proceeded by way of a systematic chronological exploration of evidenced
changes to teachers’ pedagogical practices or beliefs and attitudes towards classroom
teaching and student learning (King 2014).
Table 1. Data Collection Framework
Period Focus Data Generation
Sept-
Oct
2012
Lesson Study
Cycle 1
6 meetings
Individual teacher interviews
Audio recordings of teacher meetings
Researcher field notes and log
Teacher notes – planning & observation
Selected samples of student work from research
lesson 1
Nov-
Dec
2012
Lesson Study
Cycle 2
5 meetings
Audio recordings of teacher meetings
Researcher field notes and log
Teacher notes – planning & observation
Selected samples of student work from research
lesson 2
Jan-
Feb
2013
Lesson Study
Cycle 3
4 meetings
Individual teacher interviews
Audio recordings of teacher meetings
Researcher field notes and log
Teacher notes – planning & observation
Selected samples of student work from research
lesson 3
Feb-
April
2013
Lesson Study
Cycle 4
5 meetings
Individual teacher interviews
Audio recordings of teacher meetings
Researcher field notes and log
Teacher notes – planning & observation
Selected samples of student work from research
lesson 4
10
Transcriptions of individual teacher interviews and teacher meetings were coded according to
the framework of constructivist pedagogical practices highlighted by the revised curriculum
and outlined above (NCCA 2012, 2013; Simon 1995). Additional data of teacher notes,
research lesson plans, researcher log, and samples of student work were analysed for
evidence of changes to teachers’ practices from traditional to reform teaching and changes to
their beliefs on student learning utilising the same coding framework. For example, the first
research lesson plan focused heavily on teacher exposition and included procedural,
individual tasks for students to engage with. In contrast, the final research lesson plan was
coded for strong emphasis on the development of student understanding through
opportunities to communicate their thinking and incorporated a number of tailor-made,
contextualised tasks designed by the teachers with these specific objectives.
Sketching the bounds of the case: Organisational Supports
While this case study reports on one school only, this school represented a typical urban,
publically funded secondary school (approximately 600 pupils). The participants were
representative of mathematics teachers in the majority of secondary schools in the ROI,
where three of the five teachers were teaching ‘out-of-field’ (Riordan and Hannigan, 2011, p.
290) i.e. the subject of mathematics was not included in their qualification for teaching. Due
to the lack of designated time for PD in secondary education in the ROI (Sugrue 2006),
teachers sometimes struggled to find a suitable time for collaborative meetings. These
meetings were therefore held after school or in periods where the majority of teachers could
attend (one teacher being absent for three and another teacher being absent for two of the
nineteen meetings). All teachers were present for each of the four research lessons and
reflection meetings. As a further difficulty in working as a school-based LS group, teachers
did not have a physical work-space within the school and LS meetings were therefore held in
empty classrooms or in the busy staff room. These practicalities of organisational support
(Bubb and Earley 2010) often hindered the arranging of LS meetings but, since these teachers
had volunteered themselves to participate in the research, they maintained their flexibility and
enthusiasm to participate in LS throughout the year (explicitly highlighted by all teachers in
their final interviews).
The Baseline Picture
As suggested by Bubb and Earley (2010), before evaluating teacher learning we established a
baseline of participating teachers’ pedagogical practices and beliefs and attitudes around
11
student learning and of the curriculum reform. While there was an organisationally defined
subject department within the school, in their individual interviews teachers reported rarely
meeting as a subject group. The five participating teachers did not collaborate in sharing
resources or discussing classroom practice and none were familiar with any form of formal or
informal classroom observation. From initial observations of participating teachers’
classroom practices (excepting remedial lessons), the teaching of mathematics across the
school could be described as traditional; students worked independently and silently, with
content presented by exposition and followed by practice of textbook tasks. In their initial
interviews teachers described their attitudes towards the curriculum reform and, in order to
provide insight into the make-up of the LS group, we note these, their years of teaching
experiences and their qualifications in Table 2.
Table 2: Participating Teachers’ Year of Experience and Response to Reform
Name Years of
Teaching
Experience
Response to Curriculum Reform
Kate 3 (out-of-field) Positive about the reform, but had not incorporated
any classroom practices encouraged by the new
curriculum.
Lisa 7 Enthusiastic about the reform, but had not
incorporated any classroom practices encouraged by
the new curriculum.
Michael 6 (out-of-field) Wary of the reform and not confident in his ability to
incorporate new classroom practices.
Nora 30 Favourable towards the reform and incorporated
constructivist pedagogical practices in her teaching of
remedial maths.
Owen 1 (out-of-field) Opposed to the reform and to the pedagogical
practices espoused by the reform
All except Nora had participated in the curriculum in-service PD provided by the NCCA and,
similar to Fung (2000), felt that while the teaching and learning materials provided in these
sessions were useful, they often went unused since there was little time to trial these in class:
12
“they kind of go in the pile and I’ll say ‘I’ll come to it, I’ll look at that again’ and you
just never do.” (Kate, Interview 1)
In the following section we report on the findings of the analysis and evidence of changes in
teachers’ pedagogical practices and beliefs and attitudes towards student learning (King
2014) over the four successive cycles of LS.
Findings: Implementing New Pedagogical Practices
We present three key findings as related to the constructivist curriculum framework outlined
above. Excerpts of qualitative data are used to provide the reader with examples of teacher
learning over successive cycles.
1) Emphasising the social dimension: supporting students in communicating their thinking
The first key finding of the study was the change in teachers’ pedagogical approaches to and
attitudes towards supporting students in communicating their mathematical thinking. In the
first research lesson, Lisa wanted to incorporate opportunities for students to work together
on a shared task. The group collaboratively planned the research lesson with this objective in
mind, however, as noted by Pirie and Kieran (1992), planning for student group discussion
without appropriate cognitive tasks does not constitute “constructivist teaching”. The
activities within the research lesson plan required students to work in pairs, but the task was
procedural in nature and did not necessitate students to collaborate or communicate with one
another. During the research lesson, content was presented to students in a traditional way
and the conducting teacher, Lisa, asked only a small number of closed questions during the
lesson. Despite their shared goal of incorporating opportunities for students to work together,
desks were kept in single rows, evidencing teachers’ beliefs on structuring student learning
(de Kock et al. 2005), and the majority of classroom talk was carried out by the teacher. In
their post-lesson discussion, teachers reflected on their inadequate choice of tasks in
supporting students to communicate their thinking with one another. They suggested that, in
future, students should work on collaborative tasks from shared worksheets and referenced
their inappropriate choice of activity in this context.
Changes to teachers’ beliefs about student learning became evident in the second cycle of LS
where Owen, with encouragement from his colleagues, agreed to conduct the second research
lesson where students would work purposefully on an activity in small groups. By the third
13
planning meeting, independent of the research lesson, Lisa had changed her classroom layout
from individual desks to tables arranged for student collaboration. She reported back to her
colleagues, articulating her enthusiasm for attempting this new strategy (Edwards 2011) and
shared this change in her attitude towards student learning (King, 2014):
Lisa They can all see each other’s work. “You’re not doing that right”
[mimicking student]. I love it. I would never go back.
Stemming from her fervour on this new classroom practice, her colleagues were further
encouraged to incorporate collaborative learning activities which would require students to
communicate their thinking. Following this second research lesson, teachers reflected
positively on students’ learning:
Lisa To listen to them arguing, discussing it among themselves!
Owen Yeah!
Lisa was absolutely… There was more learning going on in that than you
could have done to by explaining, standing at the top of the class. The
groups of five – they were, you know, discussing the maths problem.
They were staying on task - I think that’s where all the learning is
coming.
While Lisa had led the change by taking a risk in her own classroom, her colleagues shared in
trialling this unfamiliar practice (Dudley 2013). Together the group refined and integrated
this new knowledge (King 2014), by incorporating the size of the student groups as a
significant factor of student learning. Kate suggested that groups of five were too large and
suggested a modification in cycle 3, where students would only work in groups of four or
less. In her mid-point interview Kate emphasised the importance of student communication in
her lessons outside of LS, demonstrating an explicit change in her pedagogical practice and
beliefs as a result of participating in LS.
As an additional refinement of knowledge in their professional learning (King 2014), teachers
further developed their incorporation of student communication by assigning roles within
each student group (Webb et al. 2009) and by including student presentations of
mathematical work to their peers. In their third post-lesson discussion teachers reflected on
these practices as beneficial to building student understanding, highlighting their transformed
14
attitudes towards the importance of student communication in student learning from previous
lessons where the teacher directed most of the talk.
Research by Fetters et al. (2002) has shown that although teachers might be supportive of
reform in theory, incorporating changes to their practices can be daunting. This was apparent
for Michael who, in the fourth and final cycle of LS, remained wary of changing his own
classroom practice to encourage more student communication despite his enthusiasm about
incorporating purposeful student interactions in previous research lessons. Over the course of
the research, this group of teachers had developed into a teaching community which mutually
supported one another in their learning (Lieberman 2009) and, in this fourth cycle, Michael’s
colleagues gently encouraged him to take a risk in his practice in planning this final research
lesson:
Owen Are we gonna do it… Is it going to be in a group work setting or is
it…?
Michael No. No. They’re in –
Lisa Single seats.
Michael They’re in the back, the ‘U’ [shaped layout of desks]
Owen Okay so.
Michael There’s no point in changing just because we’re – well, I don’t know.
Owen No, no.
Michael [Pause] I don’t mind. I mean I did go to groups [in another subject] so
I could do it again. [Pause] Sorry, sorry it can be groups. Of course it
can be in groups.
Lisa I think it would be useful, even in pairs right?
Kate Even pairs.
Michael Yeah, no. I would prefer it.
While in this excerpt Michael’s focus is solely on the arrangement of desks, this new
classroom layout marked a development in his practice underpinned by a change in his
15
attitude towards supporting students’ learning (de Kock et al. 2005). In the post-lesson
discussion, and later in his final interview, Michael reflected on his beliefs about the benefits
of specific opportunities for students to communicate their thinking and “talk through it” in
order to build students’ understanding of a topic in research lessons and in his own teaching.
While this study focuses on short-term impacts observed during the research, teachers’
collective conversations and individual interviews referenced the longer-term impacts of this
PD. Owen, having originally describing himself as “anti-Project Maths”, highlighted a
change in his attitudes and beliefs of what benefitted pupil learning in his final interview.
Owen Now I’m trying and trying [to include group work]. Even today, I was
like ‘Deep breaths Owen, deep breaths. You know you can do this. We
can do this!’ But they [the students] are learning.
Participating in successive cycles of LS provided teachers with a structure within which they
could maximise the social dimension of learning and experiment with varying forms of
classroom practice to emphasise students’ communication of their mathematical thinking.
Over the four successive LS cycles, there was a dramatic change in how student
communication was facilitated and encouraged in research lessons, as a result of changes to
teachers’ practices and beliefs about student learning.
2) Teachers as facilitators of student learning
The second key finding that emerged was teachers’ enhanced awareness of themselves as
facilitators of student learning in two new and distinct ways. These teachers initially
conducted lessons as the sole transmitters of knowledge (Lyons et al. 2003) and, at the
beginning of the research, only Nora described her role as that of a facilitator in encouraging
students to reason and present their own solutions (Goos 2004). As a facilitator, a teacher is
continuously and consciously responding to the diversity in their students’ learning by
stimulating and managing classroom interactions (Schoenfeld 1992, Simon 1995), but in the
first research lesson Lisa presented all content and assumed responsibility for telling students
all of the steps involved in completing the activity. When one particular student asked a
question related to the new content Lisa was unsure of how to respond to the uninitiated
query and ignored the students’ question. In the post-lesson meeting Kate highlighted this
students’ contribution as one which may have been beneficial for the class to discuss and
suggested how Lisa might respond in future. The group regretted the fact that they had not
16
anticipated this question and it became evident, on analysis, that the opportunity for teachers
to observe students was beginning to impact their beliefs about the importance of both
teachers’ and students’ questions in supporting student learning. This focus on the role of
questioning developed into a change of practice when, in the subsequent research lesson,
teachers collectively scripted questions which might be relevant to ask during the lesson
(Webb et al. 2009). Owen, who conducted the second research lesson, initially reported it was
“hard to let go” of his traditional approach to teaching but later, in his second interview,
revealed a transformation in his attitude towards acting as a facilitator of student learning.
Owen From these meetings, as well, I’m conscious of open ended questions
rather than ‘this is what it is. This is the answer’.
A development of practice was evident when teachers planned the third research lesson with
the explicit focus on the teacher acting as a facilitator of learning. Nora encouraged her
colleagues to plan the research lesson with a problem-solving approach to teaching and
learning (Fujii 2016), where students would independently arrive at an understanding of
graphing quadratic equations. Nora initially referenced a procedural textbook task and the
group began modifying the task and planning how the conducting teacher would guide
students’ learning through specific questioning:
Nora [Students] don’t have to think...
Kate So we kind of make it [the task] more difficult and see how they
interpret the graph themselves without instruction?
Lisa They might say, “oh, well now we know how to, so let's get on with the
table. Let's get on with this. Let's get this. Let’s get it.”
Kate And say, “Figure out what we’re being asked here…Can we draw a
graph? Can we look for patterns? Right, I’m going to give you a
similar problem”
Kate referenced her role as facilitator where she had “no teaching to do in this class…All the
lesson really involves for me is observing what's going on”, but later articulated the import of
her role in guiding students’ thinking (Webb et al. 2009):
Kate There was very little teaching invovled in it really, just kind of
facilitating, which is what it’s all about.
17
Building on this evolution of classroom practice, in the post-lesson reflection Michael noted
how Kate’s questions had prompted students to consider and justify their thinking: “You said
to the group ‘do you know what it is you’re being asked? Put it into words’ and they
explained it!” He and his colleagues’ reflective discussion demonstrated a collective
transformation from a traditional to a constructivist approach, where the teacher’s role guided
and structured students’ thinking.
In the final cycle teachers planned the research lesson with defined questions to ask students
at particular points and the conducing teacher, Michael, prepared to guide student groups
during their activities. The lesson required little exposition, but was structured and sequenced
for the teacher to facilitate students’ learning and assist students with prompts or questions if
they arrived at any difficulty. It was apparent from analysis that over the four research
lessons, teachers had developed in their pedagogical approaches and shifted from
demonstrating knowledge to facilitating student understanding.
3) Designing and incorporating contextualised content
From their very first planning meeting, these teachers identified the importance of providing
a context for students’ learning and this theme provided the third key result in this study.
Initially, teachers reflected that students were often disengaged from the subject and wanted
to provide a sense of “purpose and meaning in their mathematics” through providing explicit
applications, as suggested within the curriculum (NCCA 2012). In the first research lesson
teachers attempted to incorporate contextualised activities for students, but the tasks they
chose did not provide authentic, relevant context for students (Galbraith 2013) and were
similar to the practice-drill activities traditionally found in the textbooks (Lyons et al. 2003).
In the second research lesson, teachers wanted to explicitly address this issue by
incorporating relevant activities which would interest students and would also provide
relevant, cognitively challenging content. Unfortunately, teachers could not find such
activities in the textbooks and instead decided to create their own activities for students. This
was a daunting task for these teachers, who were traditionally reliant on textbooks as a source
of activities, but they began to enjoy the creative and collaborative process of designing
activities that would motivate and engage students. The group designed five different
activities around one learning objective and, in their post-lesson discussion, noted how the
context had prompted content-related conversations between students.
18
Kate When they [the students] said “We went to the end of the story to get the
answer” that was really, really good.
Lisa It was lovely to hear [student name] say when he was working “Now I get it.”
Designing and incorporating contextualised activities as part of their pedagogical practices
notes a development of teachers’ professional and personal practices (King 2014) as a result
of participating in successive cycles of LS. In the subsequent research lesson, teachers
wanted to again utilise contextualised problems to engage students with more abstract
mathematical content. Again, such activities were not to be found in the textbooks but
teachers were now more confident in developing their own contextual and content related
tasks (Figure 1).
Figure 1 Sample of contextualised activity designed by teachers
19
In their post-lesson discussion, teachers reflected on how interested students had been in the
application of the activities which, in turn, had benefitted students in learning about the
mathematical content.
Michael The kids were having a great chat about if he was tackled or if he was
charged down and all that sort of stuff. And they were talking about all
of these sort of things while they were doing the problem!
It was evident that teachers’ attitudes towards the importance of context in learning activities
were becoming more established as norms of their pedagogical practice in planning research
lessons (Lieberman 2009). In their final research lesson, teachers explicitly articulated the
importance of establishing context in abstract concepts and designed relevant activities for
the fourth research lesson. This activity exemplified their changed attitude towards the
importance of relating context to new content in supporting student learning.
On further investigation, this new practice was beginning to impact on teachers’ practices
outside of LS, as exemplified by Owen in his final interview:
Owen Now I’m a little bit more conscious in that if I’m teaching something
I’ll try to give some sort of a real life example to even start a topic. If
it’s a chapter with geometry – where would we use it? Why does this
relate to our lives? … From these meetings I’m conscious of open
ended questions rather than telling them “this is what it is”.
Finding or designing tasks which had meaning and relevance for their students became a
norm of teachers’ practices both inside and outside of LS.
At the beginning of the research these teachers had not felt confident in introducing any new
pedagogical practices encouraged by the curriculum, despite having participated in in-service
PD. As a result of participating in these four successive cycles of LS, each participant
reported an increase in their confidence in implementing the new curriculum in their own
classrooms. From our analysis of the data, changes in incorporating these constructivist
approaches to teaching and learning were due to a number of factors incorporated within the
model of LS: individual teachers were supported in attempting practices in research lessons
due to the shared and collaborative planning with their colleagues (Dudley 2013); teachers
felt confident in incorporating these practices outside of LS due to the supportive and
collaborative nature of the LS group (Lieberman 2009); and in observing and reflecting on
20
research lessons teachers were further able to hone their skills in critically analysing and
reflecting on student learning (Cajkler et al. 2014). These phases, built within the LS model,
(Lewis et al. 2006, 2009) allowed teachers to observe the curriculum being enacted and
supported teachers in incorporating new practices within their own teaching. The cyclical
structure of LS, where the planning and reflection of one lesson impacted on the planning and
reflection of subsequent lessons, allowed teachers to further learn and develop in their
approaches to teaching and learning.
Discussion and Conclusion
This research took place at a time of major national curriculum reform which encouraged
mathematics teachers to adopt pedagogical practices underpinned by constructivist
approaches to teaching and learning (NCCA 2012, 2013). Despite having participated in the
in-service days offered as part of the centralised curriculum reform, teachers participating in
this research were unsure and wary of introducing new pedagogical practices in their teaching
and learning. Introducing a new model of school-based PD to a secondary school in the ROI,
this research aimed to investigate changes to teachers’ practices and beliefs about teaching
and learning related to the revised curriculum, as a result of their participation in successive
cycles of LS.
Of the key findings presented above the analysis reveals that as teachers’ participation in LS
continued, their planning, teaching, observing, and reflecting on research lessons began to
more explicitly mirror the constructivist approaches to teaching and learning highlighted in
the new curriculum. As a chronological evolution of LS cycles, changes to teachers’
professional and personal practices (King 2014) became evident in their collaborative
conversations, individual interviews, planning notes, and observations of research lessons. In
planning, teaching and reflecting, teachers began to explicitly focus on encouraging students’
communication of mathematical thinking, on facilitating student learning, and on
incorporating contextualised content as part of their pedagogy in LS research lessons.
Teachers also reflected and reported on these changes in their teaching external to the LS
group. Engaging in dialogue as a professional teacher community provided teachers with the
impetus to modify and design their own mathematics problems - taking risks in their own
teaching (Dudley 2013) and increased their efficacy in incorporating constructivist
pedagogical practices in their teaching.
21
As a limitation of the research, the LS community in this case is unique and represents an
urban school where management and some external funding supported the participation of
teachers in the study. In addition, not all mathematics teachers within the school participated
in the research. However, this case study school represents a teacher population typical of
most Irish secondary schools where almost half of the mathematics teachers are out-of-field
(Ríordáin and Hannigan 2011). Nora’s participation in the school as a remedial teacher is not
a usual role in the ROI secondary system and her longer experience in teaching mathematics
may have impacted on changes to her colleagues’ practices and personal beliefs in this study.
In addition, without Nora having regularly scheduled classes, it was not possible to identify
whether or not her pedagogical practices were impacted by her participation and impacts to
her beliefs and practices can only be referenced through her collaborative and individual
conversations. It is worthy to note, however, that in her final interview she reported an
increase in her confidence in teaching new and unfamiliar content in the curriculum.
In the context of curriculum reform, it may be worthy of note that these teachers believed that
their voluntary participation in LS was an important factor in their willingness to collaborate
and trial new practices, and in their continued participation throughout the academic year.
Indicating the importance of teacher self-efficacy (King 2014), teachers reported on the
significance of their autonomy in structuring and scheduling LS within their school and
expressed the wish for such PD to be incorporated in compulsory ‘Croke Park’ hours (The
Teaching Council 2015). Teachers also referenced their necessity for official
acknowledgement for their participation in PD, an issue which will likely be addressed within
the Cosán framework outlined by the Teaching Council (2015).
Developing practising teachers’ teaching and learning practices around constructivist
approaches has long been a focus of professional development and curriculum reform
research. While constructivist approaches to teaching are often difficult to translate to the
classroom (O’Shea and Leavy 2013), analysis of the data generated in this research provides
evidence of the power of LS in encouraging constructivist pedagogical practices. The study
has implications not only for the implementation of mathematics curricula, but for other
curriculum reforms which emphasise constructivist practices and, in particular, provides
further evidence that situating teacher communities in-school can lead to notable changes in
teacher practices and beliefs on student learning. The research also verifies the possibility of
incorporating LS as a form of school-based professional development in secondary schools in
the ROI.
22
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