Investigating Lesson Study as a practice-based approach to study the development of mathematics teachers' professional practice

Abstract

The study, whose methodological approach is the focus of attention in this paper, is a qualitative, single longitudinal case study. The object of study is Lesson Study (LS), and the unit of analysis is two LS cycles. What teachers learn about teaching practice and student learning in mathematics from participating in the two cycles is investigated. LS and teaching practice are in the study regarded as object-oriented activities. It is claimed that indications of what the teachers learn during LS processes can be uncovered by the use of discourse analysis because learning is considered as a change in discourse.

Full text

Investigating Lesson Study as a practice-based approach to study the
development of mathematics teachers’ professional practice
Anita Tyskerud, Janne Fauskanger, Reidar Mosvold, & Raymond Bjuland
University of Stavanger, Faculty of Arts and Education, Norway; anita.tyskerud@uis.no
The study, whose methodological approach is the focus of attention in this paper, is a qualitative,
single longitudinal case study. The object of study is Lesson Study (LS), and the unit of analysis is
two LS cycles. What teachers learn about teaching practice and student learning in mathematics from
participating in the two cycles is investigated. LS and teaching practice are in the study regarded as
object-oriented activities. It is claimed that indications of what the teachers learn during LS processes
can be uncovered by the use of discourse analysis because learning is considered as a change in
discourse.
Keywords: Lesson Study, mathematics teachers, professional development, teaching practice.
Introduction
Recent studies have focused on the potential of practice-based approaches for developing
mathematics teachers’ knowledge and practice. In this paper, we investigate a methodological
approach to study how Lesson Study (hereafter LS) as a particular practice-based approach to
professional development can contribute to teachers’ development (Thames & Van Zoest, 2013). In
Japan, LS has been used for professional development of teachers for more than a century (Ronda,
2013). Since Stigler and Hiebert (1999) wrote “The Teaching Gap”, researchers from other countries
have become interested in LS as a structured approach to teachers’ professional development (e.g.,
Fernandez, 2002). In Norway, the Ministry of Education and Research calls for more school-
development projects, and LS is mentioned specifically in a recent strategy document (KD, 2014).
Cohen, Raudenbush and Ball (2003) suggest that teaching can be regarded as instructional
interactions among teachers and students around a certain content. Increased student learning thereby
requires a change in these instructional interactions. Thames and Van Zoest (2013) call for research
to focus more directly on these instructional dynamics. We suggest that LS provides a great venue
for studying the development of teachers’ interactions about teaching practice and student learning.
In this paper, we focus on issues related to research design and methods in a project where LS is used
to study indications of what the teachers learn during LS processes. To frame this discussion, the
paper presents an ongoing research project in a Norwegian lower secondary school, where teachers
learn and develop their professional practice from participating in two LS cycles. The aim is to
highlight and discuss some methodological issues in a study that applies a combination of two
sociocultural theories to investigate what teachers learn about own practice and student learning.
Although this is a theoretical rather than an empirical paper – some would suggest that it sits at the
border in between – we provide a brief empirical example from the study to illuminate our approach.
Context of the study
A group of mathematics teachers is observed in two LS cycles with an overall focus on what the
teachers learn about their own teaching practice and student learning from participating in these two

cycles. A sociocultural stance is used to investigate teachers’ learning and to understand the
participants’ perspectives and interactions in the LS group. Knowledge is regarded as shared and
collective rather than individual and develops through social negotiation (Radford, 2008). The role
of verbal interaction in the learning process is essential, because new knowledge is considered to
develop through talk in social interaction (Dudley, 2013). The theoretical and analytical frameworks
used in this study combine two sociocultural theories: activity theory (Leontiev, 1978) and Sfard’s
theory of thinking as communicating (Sfard, 2008). Research on human development and learning
thus becomes the study of development of discourse.
Tabach and Nachlieli (2016) propose a combination of activity theory with communicational theories
to study mathematics teaching, and our combined theoretical framework adheres to this proposal.
Activity theory is used as a grand theory, and LS and teaching practice are seen as activities in the
way Leontiev (1978) thought of activity. To Leontiev, all human activities are oriented towards an
object with a certain motive. The activities consist of three components at non-static levels: object-
motive, actions-goals and operations. In combination with this theoretical perspective, and to identify
what the teachers have learned on a discourse level, Sfards’ (2008) theory of thinking as
communicating is used as a local theory. This theoretical perspective defines learning in terms of
discourse, and it is also useful in that it presents certain characteristics of a mathematical discourse:
word use, visual mediators, routines and endorsed narratives. In this study, the development of
teachers’ mathematical discourse about teaching practice and student learning in the goal-oriented
actions and operations in the LS activity is studied.
The main data sources for the ongoing research project are video-recorded observations from two LS
cycles and focus group interviews (FGI). One LS cycle lasts about three months. The two cycles took
place in spring (first cycle) and autumn (second cycle) 2016. The school implemented LS as their
school-development project in January 2016, and this was the teachers’ first experience with LS. The
LS group consists of four mathematics teachers, one participant from the school administration (the
group leader) and one external expert (the first author of this paper). All the teachers’ meetings are
video- and audio-recorded. In addition, all documents produced by the teachers during the whole
process, and some of the students’ written works, are collected. Since conversation and
communication are crucial in the study, FGIs before and after each LS cycle are conducted.
The purpose of a FGI is to get a variety of perspectives on a given subject (Kvale, 2007). In the first
FGI, a discussion about the current teachers’ teaching practice, including making plans, teaching,
evaluation and the teachers’ thoughts about student learning is facilitated. In the second FGI, it is
important to let the participants reflect on what they have learned about their own teaching practice
and student learning. In the third FGI, the focus is on the LS process and what can be done differently
in the next cycle. In the last FGI, the most crucial topic relates to teaching practice and student
learning, and contains the same focus as the second FGI.
A combined theoretical framework to investigate teacher development
In the study, LS and teaching practice are seen as object-oriented activities. Tables 1 and 2 give an
overview of these activities. LS and teaching practice as object-oriented activities have a common
motive: to promote student learning. Otherwise, they have different objects and goal-oriented actions.

Another main difference is the teaching in LS (the research lesson). Because of the participating
observers and the teachers’ research question(s) – they are researching on their own teaching practice
– the teaching is planned in order to promote teachers’ learning and development as well as students’
learning. The focus on instructional interactions between teacher and students around content (cf.
Cohen et al., 2003; Thames & Van Zoest, 2013) is naturally embedded in LS.
Activity
Lesson Study
Objects/
motive
Investigate own teaching (object) to improve students’ learning (motive)
Actions
Plan the lesson
Teach the lesson
Observe the lesson
Evaluate the lesson
Goals
Prepare teaching
Facilitate
students’ learning
Gather data to
answer research
questions
Improve the lesson
Operations
Study other textbooks, curriculum materials, teacher journals,
and previous research
Formulate lessons goals, research question
Select artefacts, design worksheets, group work, differentiation
Prediction on students responses
Planning observation
Introduce and exemplify
Present problems
Support students' problem solving
Observe students
Observe case students
Documenting learning indicators
Interview case students
Discuss achievement
Discuss the strengths and weaknesses of teaching
Discuss observation
Reflect on improvement and make a new plan
Document and present results
Table 1: LS and Activity Theory (translated from Mosvold & Bjuland, 2016, p. 188)
When regarding LS as an object-oriented activity, researching your own practice to increase student
learning is the object/motive. In order to do so, teachers are conducting goal-oriented actions. These
actions represent each step of the LS cycle; formulate goals and plan the lesson, teach the lesson,
observe students and reflect on/evaluate the research lesson. Each action has its own goal – prepare
teaching, facilitate students’ learning, gather data to answer research questions and improve the
lesson. To constitute the goal-oriented actions, there are different operations, listed in Table 1.
To describe the meaning of teachers’ professional teaching practice, we draw upon the work of Ball
and Forzani (2009). They consider mathematics teaching as professional work and this work of
teaching mathematics does not come natural. It has to be learned through deliberate training. Teaching
practice is all about designing activities that increase student learning, but the work of teaching
mathematics can also be decomposed into several core components. For instance, a teacher must

present mathematical ideas, respond to students’ mathematical questions, find examples that illustrate
certain mathematical points and so on – all examples of what Ball and colleagues refer to as “the tasks
of teaching” (Ball & Forzani, 2009; Ball et al., 2008). This is another aspect of what they mean by
referring to teaching as professional practice. In order to carry out the tasks of teaching mathematics,
a specific knowledge is required that is connected with the work of teaching. This constitutes a
particular knowledge base that is shared within the teaching profession.
Considering teaching or “the work of teaching” as an object-oriented activity, the object/motive is
teaching in a way that it leads to student learning. The goal-oriented actions are the tasks of teaching,
and the operations are when the teachers actually conduct the tasks of teaching (see Table 2). These
operations require mathematical knowledge for teaching (Ball, Thames, & Phelps, 2008). Developing
teaching practice also includes developing teachers’ knowledge for teaching (Lerman, 2013). In this
study, Ball et al.’s (2008) knowledge component: “Knowledge of content and students” is used when
studying what teachers learn about student learning.
Activity
The work of teaching mathematics
Objects/motive
Help students learn
Actions
Mathematical tasks of teaching
Goals
Student learning of specific mathematical content
Operations
Conduct the tasks of teaching, depending on teachers’ knowledge for
teaching
Table 2. Teaching practice and Activity Theory
The following example illustrates how the local theory approach is applied in combination with the
grand theory. In the activity of LS, one of the goal-oriented actions is evaluation. Within this action,
an operation is to “discuss observations” (see Table 1). In the discussions of observations from the
second research lesson, the teachers discuss how the students had worked on a task of finding the
shape of a sandpit that can fit 500 litres of sand. They recall how one boy responded when challenged
by the teacher to try another figure than a rectangle – like a triangle. The boy responded, “Yes, then
we just double, because that is half, then…” Another teacher comments that the boy found another
solution. Although the example is limited, it displays some characteristics of a mathematical
discourse. In this action of discussing their observations, the teachers use mathematical words like
shape, rectangle and triangle. Their restatement of a student’s response illustrates a mathematical
routine that appears to involve the area of a triangle. When analysing the teachers’ discourse in the
actions of LS over time, the local theory may help us identify changes in discourse – which is how
Sfard (2008) define learning – on an object level or meta level. Introduction of new words are
examples of object level learning, whereas changes in the metarules of the discourse constitute
learning or development on meta level.
Considering the role of the researcher
In the described study – like in numerous similar LS research projects – the researcher acts as
participant observer. Being a participant observer in research – as the first author of this paper – might
lead to both advantages and challenges. Connelly and Clandinin (1990) underline one advantage

when they focus on the relationship between the researcher and the participants in the context of
research in education. They stress the importance of all parties’ equality, which gives rise to better
collaboration.
The first author is a participant observer in the way Bryman (2012) defines as being an “overt full
member” (p. 441). This means that the researcher is completely involved in the group’s work. Bryman
distinguishes between “covert full member” and “overt full member”. The differences being if the
members of the group are aware of the researcher’s status as a researcher or not. In the present study,
the participants are aware of the first author’s role as a researcher. Bryman (2012) claims that there
are some challenges associated with the “overt full member” role. As an active participant, you may
forget your role as a researcher. He refers to this as “going native”. To avoid this, it is important to
be aware of the different roles you have as a participating observer.
In the group meetings, the researcher switches between a conversation role and a member role. In the
research lesson, the researcher does not teach the lesson, but participates in activities as an observer.
Wadel (1991) refers to this role as the role of the apprentice. In addition, another essential aspect of
the researcher role in this study is “the knowledgeable other” in the LS group, the role of observer-
spectator according to Wadel (1991). The most important part of this role is to guide the group through
the LS cycle and help the teachers to keep focus on their own research. Previous research has shown
that without an external expert, teachers easily forget the research question (e.g., Takahashi, 2013)
and collaborate without actually doing LS.
Staying long in the field increases the stability of observations and dependability in a qualitative
project (Cohen, Manion, & Morrison, 2007). In this project, data collection spans over a calendar
year. The time span is particularly important when the researcher acts as participant observer in a LS
group, in order to reduce potential reactivity effects (Cohen et al., 2007). Another element that
supports the dependability in the study is the teachers’ reflections on the outcomes of their own
learning. This is useful for the analysis, because we can then compare findings (related to observed
change in discourse) with the teachers’ own reflections.
The participants’ opportunity to agree with the descriptions and interpretations the researcher makes
during the LS cycles underpin the confirmability in this research. Since one researcher is participating
in all the conversations when the teachers talk about their own reflections on a meta-level, this
researcher’s voice – repeating their different opinions – enables the participants to confirm or
disconfirm. This can only happen because one researcher is a participant observer.
In the final step of a LS cycle, the teachers have to think through what they have learned during the
whole process. Based on interpretations of the data material, the researcher attempts to make thick
description of teachers’ learning through lesson study. In the process of creating such thick
descriptions, we follow Stake (2010) who emphasizes the connection to theory in addition to
providing rich descriptions and interpretations of data – thus supporting the transferability of the
research.

Concluding discussion
In this paper, we have referred to a study of teacher learning in LS as a starting point for discussing
some theoretical and methodological issues that can be involved when studying what teachers learn
about teaching practice and student learning. In their call for more practice-based approaches to study
the development of mathematics teachers’ knowledge and professional practice, Thames and Van
Zoest (2013) argued that such efforts required “work on conceptualizing practice, formulating
questions about practice, and developing methods for studying it” (pp. 592–593). We suggest that LS
provides a useful venue for such studies, but we agree with these researchers that further work –
conceptual and methodological – is necessary. A possible approach is to use our proposed
combination of activity theory and Sfard’s (2008) theory of thinking as communicating to study
mathematics teachers’ learning in the context of LS. This might be useful in multiple ways. In the
concluding discussion of this paper, we want to highlight two potential benefits of applying this
combined theoretical framework.
First, the application of Leontiev’s (1978) activity theory provides a useful framing for a
reconceptualization of the work of teaching mathematics. Ball and Forzani (2009) propose that the
work of teaching mathematics is constituted by the recurrent tasks of teaching that teachers encounter
when carrying out this work. Their conceptualization fits within the idea of teaching as professional
practice. In the TeachingWorks (2015) project, they develop these ideas further and identify a number
of core practices that are particularly important in the work of teaching. A challenge with these and
other efforts to conceptualize the work of teaching is that the components of practice – for instance
the mathematical tasks of teaching – sometimes appear to be on different levels, and the issue of
purpose often appears absent. Using Leontiev’s (1978) idea of distinguishing between object-oriented
activity, goal-oriented actions and operations in a reconceptualization of the work of teaching
mathematics may solve both of these potential challenges while at the same time preserving the
obvious strengths of previous conceptualizations. Such a theory-based reconceptualization enables
new questions to be posed and may support the development of a theory of mathematics teaching that
communicates with existing theories of learning and development.
Second, the application of Sfard’s (2008) theory of thinking as communicating enables the
development of more operational definitions of teaching and teacher learning about teaching practice
and student learning. When applying a definition of teaching that combines perspectives from activity
theory with Sfard’s theory, the issues of motives and purpose are embedded. The proposed definition
of Tabach and Nachlieli (2016, p. 303) is a good candidate: “teaching can be defined as the
communicational activity the motive of which is to bring the learner’s discourse closer to a canonical
discourse”. This definition draws upon Sfard’s definition of learning as an observable change in
discourse, and the application of such a theory makes teaching and learning more easily observable.
In interpretative research, the goal is to understand and interpret the meanings of human behaviour
such as teachers’ talk, and it is important for the researcher to understand motives, meanings, reasons
and other subjective experiences rather than to predict causes and effects (Hudson & Ozanne, 1988).
This paper highlights and discusses some methodological issues that may arise when investigating
development of mathematical knowledge for teaching in LS from a participationist (rather than

acquisitionist) perspective (Sfard, 2008), focusing on teachers’ participation in object-oriented LS
activities and analysing their learning in terms of discourse as two different grain sizes. The two levels
occur because the theories look at learning differently; activity theory is focusing on acting humans,
whereas discourse theory is focusing on humans who communicate. Both perspectives are arguably
embedded when mathematics teachers’ professional practice is developed through LS, and an
application of such a combined theoretical perspective might represent another step towards the
efforts to understand what teachers learn about teaching practice and student learning (cf. Thames &
Van Zoest, 2013).
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