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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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