Hutchison, A. 'Mind the Gap' Doctoral Research Thesis

7/31/2019 Hutchison, A. 'Mind the Gap' Doctoral Research Thesis

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Chapter 1: Traction or Slippage in Education Policys Drive of

Pedagogical Reform?

1.1 The education reform policy context and pedagogical practice

The connection between education reform aspirations and teachers

classroom practice has assumed high-profile importance. By the end of the

twentieth century policymakers cross-nationally were making unprecedented

efforts to reform education by reforming teaching practice (Mayer 1999a:

29). This was an important change of emphasis, as historically education

reform had tinkered at the edges of the educational process (ibid),

remaining aloof from a concern with actual pedagogical practice. Earlier era

reform levers included the marketization of education, with removal of school

zoning and encouragement of competition between schools as an envisaged

improvement driver, and adjustments to funding provisions alongside a

variety of major structural changes. However these are now paralleled by a

prevailing interest at government and bureaucratic policy levels in levering

change in the fine-grained details of pedagogical practice itself (see Walsh

2006), partly through increasing efforts to specify and potentially mandateapproved teaching practices, while linking improved teaching effectiveness to

the achievement of benchmarked outcome goals.

This thesis examines how education reform policy connects with pedagogical

practice. In examining the level of correspondence between education reform

policy expectations and the actual practice of teachers, the research is situated

in the field ofpolicy impact analysis (Kennedy 1999). The study aims to

assess the impact of policy interventions which are targeted at improving

student learning outcomes by penetrating directly into prevailing teaching

practice.

In the specific context of Victoria, Australia, in April 2009 the Minister for

Education launched the instructional model for teachers, as foreshadowed

in the Governments September 2008 Blueprint 2 education reform policy.

The attempt to connect the engine of policy-level education reform with


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wheels-on-the-ground traction through classroom pedagogy is a significant

development for teachers, schools and the education system.

The particular government policy framework which the research explores is

the Victorian Governments Blueprint for Government Schools (generally

referred to in the Victorian education community simply as The Blueprint),

released in November 2003, and elaborated in a body of policy

implementation documentation and support material published

subsequently. In the primary policy itself and in ancillary policy documents,

such as Principles of Learning and Teaching P-12 (PoLT), The Blueprint is

explicitly positioned as the Governments reform agenda (DET 2004: 1). The

Blueprint set education reform expectations for the following five-year term

and is now extended in the current Blueprint for Education and Early

Childhood Development (generally called simply Blueprint 2), published in

September 2008. Blueprint 2 builds on The Blueprint and is not seen as

replacing it. This continuity between the two reform phases is important as it

assures the policy currency of The Blueprint and the associated

implementation measures.

The Victorian education reform policy taken as a whole, with its core policy

statements, myriad of support documentation, plethora of materials and

implementation strategies, and a consistently articulated, energetically

sustained reform message, is generally seen as a strong example of

thoughtfully orchestrated reform policy. It has broad credibility as a coherent

strategic approach to system-wide reform (Elmore 2007). The relative

longevity and stability of the then Government, the anchoring of its education

reform aspirations in a widely supported international agenda with broad

economic and civic credibility, combined with intricacy of detail in the

implementation strategies, makes this policy a particularly suitable one for

study. Elmore (2007: 2) portrays Victorian education reform as unusual in its

level of agreement among policy-level actors and practitioners ... In most

settings outside Victoria there are costly gaps in understanding between

policymakers and practitioners. Indeed, in Elmores analysis (2007: 5),

Victoria is on the leading edge of policy and practice in the world. This


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makes Victorian education reform policy fertile ground for study. If poorly

framed policy fails to gain traction there is little to be learned compared to theinsights to be gained by investigating the penetration of what is widely

regarded as exemplary policy.

In outlining the case for reform with an explicit emphasis on reforming the

nature of student classroom learning itself, The Blueprint (DET 2003: 8) is

consistent with education reform policies in other jurisdictions (see Furlong

2005) in its intent to impact directly on the pedagogical work of teachers as a

policy priority. In pursuance of this, The Blueprint (DET 2003: 15) explicitly

undertakes that the Government will develop principles of learning and

teaching for PrepYear 12 to support teachers in areas such as diversity of

learning and thinking styles, student-teacher relationships and in authentic

learning experiences. Teachers will use these principles to renew their

teaching practices. Blueprint 2 (DEECD 2008), presenting itself as the next

generation of reform, keeps alive the emphasis on the importance of the

learning experiences provided for students by the professional pedagogical

practice ofteachers. It sets out the strategies and the specific actions we will

take to achieve our vision. The Government specifically resolves to developand promote new models of teaching and learning such as greater

cooperation and sharing of practice between teachers and work practices that

make the best use of flexible learning spaces and technology.

This research investigates the connection between this espoused policy

intention and its enacted effects. Of particular significance in this regard is the

Blueprint 2 promise in the following twelve months (from September 2008)

to disseminate an instructional model for teachers. When formally released

by the Victorian Minister for Education in April 2009 this officially endorsed

pedagogical framework was, as had widely been foreshadowed for more than

two years, the e5 instructional model.1 Because of its importance as an

1This is a re-interpreted and re-contextualised version of the constructivist 5E instructional

model used to underpin US-devised Biological Sciences Curriculum Study (BSCS) curriculummaterials since the 1980s. According to Bybee et al. (2006: 3) this basic constructivist modelis traceable backto the philosophy and psychology of the early 20th century and JohannHerbart [whose] psychology of learning can be synthesized into an instructional model that


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envisaged reform lever, the roll-out of the Victorian instructional model is

examined in this thesis.

1.2 Education reform as a cross-national agenda

Education reform is a global policy agenda, or at least a cross-national one,

despite subtle differences between jurisdictions. In the Australian education

environment, policy ideas are strongly influenced by thinking emanating

particularly from the United Kingdom, but also the United States. There is a

travelling scholarship of influential education reform proponents. Elmore

(2007: 1), for example, presents his work in Victoria as part of a larger

program of research and practice primarily within the U.S., around the

state of knowledge about large-scale improvement efforts in public

education. Key education reform drivers adapted from the UK by Australian

states in recent decades, with varying emphases in different jurisdictions,

have included rigorously applied, socio-economic status (SES) compensated,

per capita funding, with school-managed global budgets supplemented by the

requirement of independent fund-raising; removal or modification of school

zoning to raise competition; incentives for the development of specialisations(the favoured UK reform term see Caldwell 2004: 30) in all schools;

institutionalised use of benchmarked data to assess school and teacher

effectiveness, with mandated school closures for failing schools associated

with new start programs underpinned by high reliance on a belief in

transformational principal-level leadership; and centrally dictated and funded

information and communications technology (ICT) initiatives aimed at

levering radical changes to pedagogy.

In seeking to lever change in teachers pedagogical work directly, the c urrent

education reform policy in Victoria is evolving closely in line with counterpart

policies in other jurisdictions. The desired changes can be summed up in

terms of a policy-driven move away from students learning abstract

knowledge, directed primarily through teacher explanation and the practising

begins with students current knowledge and their new ideas that relate to the currentknowledge.


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of routine procedures, towards active contextualized learning in which

knowledge is constructed by students in collaborative ways, in relation to realworld situations, and which assumes the more effective acquisition of

knowledge and skills by their immediate and direct application to practice.

Comparisons between these two sets of teaching approaches are stark enough

to be framed as virtual polar opposites (Kennedy 1999), with one pedagogical

set presenting as conventional practice and the emerging reform-oriented

pedagogy strongly promoted by policy at government and bureaucratic levels

with the support of an established and continually expanding body of

academic or quasi-academic theory and research.

Definitions of the contrasting pedagogical approaches are consistent across

jurisdictions. The rhetoric for expressing the reformist vision tends to be quite

consistent also. The Queensland Government, for instance, has committed

itself to the Queensland Smart State Strategy 2005-2015,promoting radical

change in the form of a transformation of the educators, curriculum and

learning environments so that there is relevance for students To embed the

transformation in education will require a significant culture shift for many

educators (Smart State Council 2007: 1). Underlining the consistency ofreform across jurisdictions was the rapid incorporation of related Queensland

material on the Victorian Department of Education website (accessed 9 April

2007), referring to and hotlinked to the Queensland Principles of Effective

Learning and Teaching policy under the heading Pedagogy around

Australia. The Victorian website noted that the Queensland principles are

expected to underpin learning and teaching practices across all sectors of

schooling. In England too, the Key Stage 3 National StrategyKey Messages:

Learning and Teaching policy documentation (DfES 2003) notes design of

effective lessons is fundamental to the pursuit of high quality teaching and

learning. The Strategy intends to strengthen its emphasis on pedagogy

promote the use of direct, inductive and exploratory approaches. It goes on

to declare that classroom organization need[s] to support interactivity the

Strategy will provide further advice on these aspects of classroom

organization.


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US reform policies provide parallel examples. The State of New Jersey

Department of Education Core Curriculum Content Standards placesemphasis on higher order critical thinking skills and is as concerned to specify

pedagogical approaches as it is to specify expected achievement standards for

students at key stages. These are articulated at an unusual level of detail in

providing a comprehensive range of specific Standards, each elaborated in a

descriptive statement and cumulative progress indicators describing the

student learning behaviours and understandingswhich teachers pedagogy is

expected to facilitate.

As the policy analysis aspect of the research reveals, policy nuances vary

subtly from place to place and even over the policy roll-out phases within the

one jurisdiction. For example, pedagogical practice envisaged in English

reform policy is generally consistent with but somewhat more conservative

than the Australian or New Jersey examples.

Noting the increased commitment to driving education reform at the level of

classroom instruction, Fullan et al. (2006: 27-29) caution that while

coherence between the multiple levels of schooling [systems, schools,classrooms] is an important precondition for successful school reform the

knowledge base about classroom instruction is surprisingly tenuous, and in

much policy discussion about school reform, the classroom remains

something of a black box [italics in original; explanation inserted]. More

research is required to investigate the connection, or disconnection, between

education reform intentions and actual classroom practice. As Cochran-Smith

(2005: 6) rather nicely puts it: everybody likes teacher quality and wants

more of it. The problem is there is no consensus about what it is. Reform

policy anticipates the specifying, and spreading by ostensibly best practice

transfer, of pedagogical approaches considered desirable (Cochran-Smith

2005). However, Kennedy (1999: 345-348) proposes a central problem for

policy researchers is how to document a clear path of influence that extends

from policy manipulations to student outcomes. She urges that sustained

research is needed to investigate how policies influence the intellectual

character of classroom events [and] the quality of student learning.


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1.3 Policy penetration into practice

A simplistic model may envisage the transfer from policy to practice as a

straightforward rational-technical process in which an authority determines

that a particular line of action is required and undertakes some explicitly

communicated steps to specify the action and the implementation process.

The failure of this theory to accord with reality is nicely captured in an

observation generally attributed to Dutch mathematician and computer

scientist van de Snepscheut: In theory there is no difference between theory

and practice. In practice there is.

There is already a reasonably substantial body of research investigating the

policy-practice gap in terms of education reform policy and teachers actual

pedagogical practice. Mathematics education research has been particularly

active in studying the connection between education reform expectations and

what transpires in teachers pedagogical practice. While a detailed overview of

this research is provided later, by way of introduction it is helpful to citeKennedys (1999: 346) observation that a lack of adequate research evidence

still causes education reform to depend instead on a hypothesised model of

the path of influence that leads from policy to student learning.

Absence of sufficient research evidence on influences and determinants of

actual practice is a problem in any policy field, but particularly so in the

complex case of pedagogical practice which remains insufficiently researched

and difficult to bring to the surface for close examination. Teachers

pedagogical knowledge is particularly difficult to uncover, and highly resistant

to change, because it is intricate and situatedknowledge (Mishra and Koehler

2006). It is largely tacit knowledge deeply embedded in the subtle socially

constructed contexts of teachers specific work cultures, and for better or

worse it has a stability which proves almost impervious to imposed radical

change of the kind envisaged in transformational reform policy. It is essential

to undertake investigations to cast better light on the policy-practice gap,


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particularly because theoretical frames of reference or assumptions

commonly underpinning education policy formation are not sufficientlydeveloped from a teacher practice point of view (Moss 2006). As Spillane and

Zeuli (1999: 3) observe, careful analysis of teaching practice [is] an essential,

though frequently neglected, component of policy implementation research.

Another gap in the existing research base is that there has been little research

on the ways in which the different professional communities involved in

education construct their understandings of policy and practice. This study

aims to compare the discourse about education reform policy by those who

devise it with the discourse about the same thing by those who are expected to

enact it (Eisenhart 2002: 221). Additionally, drawing on Argyris and Schns

(1996) organizational learning framework, the study examines teacher

discourse in their own descriptions of their pedagogical practice and

compares their espoused theories with their theories-in-action as evidenced

in classroom observation.

Discourse analysis, which has its own theoretical frames, is applied as a

research technique in this study. As an investigation method it is used in linewith Mayers (1999a) encouragement of detailed classroom discourse analysis

as a way of getting to deeper evidence about the actual character, including

the cognitive demand level, of the learning activities provided by teachers for

students. This is consistent with an emerging participationist and

communities-of-practice approach to students classroom learning in that

classroom discourse must be studied in detail to see beyond superficial

impressions of reform pedagogy being enacted. Additionally, discourse

analysis is applied in this study to policy documents and implementation

materials, and to the interviews conducted with members of a variety of

distinct education constituencies, leading to the proposition that education

reform is impeded by incongruent frameworks and concepts of pedagogical

practice held within the different discourse communities, and also by

insufficiently sophisticated transfer of best practice notions of teachers own

professional learning which predominate in policy models but are at odds


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with the complex reality of how teachers pedagogical practice is actually

constructed.

1.4 Theoretical frameworks

The conceptions of professional practice informing this research are drawn

from the theories of situated cognition, communities-of-practice and

organizational learning. (See Chapter 3.) While these frameworks have

discrete identities, separate origins and varying emphases, they entail a

conception of professional practice as a culturally situated activity. The

theoretical perspectives are inter-connected by an understanding of practice

as embedded and largely tacit behaviour acquired over a long period in the

presence of a complex web or network of socially situated factors. They have

considerable utility and explanatory power in building on the findings of a

body of previous research, particularly in the US mathematics education

context, which sees teachers pedagogical practice as enacting complex,

culturally embedded, implicit knowledge. An emerging discourse among

mathematics educators explicitly draws on the communities-of-practice

understanding of learning in developing a domain-specific participationistlearning model. This supports a shared discourse about learning within this

particular educational community. However, despite reform policy

aspirations to get at pedagogical practice directly, and lever it in particular

directions, prevailing policy assumptions remain largely aloof from and

oblivious to the intricacies of pedagogical enactment.

The communities-of-practice framework (eg. Brown and Duguid 1998; Lave

and Wenger 1991; Lakomski 2004) provides a theoretical foundation to

interpret the situated and contextualised nature of learning. This depends

only partially on symbolic knowledge held inside individuals heads, explicitly

expressed and verbally transmitted. Knowledge and learning are embedded

and embodied as distributed properties of organizational, communal and

collegial settings. Tacit knowledge, in the form of largely taken-for-granted

professional know-how and shared sense-making, is understood in this

conceptual framework as more potent in shaping practitioner behaviour than


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explicit, symbolically and consciously codified, verbally communicated

canonical knowledge. From this perspective, knowledge is understood to belocally produced social and cultural property (Lakomski 2005) which is highly

resistant to imposed or exhorted change.

An implication of the professional communities of practice and culturally

situated learning perspectives amassed in an extensive body of research

literature on teaching specifically (eg. Darling-Hammond and McLaughlin

1995; McGregor 2003) is the difficulty of policy-driven initiatives making any

deep impression on pedagogical practice, unless they are highly coherent,

effectively orchestrated, well resourced and energetically sustained over a very

long term. Even then, as Cohen (1995: 16) cautions, coherence in policy is not

the same thing as coherence in practice.

Elmore (1995: 357) laments the recurring disconnection between reform

policy and teaching practice, observing it often seems as if policymakers

believe that changing the regulatory structure within which schools operate is

sufficient in itself to produce large-scale reform in student learning, without

any of the complications of changing teaching practice and schoolorganization. Identifying school inertia in the form of an enormous capacity

to resist reform, Elmore contends that attempts to reform teachers practice

need to take account of the socially situated and co-constructed nature of

teachers work.

Echoing this perspective, ONeill (2003) urges an approach to research on

school reform which moves away from generic macrocosmic policy to closer

engagement at the detailed microcosmic policy ethnography level, bringing

teachers situated practice out of the black box and placing the actual work of

teachers in their professional community of practice at the centre of school

improvement efforts. Complementing this view, McGregor (2003: 127) calls

for research along lines which articulate with new theories of situated

learning ... [which] take knowledge as created through practice, so learning is

social and participative rather than cognitive. In seeking a theoretically

grounded and research based approach to school improvement, McGregor


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argues that the concept of communities-of-practice and of situated learning

has some considerable utility. In the present research, analysis of currentreform policy discourse will shed light on how far this potential utility is

recognised at the policy framing and implementation levels.

The exceptionally complex process of education reform cannot be understood

using a simple mechanical metaphor. The policy-making engine cannot just

deliver a drive thrust which then goes through a transmission system to be

converted into movement in the desired direction, delivered by the wheels of

classroom teaching. In the muddle inside a muddle reality of school

education (Gardiner 2009) there is no linear transmission process operating

across connections between inert parts. Rather, there is a bewilderingly

intricate array of partial connections, loose couplings, slippages, and parallel

competing and conflicting systems coexisting within an organic whole.

Uncovering and examining the assumptions about pedagogical effectiveness

embedded in the partially explicit but largely implicit paradigms of the

different educational discourse communities should contribute to a better

conceptualisation of how the loosely coupled or detached elements ofeducational improvement drives may be more coherently connected or, to use

a more appropriate term, aligned.

1.5 Reasons for the focus on mathematics pedagogy

While the research is not a study in mathematics educationper se, and is not

intended to propose specific recommendations for the improvement of

mathematics teaching, the area of pedagogical practice chosen for study is

middle secondary school mathematics. The priority placed on numeracy in

education reform policy cross-nationally, as well as the relatively high levels of

consistency in mathematical curriculum content across educational

jurisdictions compared to other areas of the curriculum, suggests it would be

useful to analyse mathematics teaching in assessing reform policy impact on

pedagogical practice. Therefore, the observed lessons are somewhat

controlled for curriculum content, allowing a clearer focus on the pedagogical

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dimensions specifically. While the distinction between curriculum and

pedagogy is an imperfect one, being able to standardise the discipline contextof the observed lessons to some extent enables the lens to be focused more

closely on the nature of the pedagogy itself.

Additionally, as already indicated, there is a substantial established body of

research in mathematics pedagogy specifically in the context of education

reform policy. This study is intended to add to that knowledge within a

particular Australian setting.

1.6 Specific research questions

Originally investigated in a US teaching reform context by Spillane and Zeuli

(1999), this current study asks: to what extent does teachers actual

professional practice reflect change in the desired reform policy direction?

Spillane and Zeuli identified several distinctive patterns in the ways their

mathematics teacher participants adapted, evaded, deflected or distorted

pedagogical reform intentions. The question is redirected here, in a different

decade and jurisdiction, to the teaching and learning focus of the VictorianGovernments education reform agenda.

The present study also asks why education reform policy is or is not

succeeding in gaining the expected penetration into pedagogical practice.

What socio-cultural factors in the regularities of teachers work practices

enable or impede their willingness and ability to embrace, resist or deflect

pedagogical reform policy expectations? How do teachers experience

pedagogical change expectations, including how aware of and explicitly

knowledgeable are they about them? How do they perceive their own and

others responses to education reform policy? How do teachers, members of

school leadership teams, policy framers and influencers, mathematics

education specialists, and other identifiable constituencies position

themselves within the landscape of policy discourse? Indeed, is there an

identifiable discourse positioning (Wood and Kroger 2000) generally shared

within these sets but not shared between the sets?


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By asking these questions, the field work undertaken in this study seeks toestablish why the specific policy direction is either failing or moving very

slowly, despite the best policy intentions, or why it is showing indications of

succeeding despite the complex obstacles and impediments to be identified.

The research will thus contribute to an understanding of what policy can

achieve in influencing practice and what its limitations are. It will result in

new explanations and proposals concerning the impact of policy on practice.

1.7 The research approach

While adopting and extending Spillane and Zeulis (1999) research question,

the mixed methods research approach devised for this investigation is

original. Using an original lesson observation schedule to rate two lessons

taught by each of twelve participant teachers on a measure of reform-

alignment scale, the study seeks to reflect back and forth between the

expressed and implied aspirations of education reform policies and the

observed evidence of teacher practice. Along with a pedagogical practice

survey of a larger group of over a hundred secondary mathematics teachers,the results provide important data for interpreting whether the low

correspondence between reform aspirations and actual classroom practice

reported in other studies, to be reviewed in Chapter 2, applies to the current

Victorian government education reform policy agenda.

The teaching and school administration background of the researcher

positions him as a somewhat native observer in the professional worlds of

the teacher participants and their situated work culture. While the research

does not purport to be ethnographic in the sense of deep immersion in the

experiential worlds of the participants, it takes a naturalistic approach to the

study of the teacher participants work. This is necessary because it is the

socio-cultural context which most influences beliefs, tacit assumptions and

actual work practices.


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Eisenhart (1988) defends the pragmatic adaptation of ethnographic research

approaches to the goals of educational research, clarifying that the socialimmersion called for in pure ethnography need not be the goal. Eisenhart

(1988: 100) argues that while traditional ethnography, like other useful

research approaches, speaks a distinct research language, much could be

gained in educational research by drawing on its descriptive power based on

close observation and attending to the importance of specific socio-cultural

settings.

This position is in line with Trows (1997: 14) concern that policy studies have

made little use of ethnographic research methods, the method of direct

observation of customary behaviour and informal conversation. While a

purist notion of ethnography would demand much greater immersion in the

lives of participants in the culture under study than Trow has in mind, his

view is closer to the partially ethnographic approach taken in the present

research. The study remains true to ethnographic principles in its concern

with uncovering and foregrounding (Lather 1991) the situated realities of

teachers actual professional practice, which need to be better understood if

reform policy is to have any prospect of penetrating below the surface featuresof pedagogical practice.

The study is ethnographic in so far as it places emphasis on context and thick

descriptions (Freebody 2003: 76). The picture obtained is viewed as a piece

of culture examined in depth to identify larger cultural issues and elements

(Green et al. 2003: 36). The research aims to uncover the explicit and tacit

cultural knowledge that members use (Neuman 2006: 382). Detailed

descriptions of behaviour and talk in the specific context of teaching activity

form a core element of the study (Freebody 2003), in keeping with Neumans

(2006: 381) definition of ethnography as providing a very detailed

description of a different culture from the viewpoint of an insider in the

culture to facilitate understanding of it. In selecting a naturalistic approach

to examining teachers pedagogical work it is useful to note Freebodys (2003:

127) explicit call for rich and grounded accounts of teaching and learning.


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That is, the goal here is to explore in detail what members of a culture

routinely do.

Discourse analysis, as explained in Chapter 4 both in the theoretical terms of

discourse analysis and in its direct practical application within the research

methodology, is used to uncover implicit conceptions of pedagogical practice

and its reform. Discourse analysis techniques (Wood and Kroger 2000;

Phillips and Hardy 2002) are applied to a substantial body of interview data

from participant teachers and other respondents drawn from a range of

identified education policy constituencies, with a view to establishing their

shared patterns of discourse. This leads to the identification of what are

presented as discourse communities.

A disconnect is suggested between the different discourses of identified

constituencies in the policy-practice relationship. Policy framers, policy

officers and bureaucrats, policy analysts and commentators, principal-class

school leaders, mathematics teachers and mathematics education specialists

(including researchers) emerge as distinct discourse communities. Their

discourses both reflect and actively constitute different assumptions andbeliefs about education reform and its relation to pedagogy (see Cochran-

Smith 2005). They operate as virtually self-referring separate universes.

These independent discourse worlds slip and slide past one another, touching

or bumping at the edges, spinning on the understandings of their members

and affiliates, largely oblivious to other discourses except at the most surface

level. The thesis proposes that the slippage between these only loosely coupled

discourse systems represents a significant barrier to education reform, in the

form of a critical gap between policy and practice.

1.8 Outline of the thesis structure

The thesis is organised into seven chapters, including this introduction.

Chapter 2 establishes the complexity of studying pedagogical reform in the

context of mathematics teaching specifically. The chapter reports on previous

research in this area, in the process showing how notions of reform, and the


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connotations of the term itself, vary markedly across different education

communities.

Chapter 3 explores conceptions of practice which are useful in interpreting

the policy-practice relationship, and which are drawn from key theoretical

frames widely cited in current studies of mathematics teaching specifically.

While the theoretical frames are discrete, they share in common an emphasis

on the implicit and embedded dimensions of professional practice. These

subtle, tacit dimensions are difficult for policy to penetrate in order to

produce significant changes in teachers pedagogical work. These concepts of

practice and the theories on which they rely for explanation are developed in

the chapter to clarify the theoretical and research context within which the

study is situated. They are chosen both for their currency in existing research

and for their explanatory power.

Chapter 4 explains the mixed methods research design, describing the

research approach in detail for clarity. The research combines direct

pedagogical practice observation and classification in field work conducted in

six Victorian government secondary schools, along with supplementaryteacher surveys of pedagogical approaches, and interviews with respondents

from different education policy constituencies. The detailed methodological

discussion is intended to ensure that the study is replicable in different policy

and pedagogical practice contexts.

Chapter 5 presents results of the research drawn from lesson observation and

survey data, which to some extent can be presented as measurements and

represented statistically. Taking into account the mixed methods design, the

presentation of results is divided across two chapters, with interpretive

analysis of the data drawn from open-ended (semi-structured) interviews in

different identified education communities held over and presented

separately in Chapter 6. The reason for this organizational separation is to

acknowledge the inherently interpretive nature of results drawn from analysis

of discourse, entailing an overlap between the presentation and interpretation

of results. The presentation of interview analyses, by virtue of the selection of


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material for inclusion and the application of discourse analysis, both reflects

and foreshadows emerging interpretive strands. Reasons for and possibleeffects of not quarantining the presentation of interview results from

interpretive commentary on them are discussed within Chapter 6, referring to

Freebodys (2003) and others work on qualitative research methodologies.

Chapter 7 presents the conclusion that we find predominantly slippage, rather

than traction, in current education reform policy implementation. The

reasons for this, and suggested responses, are proposed in this closing

chapter, which distils the findings, applies the theoretical frames in

developing an explanation of the observed patterns, and draws out

implications for theory and for practice.

The thesis concludes that prevailing reform policy expectations lack adequate

theoretical understanding of how enacted pedagogical practice is socially

constructed. The argument developed supports a more realistic and defensible

conceptualisation of teachers professional knowledge, proposing an

incremental improvement process (in contrast to transformational reform)

based on directly building teachers collaborative pedagogical developmentcapacity, from the ground up and within authentic and viable professional

communities-of-practice.


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Chapter 2: The Case of Mathematics Pedagogy Reform

2.1 Purpose of the mathematics pedagogy focus

This chapter sets the context for the present study, expands on the reasons for

the focus on mathematics teachers pedagogy in particular and introduces

concepts of practice used to frame the research. Some elements of these

concepts are already widely employed in existing research on mathematics

pedagogy, particularly in the context of investigating the impact of reform

agendas. These concepts of practice are drawn from a range of separate

theoretical frameworks which, while discrete, have some key elements in

common. The theoretical frames are identified in this chapter but consideredin detail in Chapter 3. This present chapter focuses specifically on the

mathematics pedagogy reform research landscape in which the current study

is situated.

A body of research (eg. Spillane and Zeuli 1999) has sought to assess and

explain the degree to which mathematics teachers are teaching in ways

aligned with reform principles. This present study aims to contribute in this

area by studying mathematics teachers pedagogy in classrooms, and eliciting

mathematics teachers perspectives in terms of how they understand and

respond to expectations of pedagogical change. Teachers in the mathematics

domain encounter a complex array of inconsistently defined and competing

pedagogical reform expectations. While demands for reform at the level of

classroom teaching press from all around, what is actually envisaged by this is

inconsistently framed. As will be seen, some reform propositions are

incongruent with others and even oblivious to other constructions of reform.


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Inconsistencies lie in nuances and in the envisaged scale of reform.Technically the term reform means improvement through the removal of

system faults or errors (Concise Oxford English Dictionary). It is not

inherently transformational in pitch. However a prevailing cross-national

reform policy agenda (eg. Gladwell 2001; Caldwell 2004; Hargreaves 2004)

envisages radical transformation of schooling as part of a new imaginary

(Beare 2006) which would see the very notion of the classroom as largely

obsolete. However other education reform agendas appear on the surface

considerably more modest in envisaging improvement in classroom learning

not as an overall educational restructure but as more effectively inter-

connecting learning across disciplines and between school-based learning and

real life applications. This vision of making school-based learning more

relevant and therefore more engaging is part of the thrust of current Victorian

education reform policy, which strongly emphasises building the inter-

connectedness of student learning with the development of confident,

engaged and contributing members of society. Even given the apparent

relative modesty of these aspirations here, as will be discussed, achieving real

change at the fine-grained level of classroom learning is still highly elusive.

Working virtually on a different page altogether are calls for reform within the

tightly defined realms of individual subject disciplines. Nowhere is this more

apparent than in the area of mathematics education. Within the mathematics

realm reform is highly contested territory, so much so that in the United

States the debate has been dubbed the Math Wars (Schoenfeld 2004; Klein

2007). Essentially the contention revolves around the question of whether

mathematics learning at school level is inherently undermined by attempts to

make mathematics more instrumental to serving other disciplines, and

trivialised by supposed real life applications. Reform mathematics, as

articulated in the US National Council of Teachers of Mathematics (NCTM)

mathematics standards and associated curriculum and pedagogy materials, is

generally consistent with the inter-connectedness thrust of more generic

pedagogical reform policy such as that in Victoria. However the mathematics

reform debate is extremely fine-grained as it involves counter- propositions


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about authentic reform residing essentially in attempts to move to less

repetitious computation and increased higher-order thinking through diversehigh-cognitive demand tasks, while remaining purely mathematical in

construct and intent. The practical implications of this specialist vision of

reform may be quite incompatible with the more generic reform thrust that is

concerned with making mathematics more relevant by integrating

mathematics with other disciplines and presenting its value as primarily

instrumental in serving direct practical applications.

A central point which will emerge in this thesis is the disconnectedness from

one another of the concepts of education reform held within the discourses of

different communities. In the discussion the term policy community will be

used to indicate an identified common interest group which formulates,

influences, or is affected by, policy decisions and policy initiatives. The term

discourse community will be used to indicate an interest group which acts on

a particular understanding of what is entailed in the reform agenda and,

regardless of whether consciously contesting another construction, frames

discussion in terms commonly understood within that particular community.

As indicated in the introductory chapter, the reform focus on the nature of

pedagogy itself characterises prevailing reform agendas, no matter how

otherwise diverging they may be. This reflects findings of numerous studies

(eg. Hill 2003; Hattie 2003; Rowe 2004; Jensen 2010) that the effect size on

student learning of teachers pedagogical efficacy outweighs all other school-

based factors affecting student learning outcomes. So the importance of

bringing about pedagogical improvement in every classroom is generally

acknowledged, even though there may be little functional agreement about

what constitutes effective pedagogy beyond some broad generic principles.

The difficulty of changing teachers pedagogical practice is well documented.

Hattie (2008) found that reducing class sizes had minimal effect on student

learning because teachers do not alter their teaching practices even if group

sizes are reduced. Numerous studies have investigated limitations on the

degree to which and ways in which teachers have the capacity to modify their


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pedagogy (eg. Firestone et al. 2004). While some studies have attempted to

suggest ways of enabling change, others have proposed factors in theconstruction of teachers work which help explain observed resistance to

change in pedagogical practice.

As will be described in this chapter, the research is particularly well-

developed in the area of mathematics teaching. It is for this reason, and also

because of the generally agreed central importance accorded to numeracy

skills in education reform in virtually every government jurisdiction, that this

study focuses specifically on mathematics pedagogy. A vast body of existing

research in this area has attempted to measure, assess and explain the

construction of teachers pedagogical practice. In doing so, some of the

research to be cited has drawn explicitly on the explanatory power of concepts

of practice based on established theoretical frameworks such as communities-

of-practice, socio-culturally situated cognition and organizational learning.

There is considerable overlap in the key principles of concepts of practice

drawn from the respective theoretical frames. These will be detailed in the

next chapter, but in essence they share an emphasis on the shaping of practiceby forces and factors which are tacit, implicit and embedded, and therefore

resistant to conscious deliberate modification. Much of the research in

mathematics pedagogy draws directly on the theoretical frames to be utilized

in this current study. For example, Mishra and Koehler (2006) propose a

framework for understanding the nature of mathematics teachers

pedagogical knowledge which they are expected to modify in the highly ICT-

enabled teaching environment of the contemporary school. In line with other

researchers who pay close attention to the nature of teachers enacted

practice, Mishra and Koehler (2006: 1017-18) draw attention to the complex,

situated form of knowledge that teachers require. In denial of some reformist

expectations of ICT proving the magic bullet for transforming pedagogy

(based on ICT transformation in some other work domains), Mishra and

Koehler observe in education the reality has lagged far behind the vision.


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The elusiveness of pedagogical change is partly because of the inadequate use

of theoretical frameworks to interpret and understand the nature of teacherspractice and how their professional knowledge is formed and maintained.

Mishra and Koehler (2006), writing primarily in a mathematics context, cite

Selfes (1990) largely unheeded plea for the development of a theoretical

framework for understanding how mediating factors such as ICT intermesh

with the complex, situated nature of pedagogical work across all subject areas

including English. They argue that this is the only way to avoid myopic, ad

hoc, and isolated efforts to bolt on to existing pedagogy some disjointed

extension offered through ICT interventions, with little change or

improvement to the foundations of practice to which ICT becomes loosely and

unevenly attached.

It is useful to give close consideration to Mishra and Koehlers (2006) work

because it provides a substantial framework for understanding how

discipline-grounded notions of pedagogical practice and pedagogical reform

may be at odds with more generic policy level education reform constructs,

both in practice and theoretical framing. Mishra and Koehler (2006: 1020)

propose that the difficulty of implementing new approaches so that theybecome embedded, rather than remaining inconsistently assimilated add-ons,

reflects that teaching is a highly complex cognitive skill occurring in an ill-

structured, dynamic environment. They question the reform reliance on

professional development which emphasises generic pedagogical principles,

decoupled from discipline-specific subject matter, and argue for the integrity

of pedagogical content knowledge (PCK) as the foundation of effective

teaching. The argument is that deep content knowledge is a necessary, while

insufficient, condition for effective teaching. It provides the essential

foundation. It follows that shallow content knowledge cannot be transformed

into effective teaching by any generic form of content-free pedagogical

competency. Mishra and Koehler (2006: 1026) cite a body of theory and

previous research which suggests that neither technology nor pedagogy can be

understood as context-free or neutral:

Teachers must know and understand the subjects that they teach,including knowledge of central facts, concepts, theories, andprocedures explanatory frameworks that organize and connect


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ideas the rules of evidence and proof the nature of knowledge andinquiry.

The foundations of this pedagogical knowledge are discipline specific.

Pedagogy cannot be approached as if it were a form of applied technocratic

rationality (Mishra and Koehler 2006: 1031). However, as will be seen, this

view of pedagogical knowledge is not at the core of prevailing government

level reform policy agendas.

At the heart of Mishra and Koehlers (2006) contribution is their insistence

that teachers pedagogical knowledge must not be simplified, underestimated

or undervalued. It is complex specialist knowledge belonging to specific sub-

communities of teachers, and which is more than the sum of its parts because

it is integrated and socially situated. This knowledge is different from the

knowledge of a disciplinary expert and also from the general pedagogical

knowledge shared by teachers across disciplines. Quoting Marks (1990),

Mishra and Koehler present pedagogy as a class of knowledge that is central

to teachers work and that would not typically be held by non-teaching subject

matter experts or by teachers who know little of that subject. Drawing

explicitly on the situated cognition and communities-of-practice theorieswhich the mathematics education reform community widely uses in its shared

discourse, Mishra and Koehler portray effective teachers as skilled facilitators

of students carefully graduated immersion as practitioners of a discipline

rather than passive learners abouta discipline. Ogawas (2003) work provides

further support for this view of teachers pedagogical practice as a highly

developed form of socially mediated specialised expertise.

It seems highly unlikely that a transmitted instructional model, no matter

how elegant and coherently presented, will produce this high quality

pedagogical knowledge in the absence of collaborative work by teachers

anchored in their own subject disciplines, informed by theories congruent

with the participationist notion of student learning and involving the

profession itself as co-developers in conjoint agency with curriculum area

specialists at university level. There is a sense of excitement and energy about

pedagogical reform in these discourse communities, but their meaning of


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reform is radically different from that envisaged in the centralised education

reform policy framing, to be examined with specific reference to the exampleof the Victorian agenda.

2.2 Education reform policy and mathematics reform

specifically

Much reform policy discourse is infused with hyperbolic rhetoric around a

vision of transformational change. As one interview respondent in this study,

a UK-based international mathematics educator2, put it: We cloak it in all

this tipping pointstuff. This was in reference to the global education reform

policy discourse as framed, for example, by Caldwell (2004: 16) who, in

endorsing the Blair Government education reform strategy of relentless top-

down insistence on reform, proclaims expectations for schools have

changed. Nothing short oftransformation is now expected. Caldwell asserts

that education isbeing successfully transformed and citing Gladwells (2001)

metaphor of the tipping point proposes that we have reached a watershed

where fundamental reform of schools will be not only achievable but also

irresistible. Sliding his metaphor into that of an educational epidemic,Gladwell (2001) proposes that belief assures success: what must underlie

successful epidemics is a bedrock belief that change is possible, that people

can radically transform their behaviour or belief in the face of the right kind

ofimpetus (cited in Caldwell 2004: 76).

However, different discourse communities hold conflicting views on

education reform in two senses. Firstly there is lack of agreement about the

pace of reform which is both possible and advisable; gradual incremental

improvement in collaborative professional practice is a very different

proposition from the transformational scope associated with mega-reform

policy discourses. Secondly, there is lack of agreement about the locus of

reform. The mathematics education community proposes incremental

improvements to mathematics pedagogy which are informed by emerging

2Anonymity was a condition of all interview respondents participation, except in cases of

established writers or academic researchers whose words are cited, with their agreement, asrepresentative of their published body of work.


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theories and research anchored in a discipline-specific understanding of

mathematical knowledge. Whether education reform policy at the macro-scale can spiral down to connect with cautious micro-scale adjustments

envisaged in the specialised mathematics education community is a major

question. Reading literature emanating from the different policy discourse

communities can seem like moving between parallel universes.

Specialised mathematics education research forms a distinct community of

practice with its own frames of reference. Different professional communities

can appear almost hermetically sealed, with a taken-for-granted prevailing

discourse enacting understanding within but not between the different

communities. One of the participant teachers in the current research, who

emerged as a highly reflective practitioner with a detailed knowledge of

mathematics education theory and research internationally, commented that

in overseas educational settings, Theyve never heard ofPoLT[the Victorian

Principles of Learning and Teaching]. In retrospect itll just be the latest fad

that went away. This observation is included here as a bridge to the

discourse on mathematics education reform which operates not only in an

academic community but also in a research-in-schools universe removedfrom Victorian education reform policy discourse. It is specialised, reflective

and based on a strong body of research and theoretical literature.

Yet this is set against a prevailing popular image of secondary mathematics

teachers and tertiary mathematics specialists as belonging to an unreflective

reproductive culture. As will be seen in the presentation of the research

outcomes, mathematics educators tend to be caricatured as die-hard

conservatives with an attributed failure to connect with reform aspirations.

However, mathematics specialists are deeply interested in reform, albeit in a

different discourse frame. While there is overlap in terms of a seemingly

shared concern for high cognitive demand complex thinking tasks to be

incorporated into student learning, the operational definitions of higher

order thinking skills are framed in distinctly different ways in the respective

communities. This conceptual disconnection contributes to a policy-practice

gap.


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2.3 The specificdiscourse of mathematics reform

As an international professional cohort, mathematics education specialists

may never have heard of PoLT but many have certainly heard of

communities-of-practice. As models of student learning evolve, conceptual

tools used to understand and frame the nature of effective pedagogy develop

in parallel, and thereby create perhaps unexpected connections. In a person

in the street view, improving secondary mathematics teaching may be

envisaged as a fairly straightforward technical process. It may be thought that

there is little connection between this and complex theoretical frames such as

organizational learning, communities-of-practice and socio-culturally

situated cognition. Nevertheless these links are established. In an emerging

mathematics education discourse (eg. Lerman 2001) effective student

learning is envisaged as dependent on participating as a novice in a

classroom community-of-practice, where the teachers role is that of an

experienced facilitator and collaborator in developing specialist mathematical

knowledge. The learning is seen as co-produced by teachers and students

within normative socio-mathematical practices. A substantial body ofcontemporary research on mathematics pedagogy frames student learning in

terms considerably beyond the basic constructivist model of learning

apparent in prevailing education reform policy discourses, including in

Victorian policy currently. Leading international proponents of this

specialised discourse include Paul Cobb (Vanderbilt University) and his

numerous collaborators; and Anna Sfard (University of Haifa, Michigan State

University, and the Institute of Education, University of London).

Taking a participationist view of mathematics learning, as an extrapolation

from the sociocultural approach to cognition, Sfard (2001: 28) proposes

mathematical learning must be defined as an initiation to mathematical

discourse, that is, initiation to a special form of communication known as

mathematical. This requires that mathematical learners are inducted into a

community of practice which understands the use of the mediating tools of

mathematical discourse and the meta-discursive rules that regulate the


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discourse among the initiated (whether experts or novices) and which

usually remain tacit for the participants of the discourse (Sfard 2001: 13).

Sfards work belongs within an emerging body of mathematics education

research supporting the participationist model of student learning. Her

findings cohere with the extensive research conducted by Cobb and others

emphasising the central importance in learning (in fact, constituting the

essence of the learning itself) of students being inducted into socio-

mathematical norms. A keyattribute of these norms according to Yackel and

Cobb (1996: 458) is that they constitute normative aspects of mathematical

discussions that are specific to students mathematical activity, explaining

how students develop a mathematical disposition [with] the teachers role

as a representative of the mathematical community. This notion of

developing a mathematical disposition is a widely shared concept within the

mathematics education community, the term being embedded in the

influential US NCTM [National Council of Teachers of Mathematics]

Principles and Standards for School Mathematics (1991, and subsequent

versions). Mayer (1999a: 30) notes prominent science, mathematics and

technology education reform movements throughout the United States andother developed countries [are] heavily influenced by the NCTMstandards.

In essence the NCTM approach is reformist in its emphasis on application,

reasoning and conceptual understanding, achieved through engagement,

participation and collaboration, rather than memorisation and mastery of

routines.

Going further and building on the Vygotskian communicational approach to

cognition principle that communication should be viewed not as a mere aid

to thinking, but as almost tantamount to the thinking itself, Sfard (2001: 13-

14) develops the notion of learning-as-participation. She cites extensively

the established communities-of-practice and situated cognition literature,

including Lave and Wengers (1991) seminal Situated Learning: Legitimate

Peripheral Participation, in which the authors argue for a learning model in

which students as novices are inducted into a particular learning community

by graduated immersion, in the presence of existing holders of the socio-


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cultural norms. Also cited by Sfard is Brown, Collins and Duguids (1989: 32)

exposition of learning as a kind ofcognitive apprenticeship which honorsthe situated nature of knowledge.

Pointing to the slow pace of reform in practice, Sfard (2001) highlights that it

is many decades since mathematics educators like Brownell (1935) urged a

move away from a learning-as-acquisition model to a model which

combined a constructivist notion of learning with a concern for deep

thinking. Brownell (1935: 31) proposed that we need full recognition of the

value of childrens experiences and must make arithmetic less of a

challenge to a pupils memory and more a challenge to his intelligence. Sfard

(2001: 18) sees effective teachers as relying on a set of intuitions based on

their domain-specific, discipline-framed, pedagogical content knowledge, in

constructing opportunities for what she terms meaningful learning or

learning-with-understanding.

As a mathematics educator, Sfards interest in a participationist model of

learning stems from the proposition that in still prevailing learning-as-

acquisition models, teachers do not have well-developed techniques foridentifying the cognitive reasons for students failure to understand presented

concepts. Testing, whether formal or informal, indicates only that there is or

is not a desired level of understanding, but provides no guidance about how to

get to the cause, or process of understanding. This results, at best, in the re-

presentation of the same concepts in a marginally reframed way. However,

adoption of a constructivist approach does not address this problem either.

Sfard (2001) presents this approach as little more that an extension of a basic

knowledge-as-acquisition model, in that acquisition may take place either by

passive reception or by active construction. In Sfards (2001) analysis the

dominant cognitivist approach has:

equated understanding with perfecting mental representations anddefined learning with understanding as one that effectively relatesnew knowledge to knowledge already possessed knowledge itselfisconceptualized as a certain object which a person either possesses ornot, and learning is regarded as a process of acquiring this object.


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Sfard (2001) reports analysis of student discourse in collaborative classroom

interactions to show the difficulty of getting to the root of mathematicalmisunderstanding, and the consequent difficulty of determining how re-

presentation of concepts can overcome misunderstanding if the causes of this

are not understood. Explicitly citing the Brown et al. (1989) phrase cognitive

apprenticeship, Sfard proposes a sociocultural approach to pedagogy

emphasising the process of interaction which leads to the students alignment

with the teacher and with the knowledge co-constructed in the interaction of

initiated expert and novice. Sfards overall body of work is concerned with the

development of an approach to pedagogical research which enables

convincing explanation not just description of students learning activity. Part

of this explanation she argues (eg. Sfard, 2001: 36) resides in the mediating

role of mathematical artefacts in the learning discourse.

While Sfards work can be considered reform-aligned in the general

education reform policy sense of emphasising relational elements of learning

and the interconnectedness of learning processes, it demonstrates a more

intricate level of discipline-specific grounding entailing a different notion of

reform from that envisaged in generic education reform policy. This suggeststhe latter may be of dubious applicability to better understanding and

improving pedagogy in practice.

In line with Sfards position, Yackel and Cobb (1996: 459, quoting Bauersfeld

1993) extend the basic constructivist learning model towards a model of

participating in a culture rather than a model of transmitting knowledge. In

this socially-grounded model, students learn mathematical know-how, in the

sense of being deeply adaptive in knowing when and how to do what. In

Yackel and Cobbs (1996: 460-464) understanding of effective mathematics

classrooms students learn mathematics socio-culturally, reflexively co-

constructing acceptable mathematical activity. This entails co-construction

of shared norms about what counts as different, sophisticated, efficient and

elegant solutions. Difference is particularly valued here as it supports

students reflective activity on mathematical processes. In this model,

didactic procedural instructions are occasional and peripheral rather than


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the core pedagogical methodology prevailing in conventional mathematics

teaching.

While their primary research interest is mathematics teaching specifically,

Yackel and Cobb (1996: 460) consider that similar principles should operate

in other domains, such as science and literature classes. Relevant to the

current thesis is their model of teacher professional development in the form

of guided small-group collaborative teacher enquiry in situ to help them

radically revise the way they teach mathematics. This proposal rejects the

prevailing reform policy approach oftransplanting an imported best practice

instructional model. Yackel and Cobb (1996: 467-468) propose that effective

professional learning comes from teachers working collaboratively in their

own work settings on changing the actual activity of mathematics, where

teachers were typically the only members of the classroom community who

gave explanations. They contend that in the absence of a deep and sustained

cultural change created through close teacher collaboration, working at the

level of their own classes, children interpret traditional mathematics

instruction, as arbitrary procedures prescribed by their classroom authorities

the textbook and the teacher.

To differentiate between participationist constructivism and fuzzy brands of

discovery learning, Yackel and Cobb (1996: 474) cite their earlier proposition

(Cobb, Yackel and Wood 1992: 27-28): given our contention that

mathematics can be viewed as a social practice or community project the

suggestion that students can be left to their own devices to construct the

mathematical ways of knowing compatible with those of wider society is a

contradiction in terms. Their envisaged participationist approach does not

reduce the importance of the teachers role; it underscores it as that of an

experienced participant in a mathematical community of practice.

Clement (1991: 423-426) agrees that while still transmitting mathematical

content, a major part of the teachers role is seen as providing conventions for

mathematical language as a tool for communication among the students. For

a skilled pedagogical practitioner this is a reflexive process: Teachers are also


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constructors of learning environments through their efforts to modify or

construct (rather than transmit) the curriculum. The teacher also listenscarefully and converses interactively with students. However, understanding

this and actually doing it are two different things. As Sfard (2001) cautions,

when collaborative problem solving is claimed to be incorporated into

teaching it may be operating only superficially and, in the absence of detailed

discourse analysis, an impression of collaborative approaches adopted by

teachers in problem-solving conversations with students may constitute an

illusion of deep learning rather than an achieved reality.

Overall for Yackel and Cobb, Sfard and the identifiable education community

in which their work resides, education reform is subject discipline-embedded,

not a disembodied activity. Reform mathematics itself is a contested forum

and the term does not connote the same thing to all parties. However in the

cultural participation model of mathematics education it is clear that there is

at least some general alignment with generic education reform principles.

Yackel and Cobb (1996: 469-473) contend that in the participationist

classroom students learn by generating their own personally meaningful

ways of solving problems instead of following procedural instructions theirexplanations were conceptual rather than calculational. Their reform

perspective is that the development of intellectual and social autonomy is a

major goal in the current educational reform movement, more generally, and

in the reform movement in mathematics education, in particular. Yet, a

practical problem for education reform policy expectations resides in the very

generality of this alignment. The current research examines the utility of

generic education reform principles for change in teachers discipline-specific

and socio-culturally situated practice, given the micro-levels at which the

specialist literature shows pedagogy must be orchestrated.

2.4 The inseparability of pedagogical reform and subject

discipline framing

Challenging the notional separation of curriculum and pedagogy, Cobb,

Yackel and Wood (1992: 27) propose that in skilled participationist teaching:


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what is traditionally called the content could be seen to emerge in thecourse of the teachers and the students interactions as the teacher

guided both the individual students constructive activities and theevolution of the classroom communitys taken-as-shared meaningsand practices knowing has a social as well as cognitive aspect in thatto know is to be able to participate in a social practice.

In a witty turn of phrase Cobb, Yackel and Wood (1992: 3) dismiss the

representational view of knowledge, if taken literally, as akin to a belief in

immaculate perception.

This conception of knowledge as culturally specific and socially embedded

entails rejection of the importation of generic reformist approaches into

mathematics pedagogy. Citing the reform-aligned emphasis on making

student learning concrete through the use of physical models as external

representations, Cobb, Yackel and Wood (1992: 24-25) caution that while

their research findings are:

partially compatible with several other analyses of learning ininstructional situations that emphasise the experiential aspects materials typically characterized as instructional representations areof value [only] to the extent that they facilitate students individualand constructive activities and thus their increasing participation inthe mathematical practices.

Transplantation of generic prescriptions for adopting models and

manipulatives have little or no positive effect if simply bolted on to existing

practices. What follows is that correctness does not mean conforming to the

dictates of an authority it means making mathematical constructions that

have clout. Emerging from this analysis is the importance of drawing on

grounded research on learning and teachers' construction of pedagogy. In

proposing this, and in endorsing microsociological analyses, the authors

have a far more fine-grained conception of careful pedagogical research than

passes for data-informed enquiry in much of the more generic education

reform discourse.3They highlight clashes in different teaching models and a

close reading of their examples raises questions about internal inconsistencies

in pedagogical principles promulgated in the current Victorian education

reform context, for example the reliance on the cross-discipline pedagogical

leadership of principals.

3See the examples provided in Chapter 6 of this thesis in Section 6.5


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Cobb (2008) elaborates on the relationship between fine-grained pedagogicalresearch and large-scale education reform policy drives. In cross-referencing

reform discourses, Cobb cites Elmore [exact source not stated by Cobb] as

observing that the closer policy gets to the decisive interactions between

teachers and students, the less likely it is to be implemented and sustained.

Reflecting on various education reform levers which have been used across

jurisdictions, Cobb highlights the unanticipated obstacles encountered when

centralised reform principles collide with other existing initiatives, producing

conflict over priorities and resources and contributing to policy fatigue. Cobb

argues that it has proven difficult for centralised reform initiatives to connect

with specialised local knowledge [in the cultural sense] and penetrate

existing knowledge structures.

Cobb argues that for reform aspirations to gain traction it is necessary to map

backwards from an identified local culture agreement on what constitutes

high quality instruction in any particular discipline context. Cobb cites a key

figure from his own discourse community, Ball (1993), as proposing that an

advance in teaching effectiveness depends on each teachers professionalcapacity, primarily in form of deep pedagogical content knowledge, to drill

down to interrogate and bring to the surface students conceptual

understandings. While on the surface this may sound like a form of

constructivism compatible with more generic current education reform

agendas, the disconnection lies in the depth of specialised discipline-specific

knowledge envisaged as a necessary precondition of being brought to bear

effectively on the task.

Coming from a researcher situated in a specific mathematics education

discourse community, what is striking is Cobbs (2008) emphasis on the

intricate pedagogical content knowledge required by the teacher to make

explicit the basis of students mathematical understanding. The teacher is

envisaged as making continual micro-adjustments as s/he reads and

interprets students mathematical reasoning in fine-grained detail. Cobb

endorses the viability of educational improvement only if school and system


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resources are directed at overcoming teachers professional isolation so they

develop shared specialist pedagogical knowledge. In Cobbs (2008) analysisthis requires collaborative participation, with expert consultative guidance, to

co-construct high-quality practice; it cannot be achieved merely by dispensing

best practice pedagogical advice. Resourcing remains a challenge, with

adequate time-release for professional collaboration a necessary, although not

sufficient, condition replacing the prevailing professional development by

seminar attendance approach (which itself relies on the discredited

knowledge-as-acquisition model of learning).

Cobb (2008) presents an optimistic view of educational reform at the fine-

grained level, given a reversal of the top-down from the system to the school

to the classroom direction of reform. He identifies blockers to improvement

in the form of schisms between conflicting agendas. A key claim of Cobbs is

that a shallow emphasis on the form rather than the function of reform-

aligned indicators favoured by bureaucratic and leadership communities

obfuscates the things which actually need to be addressed. Cobb (2008)

provides as examples of a superficial focus on pedagogical form the generic

reform policy promotion of the use of models and manipulatives and theallocation of a large proportion of lesson time to discussion, as if these

constituted inherently positive developments. In policy-level reform these are

promulgated without in-depth analysis or understanding of their function and

outcomes in learning. Cobb argues that policy makers and their bureaucratic

change agents must bring forward for identification and examination their

own theories of learning. Citing the body of research of another leading

member of the mathematics education specialist community, Mary Kay Stein

[exact sources not identified by Cobb], Cobb argues that to be credible

leadership agents must be able to demonstrate detailed content knowledge.

Principal-level feedback to teachers is of little value if it is located at a surface

impression level, where certain generic indicators of reform-aligned practice

such as the use of student discussion groups and innovative presentation

methods are assumed to constitute high quality pedagogy. Principals are

placed in a difficult situation because they are not equipped to provide

convincing pedagogical leadership, partly because policy can provide them


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with only a nebulous picture of what high quality instruction actually entails

in a specific domain. Mathematics teachers themselves need to acquire theshared professional discourse to account for their own instructional practices.

Taking account of this overview of the fine-grained discussion of mathematics

learning and teaching which is situated in the domain-specific context of the

particular discipline, there are grounds for profound scepticism about a

generic transfer of best practice model of pedagogical reform, mediated

through principals instructional leadership. The degree to which the different

reform discourses connect in their conceptions of practice and of pedagogical

improvement is investigated further in this current study.

2.5 Previous research on reform alignment in mathematics

pedagogy

Moving from concepts of practice and models of learning underpinning the

mathematics education discourse, to an overview of existing research on the

question of mathematics teachers pedagogical reform alignment, the

complexity and richness of the field is clear. The theories of knowledge andconceptions of practice which the literature reflects are further developed in

the theoretical frames to be described more fully in the next chapter. The

discussion which follows on previous research on mathematics teachers

pedagogical approaches also gives rise to methodological considerations

which are taken up in the discussion of the research methodology adopted for

the current study, as described in Chapter 4.

The participationist learning models of Sfard, Cobb and others already

discussed are grounded in classroom discourse analysis as a method of

researching how mathematics pedagogy is and could be enacted. Across a

broadly-based mathematics education field there is a rich and diverse

literature documenting a wide range of pedagogical research, some explicitly

in relation to questions about reform policy penetration. Spillane and Zeuli

(1999: 3), for example, view direct teacher practice observation and lesson


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analysis as an essential, though frequently neglected, component of policy

implementation research.

Kennedy (1999) makes a significant contribution to the assessment of

potential measures of classroom instruction when applied specifically with the

aim of gauging the influence of reform policies. She examines a range of

frequently advocated pedagogical research approaches in terms of their

potential to inform policymakers about policy influences on student

outcomes, leading to the conclusion (Kennedy 1999: 362) that the best first-

level approximation available to researchers would be classroom observation

focusing on the nature of intellectual work students do in class. As a

mathematics education researcher, Kennedy (1999: 358) pursues an interest

in a central problem for policy researchers:

how to document a clear path of influence that extends from policymanipulations to student outcomes. Education reform policyresearch must ultimately aim at better understanding how policiesinfluence the intellectual character of classroom events and thequality of student learning.

Kennedy (1999) cites Argyris and Schns (1996) foundational work on

organizational learning, to be described in the next chapter, in the context ofexplaining that teachers self-reports on their pedagogical alignment are

unreliable because their espoused theories-of-action reflect the dominant

discourse while their theories-in-use (ie. enacted practices) do not. From this

point of view surveys can yield only very limited insight into the nature of the

learning experiences provided by teachers for their students. Interview

responses, similarly, must be interpreted with great caution because, as

Kennedy argues (1999: 354), they are best thought of as revealing teachers

espoused principles of practice; they may not reveal much about teachers

theories in action.Kennedy cites as a caution Olivers (1953) research finding

that the correlation between these two measures espoused practices and

observed practices was only .31. Spillane and Zeuli (1999) investigate how

teachers deflect policy by adapting to it in ways that undermine the core

intent of reform. This accords with Handal and Herringtons (2003) overview

of an extensive range of research showing that even when teachers explicitly


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express support for reform-aligned teaching, their actual pedagogical

enactment tends to distort or deflect key reform principles.

Consistent with this concern is a body of research (eg. Mayer 1999a) warning

that while education reform policy relies on data purporting to measure

instructional practice, data are commonly in the form teacher self-reports,

through interviews or

Hutchison, A. 'Mind the Gap' Doctoral Research Thesis

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