changing mathematics teachers’ conceptions of assessment and feedback

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Changing mathematics teachers’conceptions of assessment andfeedbackHelen Dixon a & Mavis Haigh aa Faculty of Education , The University of Auckland , Auckland,New ZealandPublished online: 22 Jul 2009.

To cite this article: Helen Dixon & Mavis Haigh (2009) Changing mathematics teachers’ conceptionsof assessment and feedback, Teacher Development: An international journal of teachers'professional development, 13:2, 173-186, DOI: 10.1080/13664530903044002

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Teacher DevelopmentVol. 13, No. 2, May 2009, 173–186

ISSN 1366-4530 print/ISSN 1747-5120 online© 2009 Teacher DevelopmentDOI: 10.1080/13664530903044002http://www.informaworld.com

Changing mathematics teachers’ conceptions of assessment and feedback

Helen Dixon* and Mavis Haigh

Faculty of Education, The University of Auckland, Auckland, New ZealandTaylor and Francis LtdRTDE_A_404573.sgm(Received 12 August 2008; final version received 9 March 2009)10.1080/13664530903044002Teacher Development1366-4530 (print)/1747-5120 (online)Original Article2009Teacher Development132000000May [email protected]

Informed by an amalgam of notions drawn from constructivist, socio-cultural,metacognitive and self-regulation theory, the discourse created to describeassessment to enhance learning has gone through a number of iterations ordiscursive shifts. As a result, the current discourse is both ambitious and complexwith the roles and responsibilities assigned to teachers and learners in learning andassessment radically transformed. Sponsored by the New Zealand Ministry ofEducation, the Teaching and Learning Research Initiative (TLRI) seeks to developteachers’ research capability and to build knowledge about teaching and learningwith the intention of improving outcomes for learners. Using a range of qualitativedata generation strategies this TLRI research project investigated secondaryschool teachers’ and students’ conceptions of assessment and feedback. This paperreports on the professional learning that accrued for these teachers using the datagained from the four mathematics teachers in the project. It also details changes inthese teachers’ thinking about the roles and responsibilities of teachers andlearners in the assessment process and documents reported changes to theirprofessional practice resulting from these changed views. Whilst it is argued thatinvolvement in the project became a valuable form of professional learningwhereby these teachers, to varying degrees, achieved accessibility to, and greaterunderstanding of, the current discourse of formative assessment, the mediatinginfluence of teachers’ efficacy beliefs is also acknowledged.

Keywords: formative assessment; professional learning; discourse; mathematics;practitioner research

Teacher professional development: the context for the study

Defined in the early 1990s as those activities ‘carried out by the individual or systemto promote staff growth and renewal’ (Connors 1991, 54), professional development(PD) is usually identified as ‘all types of professional learning undertaken by teachersbeyond the point of initial training’ (Craft 2002, 9). In New Zealand there has been aconcerted focus on continuing professional learning of teachers, initially encouragedfor purposes of improving teacher practice and, latterly, with a strong focus on teacherlearning to improve the outcomes for learners (e.g. Educational Review Office 2000;Timperley et al. 2007). Linking improved teacher practice to the improvement ofoutcomes for learners has been a global movement as indicated by writers such asCraft (2002) in England and Hargreaves (2000) in Canada.

*Corresponding author. Email: [email protected]

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174 H. Dixon and M. Haigh

Continuing professional development (CPD) for teachers can take many forms.While it is recognised that teacher research is only one of a multitude of CPD oppor-tunities (Kennedy 2005) it is one shown to have impact when shared in a communityof practice and inquiry (Wenger 1998; Weiner 2002). It is this kind of professionaldevelopment that we are reporting on in this paper.

Established in 2003, New Zealand’s Teaching and Learning Research Initiative(TLRI) is a contestable research fund. It aims to build a cumulative body of knowl-edge about teaching and learning within the national context, with the expressed inten-tion of improving outcomes for learners. Further, through engagement with and inresearch, it is anticipated that teachers will adopt evidence-informed approaches toteaching and learning. The promotion of practitioner research, a key feature of theInitiative, has given this form of CPD and teacher professional learning prominenceand legitimacy in New Zealand.

As in many countries, New Zealand teachers have been faced with what has beentermed the problem of enactment (Kennedy 1999). The implementation of assessmentpolicy requirements has proved to be neither simple nor straightforward. An evalua-tion of the Assessment for Better Learning professional development programmesrunning between 1995–1999 indicated teachers had yet to achieve a genuine under-standing of formative and summative assessment. Furthermore, while a moderatepercentage of teachers (52%) reported a ‘high level of success in terms of an under-standing of the nature of effective feedback’ (Peddie 2000, 57), they were generallyunable to articulate clearly how feedback was used to enhance student learning. Morerecently, the development of teachers’ assessment literacy and practice has beensignalled as a priority in New Zealand (Ministry of Education 2001). Given thispriority our two-year research project investigating teachers’ and students’ concep-tions of assessment and feedback (CAF), and their impact on learning and pedagogy,was seen as being of strategic importance. Our research collaboration, establishedbetween the University of Auckland and four large, diverse secondary schools in theAuckland area, was fortunate to receive one of eight, medium-sized TLRI grantsawarded in 2004.

As a starting point for the project, data were gathered from the participating teach-ers and a random sample of their students in relation to conceptions of assessment andfeedback. Throughout the duration of the project a key task for the teacher-researcherswas the development and implementation of a data collection tool or an instructionalactivity that could provide them with greater insight into their students’ conceptionsof assessment and feedback. The teachers’ student achievement data, gained throughthe use of asTTle,1 became an additional source of evidence that was analysed anddiscussed in an ongoing manner. Based on the four specialist mathematics teachersinvolved in the CAF project, this paper reports on the nature of the tools developedand documents the teachers’ evolving understanding of the discourse of assessmentfor learning including their role and that of students.

From formative assessment to assessment for learning: a series of discursive shifts

While information gained from assessment is intended to fulfil a number of purposes,its primary purpose is now the enhancement of learning (Gipps 1994). Significantattention has been paid to conceptualising the integrated nature of teaching, learningand assessment (Sadler 1989; Torrance and Pryor 1998; Bell and Cowie 2001).

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Teacher Development 175

Influenced by changes in thinking about what constitutes effective learning, theseconceptions have gone through a number of iterations over the past two decades andreflect a developing discourse of assessment to enhance learning. A developing under-standing of the integrative nature of learning, teaching and assessment has resulted ina number of discursive shifts within the discourse itself. These shifts have beenreflected in a change in the language used and the roles and responsibilities assignedto teachers and learners in the processes of learning and assessment (Dixon 2008).

The early discourse of formative assessment paid far greater attention to theteacher’s role (e.g. Tunstall and Gipps 1996; Harlen and James 1997; Harlen 1998)than to investigating and articulating a role for the learner. Indeed, Torrance and Pryor(1998) argued that early iterations did little to challenge the roles traditionally playedby teachers and learners in assessment. Locating formative assessment in the act ofteaching placed the teacher in control of the assessment process and maintained thestatus quo in regard to the nature of the relationship that existed between teacher andlearner. The learner was still dependent on the teacher to make the appropriate judge-ments and decisions.

Drawing on developments in the fields of socio-cultural learning theory, and meta-cognitive and self-regulation theory, a number of writers (Sadler 1989; Black andWiliam 1998; Torrance and Pryor 1998) began to argue more strongly that the learnerhad to be assigned a key role in the assessment process. Of central importance was theneed for the learner to be able to assess and improve the quality of the work producedthrough the application of the skills of self-monitoring and self-regulation (Butler andWinne 1995; Perrenoud 1998). As a result, during the 1990s the concept of assessmentfor learning first appeared in the assessment literature and has now become a part ofthe discourse of assessment (Gardner 2006). While in Gardner’s opinion the termsformative assessment and assessment for learning embody the same set of practices,assessment for learning is more appropriate. A central role is assigned to the learnerwho is charged with the responsibility for using assessment information to enhancehis/her learning. Consequently, teachers are expected to help students acquire thereflective habits of mind that will enable them to share responsibility for learning andassessment. Promoting student autonomy in learning is now part of a teacher’s role(Cowie 2005; Marshall and Drummond 2006; Buhagiar 2007).

Significantly for New Zealand teachers, various discursive shifts in understandingcan be found in assessment policy developed to shape and inform assessment practice.In recent times the strategic directions for assessment at the system, school and class-room levels have been brought together under the umbrella of a National AssessmentStrategy (Ministry of Education 2001). Attention has been drawn to the need forteachers to: set specific and challenging goals with learners; foster partnershipsfocused on learning; and use assessment to improve learning. Since the original publi-cation of the Strategy, the notion of quality feedback has been emphasised as a criticaland vital aspect of teachers’ practice (Ministry of Education 2004).

However, the relationship between policy and practice is not simple (Hutchinsonand Hayward 2005). Even if policy is robust and grounded in research, and teachersare willing and committed to its implementation, there is the problem of enactment(Kennedy 1999). Teachers are faced with the difficulty of translating what they knowabout effective practice into action. It was hoped that, through their engagement in theCAF project, the teachers, like others overseas who have had similar professionaldevelopment opportunities (e.g. Torrance and Pryor 2001; Black et al. 2003), wouldgain greater understanding of the assessment discourse and begin to make it their own.

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The research design

This research was a case study bounded by the framework of the project. The fourschools in the project were large urban secondary (Years 9–13) schools. Theyrepresented a mix of culture, ethnicity and socio-economic groupings. This paper isbased on the work of four teachers of mathematics, one from each school, all of whomwere experienced classroom practitioners. Pseudonyms have been used to protectanonymity.

As part of the project the teachers were supported to design ways to assess theirstudents’ beliefs about assessment and feedback. Following the project’s commitmentto collaborative research practices (Wagner 1997) and the development of a commu-nity of practice (Wenger 1998), regular group feedback and planning meetings werean essential component of the research project. Over the course of the two years of theproject the university researchers and the teacher researchers met as a group eighttimes, for four hours at a time. At these meetings the teachers shared stories aboutprogress with their research projects, and asked questions of each other and the univer-sity researchers around the research process or contextual factors impacting on boththe progress of the research and the findings. Such talk allowed them to engage insubstantive discussion about both assessment and research. During these meetings thediscussions were audio-taped and the university researchers took field notes. In addi-tion, the university researchers met on a frequent basis with individual teachers toprovide support around the theoretical framing concepts of assessment and feedbackand in data gathering and analysis. At the end of each of the two years each teacherresearcher was interviewed about their research journey and their professionallearning. The second interview was conducted by an independent interviewer.

The findings presented here have drawn on qualitative data from the semi-structured interviews undertaken with each of the teachers at the end of the first yearand again at the completion of project as well as the final reports written by eachteacher. The data were analysed using an approach similar to that described by Milesand Huberman (1994), whose framework for qualitative data analysis has three maincomponents – data reduction, data display, and drawing and verifying conclusions.During data reduction and display, conclusions were drawn and verified with bothauthors presenting and defending ideas and supporting or challenging those of theother author.

Investigating students’ conceptions of assessment and feedback: considerable, moderate and minimal impacts on teachers’ understandings and practice

The mathematics teachers’ research focused on finding out students’ views of assess-ment in broad terms or students’ perceptions of the learning value of different typesof feedback within assessment practice. While each of the four teachers acknowledgedthat assessment and feedback were areas of his/her practice that could be improvedupon, each followed ‘different trajectories of change – so that not only their startingpoints, but also the routes they travelled were different’ (Black et al. 2003, 83). Carry-ing out these small-scale research projects had a variable impact on the teachers’professional learning though all believed that engaging in a substantive conversationabout teaching and learning (Cochran-Smith and Lytle 1999) had had some impact ontheir everyday classroom practice. The impact of the research process on their think-ing and their practice can be classified as considerable, moderate and minimal.

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Dee and Kate: cases where involvement in the project produced a considerable impact on thinking and practice

Kate believed that her students should be ‘active in the learning process’ (Kate,Research Report). They should have the opportunity to express their views about theirlearning. Therefore the focus of Kate’s research project was her students’ perceptionsregarding the value of different types of assessment. She provided her Year 10students (14–15 year-olds) with a list of 10 assessment activities such as ‘closed booktests’, ‘examinations’, ‘self-assessment’, and ‘talk with the teacher’ and asked them toindicate what they considered to be ‘most important’ to ‘least important’ using adiamond ranking tool.2 As there were nine possible positions within the diamond and10 assessment types, one was not placed and considered to be ‘not important at all’.Students were also asked to give reasons for their placement of the various activities.Although Kate’s original intention had been to administer this data generation task‘once during the year’, later she decided it would be ‘useful to administer the diamondagain at the end of the year to ascertain whether or not there were any changes instudent thinking’ (Kate, Research Report). The data gathered by Kate were analysedboth quantitatively and qualitatively. The Year 10 students considered examinationsas the most important assessment activity at both the beginning and the end of year.At both times self-assessment and homework assignments were considered to bemoderately important and ticks in books were either least important or (at the end ofthe year) not important at all. The students also indicated that ticks in books did notprovide any indications as to how they might improve their work. Of particular inter-est was the movement of the activity called ‘talking to the teacher’. This activity hadmoved from being relatively unimportant to important across the year. Kate believedthat this change in position had been influenced by the increased emphasis placed onfostering student discussion during class sessions.

Being part of the TLRI research project and carrying out her own research projecthad provided Kate with considerable opportunities for professional development. Notonly had she gained deeper insight into her students’ thinking, she had also been ableto use assessment information gained from the asTTle tests to assist her students’learning in both a planned and an interactive formative manner (Cowie and Bell1999). Her approach to lesson planning had changed and she had begun to share learn-ing objectives with her students in a formal manner at the start of the mathematicslessons. She also utilised ideas gained from her now much wider professional readingwhen planning relevant classroom activities, for example the ‘traffic light’ activitysuggested by Black et al. (2003) as a means of students’ self-assessment of theirprogress. In addition, her ‘expectations of students as they are engaged with groupwork’ had expanded. She believed that her students were beginning to ‘see assessmentas integrated with learning not as a separate activity’ (Kate, Research Report).

Kate acknowledged some rich learning associated with her engagement in theTLRI project:

As a mathematics teacher I always wanted to ‘play’ with quantitative data and I tendedto forget the human element. The action research project has made me consider that therich conversations that I have with the students is making more of an impact into what Ido and why I do it. … I feel that students are more aware of the formative value ofassessment. (Kate, Research Report)

From her perspective both she and her students had become much more involvedin the learning processes going on in the classroom:

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In sharing the learning objectives and giving students more power and control over theirlearning, I feel they are becoming insiders in the processes of learning and assessment.Also in administering the assessment diamond I feel I have become more of an insider,in regard to students’ thinking. (Kate, Research Report)

Kate was convinced that her focus on improving levels of student engagement intheir learning had contributed to a rise in the level of their mathematics achievement,as measured by improvement on their end-of-year asTTle scores, with a much higherpercentage of her class achieving at expected levels at the end of the year.

Dee, the other teacher whose professional learning throughout the project couldbe considered significant, was particularly interested in finding out her students’preferences for different forms of feedback and the timing of this feedback. Previ-ously she had developed a format for providing feedback that was largely grade orachievement related, at times accompanied by a limited commentary. Through herengagement in the TLRI project Dee had been provided with a series of readings inthe area of assessment and feedback and from these readings she had ‘realised that[her] feedback to her students was poor’ (Dee, Research Report). She was alsoconcerned that when feedback was provided it appeared to be largely ignored by herstudents. Unlike some teachers who may have attributed this state of affairs to thestudents, Dee felt she must shoulder some of the responsibility – perhaps her ‘feed-back was too general … and not helpful in improving student understanding andlearning’ (Dee, Research Report).

Dee carried out her research project with a Year 10 class who were consideredable to undertake Year 11 mathematics and sit the national assessment at this level.She decided to seek her students’ impressions of three different kinds of feedbackthat she had been using. These were: percentage grades, an asTTle test score withindications of individual learning pathways (ILPs) and a Year 11 assessment thathad been marked and returned with written indicators of ‘not achieved’, ‘achieved’,‘merit’ and ‘excellence’ (NAME grades). She devised a questionnaire that soughttheir response to a series of questions relating to these three systems. Studentresponses revealed that there was an almost equal split of preferences for the threetypes of feedback. Of greater interest, however, was students’ lack of response tothe feedback provided. While 75% of the class indicated that they appreciatedreceiving the ILP feedback, not many indicated that they had acted on this informa-tion. Furthermore, when Dee spent a considerable length of time writing commentsindicating how a grade had been awarded she found that the students were notparticularly interested in her comments. These findings proved to be a catalyst forchange. Dee decided that the students could write a learning commentary based onan analysis of their examination scripts. A follow-up questionnaire related to thisself-assessment exercise indicated that over two-thirds of the students in the classfound it helpful and she plans to repeat this exercise with all her classes in thefuture.

As Dee reflected about her learning from this evidence-generating project sherealised that she needed to make her students much more responsible for their ownlearning; also she needed to provide feedback that was accessible to the students sothat they could ‘move forward in their learning and make progress’ (Dee, ResearchReport). She realised that such an approach would ‘involve a time investment on theteacher’s part to train the students to “send and receive” this kind of feedback’. Shealso recognised that she and her students had not:

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… always interacted in ways that led to learning and that students are not often askedtheir opinions about things that impact on their learning. Time for discussion and ponder-ing questions is vital if the learning is to be enhanced. (Dee, Research Report)

Whilst Dee indicated that involvement in the project had required a considerabletime commitment since the research was ‘on top of a full teaching load’ she had foundit ‘enormously beneficial in terms of what I learned whereas previously I would havemade assumptions based on the students’ reactions’ (Dee, Int#1). Being part of theproject was ‘stressful at times, inspiring at others and challenging to my comfortzone’, but if the support network is there for the teacher then ‘seeing the passion [that]others feel for the profession is amazing’ (Dee, Int#2). Dee made considerablechanges to her professional practice as a result of being challenged by the findingsfrom her project. She also found that sharing and discussing her findings in thecommunity of practice developed during the TLRI project supported her as sheconsidered her findings and made changes to her practice, an effect noted by research-ers such as Weiner (2002).

Feedback is now conceptualised as the crucial interaction that occurs betweenteacher and learner(s) during learning and teaching, which will aid the improvementprocess through the identification of a learning gap and the actions necessary to closethat gap. At the start of the current project, feedback was seen by both Dee and Kateas an area they ‘had never been particularly good at’ (Dee, Int#1). Dee confessed thatit was an area of practice that had received little of her attention. She, like other of herpeers in this project, had primarily used marks and grades to feed back to students.

Throughout the duration of the project Kate took a pro-active stance, remainingpositive and enthusiastic. From the very start she had a clear idea of what she wantedto achieve. Conversely, it took some time for Dee to decide on her investigative focusand there were numerous times when she felt disheartened and considered withdraw-ing from the project. Despite these differences both teachers believed that their under-standing of the nature and purpose of feedback had changed:

I think I’ve moved dramatically and I think it’s been quite a steep learning curve. (Kate,Int#1)

I think the way I give feedback has changed and it’s made me aware that just putting ananswer down isn’t that helpful if you don’t say this is where you went wrong and this iswhat you need to do next time. (Dee, Int#2)

Previously Dee had thought about feedback as a means to communicate informa-tion about achievement to students. One of the most significant changes in her think-ing was in regard to feedback’s formative function. She had moved toward therealisation that for feedback to enhance learning it had to reduce the disparity betweena student’s current understandings and performance and a goal. Feedback had toprovide answers to the following questions – ‘Where am I going?’, ‘How am Igoing?’, ‘Where to next?’ (Hattie and Timperley 2007). As a result of these insights,Dee reported that she had started to feed back to students in a more individualisedmanner. Time spent on whole-class feedback sessions, which had previously been themain way in which achievement and improvement-related feedback information wascommunicated to students, was reduced. More time was allocated to talking withstudents ‘one on one’. Another crucial insight for Dee was that feedback was onlyeffective if students understood the meaning of it. She had started to realise that

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feedback as a communicative exchange (Sadler 1998) was not straightforward. Oneparty might have different understandings from another as to the meaning of thefeedback. Time therefore had to be spent ensuring that a shared understanding wasachieved.

Kate’s gain in understanding about formative assessment and feedback was alsoconsiderable. She had recognised that it is the learner’s action which is critical tolearning (Bell and Cowie 2001) and that the learner acts with agency (Torrance andPryor 1998). Kate believed that there would be less chance of the learner acting onfeedback information if it were framed in terms of directives to be carried out (Stobart2006). She understood that the effectiveness of feedback was dependent on ‘teachers’and learners’ mutual engagement in a process which involves them eliciting, interpret-ing and acting on assessment information’ (Bell and Cowie 2001, 12). In a similarmanner to Dee, Kate spent far more time talking with and listening to her students asshe engaged them in ‘rich conversations’ (Kate, Int#2) which, from her perspective,had resulted in the students being ‘much more confident to talk about what they thinkand where they perceive they are going to and how they are going to get there’ (Kate,Int#1).

By their own admission both Kate and Dee had begun to view their studentsdifferently and hence, their role in learning and assessment differently. Rather thanbeing seen as passive participants in the processes of learning and assessment,students were being viewed as active beings, capable of making valuable contribu-tions to discussions surrounding their learning and the assessment of it. As aconsequence, greater onus was being placed on students to take ownership andresponsibility for their learning. In Dee’s words:

The students are going to have to be more responsible for their learning [and] as thefacilitator I have to help them become more responsible. Instead of just turning up andsitting down and going through the motions, they have to see that if they want to succeedthey have to have input. (Dee, Int#2)

Moreover, both Kate and Dee felt it was the teacher’s role to encourage studentsto become more active and responsible for their learning, a task each teacher thoughtshe was capable of achieving.

Sadler (1989) has written about the need for teachers to download their evaluativeand productive knowledge and expertise to students so that students become insidersin formative assessment and feedback. One authentic way in which teachers’knowledge and expertise can be downloaded is by making the goals of learning andstandards of expected performance explicit to students. Kate (Int#1), using the meta-phor of a jigsaw puzzle, talked about the need for students to become insiders (Sadler1989). She emphasised the need for students to see ‘the picture on the box’ as it was,in part, this picture that helped them to achieve insider status. Hence, in an attempt tomake learning explicit she was spending more time, sharing the learning intentionswith students and showing ‘them where the pieces go’ (Kate, Int#1).

As can be seen Kate and Dee came into the project at different starting points andtheir trajectories of change were different. Yet both teachers gained considerableunderstanding. As has been described elsewhere (Haigh and Dixon 2007), at thebeginning of the project Kate was an eager participant who was keen to extend herknowledge and skills in the feedback area. She recognised that the teacher’s interestlevel was a significant contributor: ‘it has to come from you. Teachers cannot be

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coerced. If the interest is not there it’s not much use’ (Kate, Int#2). Additionally, sheindicated that the ongoing support from the university researchers was a significantfactor in her professional learning during the project: ‘I could not have managed asmuch as I’ve completed without constant support and expertise’ (Kate, Int#2).

In contrast Dee had joined the project as a favour to her departmental head. Whilstshe had volunteered to participate, assessment was not a particular area of interest.There were times that Dee indicated to the university researchers that her continuationin the project was challenging as she was ‘getting snowed under with school work ingeneral’ (Dee, Int#1). However, she persevered as she could see that it would be‘worthwhile because for myself as a teacher I can only improve’ (Dee, Int#1). A factorinfluencing Dee’s perseverance was the ongoing support and encouragement from thegroup and university researchers.

Robert: a case where involvement in the project produced a moderate impact on thinking and practice

Prior to his involvement in the project, Robert perceived that his students respondeddifferently to feedback framed as percentage grades, standards-based criteria state-ments, and written comments. Subsequently, he carried out a comparative study witha Year 11 class, to see if these different types of feedback impacted differentially onthe students’ achievement by investigating their achieved grades in the common test.Using a questionnaire to generate his data Robert collected student evaluationcomments regarding the three main types of feedback that he had used. One unex-pected finding was that the students were very keen on getting grades during practicetests to provide some indication of their grade in the final common test.

Discussions around feedback and its impact on learning had not previouslyfeatured in Robert’s classroom interactions and he was surprised at the level of hisstudents’ understanding:

I was really impressed with the way that some of them had some good ideas basicallyabout good and bad points [of different ways of providing feedback]. Some of the thingsthey were saying I was a bit surprised at … I was just impressed that they were able tohelp in the way they did basically and I think I learnt a lot of them had a lot more matu-rity than I’d at first thought. (Robert, Int#1)

There were only 24 students in Robert’s class so correlations of type of feedbackand improved student achievement could only be tentative. It did appear that provid-ing standards-based criteria statements as feedback had the most impact on conse-quent student achievement but, as Robert indicated, ‘a more rigorously controlledstudy with a larger sample of students is required before definitive findings can bedeclared’ (Robert, Research Report). However, it was a finding that Robert ‘spokeabout to my students at great length … which made for excellent class insight into theuse of feedback itself’ (Robert, Research Report).

Robert had altered his feedback approaches and he had began to talk with hisstudents about wider issues pertaining to learning and assessment. This change to thestudent–teacher relationship in his class was significant to him and his advice to otherteachers who were considering becoming part of a similar project was to ‘preparethemselves to be open to discussions with students’ as he had realised that ‘gettinginformation from students is very, very important and I think teacher research isprobably one of the best ways to do that’ (Robert, Int#2).

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Robert too had experienced a shift in his thinking about the role of learners inlearning and assessment. Whereas previously it appeared that Robert had constructedstudents as passive recipients of feedback he was now attempting to hand moreresponsibility over to them by asking them to make judgements and decisions abouttheir work. While in the past Robert had the tendency to take the lead, to tell studentswhat warranted attention or what strategy to use to effect improvement, he was nowspending ‘a lot less time at the board saying this is what you do next’ (Robert, Int#2).However, while some responsibility was given to the students there was still a sensethat it was Robert in control of the discussion: ‘You can go about it in other ways andshow them what is right, that’s wrong and go through and show them how to do it andthen they can see for themselves’ (Robert, Int#2).

Overall, Robert indicated that his participation in the project had impacted on histeaching. For him, the major contributor to his learning was ‘hearing what otherpeople have done and hearing they’re in the same boat’ (Robert, Int#2).

Fran: a case where involvement in the project produced a minimal impact on thinking and practice

Even after several group sessions together with the other teacher-reseachers and theresearch team, Fran found the formulating of her research focus problematic, but shefinally made the decision to look at students’ attitudes towards assessment. This deci-sion was informed by anecdotal evidence she had gathered previously about students’reactions to assessment. In her opinion these reactions highlighted their anxiety aboutassessment: ‘When you say there is a test. They all get panicked and say no, not today,not today, next week and they try to postpone it which tells me that they don’t feelcomfortable’ (Fran, Int#1).

Thus Fran thought that it would be useful to collect evidence in a more systematicmanner to either confirm or refute these perceptions of her students’ attitudes toassessment. She designed a survey questionnaire that sought student responses to thetypes of assessment they currently experienced such as individual assessments, groupassessments, tests, examinations, quizzes and homework assignments. She adminis-tered the questionnaire to an average-ability Year 10 class. The results of the surveyindicated that homework assignments were their most preferred form of assessment.The students’ explanations as to why they favoured homework assignments weresomewhat of a surprise to Fran and provided her with insight into how her studentsthought they learned. In contrast to the other forms of assessment the students claimedthat homework assignments allowed them to seek help from more expert others. Theyindicated that this help enabled them to complete tasks as compared to non-comple-tion when they had to work independently. While Fran found this information inter-esting she found it difficult to rise above early negative feelings generated when shecould not find ways to use the data that she had collected. As she explained later: ‘Youwere looking for an answer and when you couldn’t do it the way you wanted to it wasvery disappointing’ (Fran, Int #2).

Fran thought, as suggested by Craft (2002), that participating in a teacher researchproject provides opportunities for professional learning. She indicated that teachersshould be challenged so that they learn professionally since ‘they won’t be so [effec-tive] after a few years of teaching’ (Fran, Int#2). However, whilst she had engaged inthe inquiry process her engagement did not appear to have been a strong professionallearning activity for her, though in an interview at the end of the project she claimed

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that the project had made her realise that if she did more frequent assessments thenshe could evaluate the effectiveness of her teaching. She also indicated that she hadbecome ‘more careful with the words and phrases I use when I give feedback tostudents’ (Fran, Int#2).

While Fran stated that involvement in the project had made her ‘focus and findmy way’ (Fran, Int#2), the change to her understandings about formative assessmentand feedback appeared to be minimal in comparison to the other participants. On apositive note, a critical understanding for Fran had been in the use of assessmentinformation. The planned use of formative assessment (Cowie and Bell 1999) hadbeen brought to her attention. From her descriptions of practice, she was now usingassessment information to inform planning and subsequent teaching. As Franexplained, her learning from the TLRI project had influenced her planning not only inregard to written plans but also in relation to the setting of relevant activities. She wasnow taking into consideration student need through the examination of assessmentevidence, and hence was prompted to think about the match between activitiesplanned and student capability:

In the past [when I was planning] what was in my [mind] was the curriculum and thegoals … but now I have my assessment evidence in front of me and I think about: ‘Willthey be able to do it or not?’ ‘Have I covered that or not?’ Have I done enough activitiesin that area?’ (Fran, Int#1)

With one or two exceptions (e.g. Sadler 1989), the earlier discourse of formativeassessment placed onus on the teacher in regard to the subsequent actions that neededto be taken to enhance learning. In the case of Fran it would appear that her under-standing of formative assessment reflects this early discourse. She seemed to viewherself as the major beneficiary of assessment. ‘If I do more frequent assessment thenI can see where I have been and where I am going’ (Fran, Int#2). Whilst Fran hadtaken time to gather students’ views, arguably the information gained from such anexercise had little impact in regard to her thinking and her practice. Fran was yet toconsider a more expansive role for learners in learning and assessment. In contrast tothe other three teachers the group meeting structure did not appear to support Fran’sprofessional learning or strengthen her efficacy. She seemed unable to relate to theother teacher-researchers’ stories. Her perception of the difference between herstudents coming from low socio-economic backgrounds and the students at schoolswith a higher socio-economic rating clouded her receptiveness to others’ ideas, lead-ing her to reject them as inappropriate: ‘[I listen and think] this is nice but … no it’snot going to work with my classes’ (Fran, Int#1).

It appeared that she could not consider the ideas and adapt them to fit her situation.

Conclusion: teachers’ evolving understandings of the discourse

Evolving conceptualisations of formative assessment and feedback have becomeincreasingly ambitious and complex (Perrenoud 1998; Shepard 2005; James 2006)with new ways of ‘behaving, interacting, valuing, thinking, believing and speaking’(Gee 1996, xix) articulated. In the current study, there was evidence to suggest thatinvolvement in the current project had, to varying degrees, increased the participatingteachers’ understandings of formative assessment discourse. These understandingsrelated to the nature and purpose of feedback in the enhancement of learning and tothe changing roles assigned to teachers and learners in the processes of learning and

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assessment. To varying extents three of the four teachers had realised that new normsof teacher and student behaviour have to be promoted to place students at the heart ofthe assessment and feedback processes (Sadler 1989; James 2006).

Gee (1996) has contended that newcomers to a discourse need to be scaffolded,coached and guided by ‘masters of the dance’. Through reflective and sustained inter-action with those more adept in the discourse, newcomers’ attention can be drawn tothe ‘most fruitful aspects of new experiences’ (Gee 1998, 15). Evidence from thisstudy suggests that teachers’ participation in research projects such as the onedescribed is an authentic and meaningful way in which they can begin to acquire thecurrent discourse of formative assessment.

However, cognisant of the pervasive influence of teachers’ beliefs on practice(Nespor 1987; Kagan 1992) it can be argued that within this study the teachers’ self-efficacy beliefs were a mediating influence on their understanding and acceptance ofthe new discourse presented to them within the professional development aspect of theproject. Comprised of two components, self-efficacy includes an efficacy expectation,which represents the belief in one’s ability to perform the desired behaviour, and anoutcome expectation, which relates to the belief that performance of the behaviourwill have a desirable effect. Without a strong efficacy expectation an individual is,therefore, unlikely to take action, even if it is believed that the required behaviour willlead to a desirable outcome (Bandura 1977). In the current study, in the cases of bothKate and Dee their seemingly robust efficacy beliefs allowed them to persist and to beresilient even in the case of setbacks. They were more willing and open to new ideasand more willing to experiment with new practices. Their outcome expectations werestrong in that they believed that a change in their behaviour would have beneficialeffects for themselves and their students. Conversely, in the case of Fran, both her effi-cacy expectation and her outcome expectation weakened over time. In the initialphases of the project Fran attempted to change her teaching approaches but, faced withsetbacks in regard to how she could use the data she was generating, she was unableto see that the practices she was attempting would produce desirable effects for herstudents. Furthermore, although she was working within a community of practice withother teachers, listening to the success stories of others did little to strengthen eitherher efficacy or her outcome expectations.

Notes1. asTTle (Assessment Tools for Teaching and Learning) is an educational resource, available

to all schools in New Zealand, for assessing literacy and numeracy in Years 4–12. Devel-oped for the Ministry of Education by a team from the University of Auckland led byProfessor John Hattie, asTTle provides a comprehensive range of data including: students’levels of achievement in relation to curriculum outcomes; information about students’ indi-vidual learning needs; and national norms of performance.

2. A diamond ranking tool involves ranking items from ‘most important’ (1 item), ‘reason-ably important’ (2 items), ‘moderately important’ (3 items), ‘not very important’ (2 items)to ‘least important’ (1 item).

Notes on contributorsHelen Dixon is a Principal Lecturer and Associate Dean (Academic Programmes) in theFaculty of Education, The University of Auckland. Her teaching and research interests are inthe areas of assessment for learning and teacher beliefs. Her involvement is assessment relatedresearch projects include teachers’ understandings of the purposes of assessment; teachers’ use

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of assessment information to enhance literacy learning and the formative and summative usesof a school entry survey for children beginning school. Helen’s doctoral study, which won anational award, examined teachers’ conceptions and use of feedback to enhance students’learning.

Associate Professor Mavis Haigh is Associate Dean Postgraduate in the Faculty of Education,The University of Auckland, where she lectures in teachers’ professional learning and super-vises masters and doctoral research students. She has lectured in science education, profes-sional inquiry and research methods at the tertiary level and has taught extensively in NewZealand secondary schools. Her research focuses on teachers’ learning, that of pre-servicestudent teachers during practicum placement and with teachers who are furthering theirprofessional knowledge, either in the practice context or during tertiary studies. Recently shehas been a member of a large-scale, three-year national research project focussing on theearly career development of secondary school teachers.

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changing mathematics teachers’ conceptions of assessment and feedback

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