The present paper presents preliminary findings from a study of students` and teachers` perceptions of feedback in mathematics in 10 lower secondary schools in Norway through an intervention period. The study is part of a larger study investigating how an intervention among 40 math teachers developed both students` and teachers` perceptions of feedback and feedback practice. The intervention was carried out during seven months focusing on different aspects of feedback and feedback practice in mathematics. The overall aim of the study was to investigate the impact of a feedback intervention on students’ learning, defined as math achievement, self-regulation (Pintrich, 2000; Zimmerman, 2002) and self-efficacy (Bandura, 1997; 2006). This paper presents a sub study in the project that focuses on changes in the perception of feedback among students and teachers during the intervention. Our research question is: How can an intervention study contribute to changes in perceptions of feedback practices among students and teachers in mathematics?

Feedback is a central concept in the discourse of assessment for learning (Shute, 2008; Wiliam, 2011). The concept assessment for learning describes assessment that promotes learning and provides useful information to students about their learning (Black & Wiliam, 1998; 2009). Black and Wiliam (1998) propose that assessment for learning refers to all assessment activities carried out by both students and teachers that produce information about their learning. Such assessment becomes formative when the information forms a basis for improvement of both students` learning and teachers` teaching and instruction (Black & Wiliam, 1998; Wiliam, 2011). Feedback, is in this context described as interaction between students and teachers. The interaction is understood as responding to information provided, which makes it an important feature of assessment and forms a basis for further learning.

There are several key features to feedback that are prerequisites for further learning and development. Shute (2008) argues that quality of feedback is related to the timing of feedback and that it should point to specific features of the task. Wiliam (2001) argue that feedback must be domain specific and specific in what the student should do to improve: When providing feedback to students learning mathematics, it is not helpful to tell them that they need to improve their work, even if this is true. It is more helpful to point out what kinds of errors they are making, and what they need to do to improve (Wiliam, 2001, p. 4).The form of the feedback can influence students` responses to the feedback from teachers, and especially informal feedback is found to be more useful than formal feedback (Havnes, Smith, Dysthe, & Ludvigsen, 2012). Gamlen and Smith (2013) find that different types of classroom feedback influence in different ways on students` experience of usefulness. Based on our study, we can add that students seem to have conceptual distinctions of feedback valence (usefulness) related to teachers’ practice of providing opportunities and time to apply feedback in revising their work (Gamlem & Smith, 2013, p. 166).

To make the feedback improve on student learning, Hattie and Timperley (2007) distinguishes in their feedback model between three key questions to be asked: Where am I going? How am I going? Where do I go next? Information answering these questions should be provided and processed by students in order to enhance learning. Hattie and Timperley also argue that information about the three questions in a learning process should be related to the four levels - task, process, self-regulation and the self (Hattie & Timperley, 2007).

The overall intervention design consisted of a framework for the intervention designed by the researchers focusing on development of teachers` feedback practices, and especially on giving feedback to students on task, process, self-regulation and self-efficacy. The participating teachers were involved in creating the actual intervention activities in the math classrooms. Data for this sub-study was collected before and after the intervention period by using group interviews with all participating teachers from the ten schools and focus group interview with students from all the participating schools, six students in each group. The interviews with both students and teachers were conducted by the use of an open thematic interview guide, including the same themes for both informant groups, both pre and post the intervention (Kvale & Brinkmann, 2009; Liamputtong, 2011). The themes were questioning definitions of the concept feedback, perceptions of the importance of feedback in mathematics, use of feedback, features of the feedback teachers give and students get, assessment criteria and student involvement in assessment. The interviews were transcribed and all transcripts (N = 40) were analysed using Nvivo software 11 (QSR International). The initial coding was done as a manual coding of all transcripts by two researchers, aiming to get an overall impression of the information given by students and teachers. The second coding was deductive, using Nvivo 11 software, according to the concepts feed up – feedback – feed forward. These tree concepts were chosen as constructs for teachers` and students` feedback practice (Hattie & Timperley, 2007), and all transcripts were analysed within this framework. The third coding focused on making sub-codes on feed up, feedback and feed forward, i.e. feedback activities, quality, use of feedback and timing. The final analysis combined both sub-codes from the third coding and the initial manual coding. Interrater reliability check in Nvivo was conducted on 20 % on the transcripts in the second and third coding phase (ref). In the analysis we identified features of feedback according to the themes in the interviews with students and teachers, pre and post the intervention. The analysis focused next on what changes from pre to post interviews with students and teachers that could be identified.

The preliminary findings showed changes from pre to post intervention on some crucial feedback concepts, and understanding of the nature of feedback as a feature of assessment for learning, for both students and teachers. The most obvious changes relates to assessment activities in math classrooms, as well as increase of student engagement in assessment for learning. Self-assessment and peer-assessment is the most common reported change of feedback activities. Teachers stress their change of attitudes towards feedback, especially the importance of timing of feedback and students involvement. The analysis is to be continued and finished within February 2018.

Bandura, A. (1997). Self-efficacy: The exercise of control. New York: Freeman. 14 Bandura, A. (2006). Toward a Psychology of Human Agency. Perspectives on Psyhological Science 1(2). Black, P. J., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education: Principles, Policy and Practice, 5(1), 7–74. Black, P. J., & Wiliam, D. (2009). Developing the theory of formative assessment. Educational Assessment, Evaluation and Accountability, 21(1), 5–31. Gamlem, S. M. & Smith, K. (2013) Student perceptions of classroom Feedback. Assessment in Education: Principles, Policy & Practice, 20(2), 150–169. Hattie, J. & Timperley, H. (2007). The Power of Feedback. Review of Educational Research. 77(1), 81–112. Havnes, A., Smith, K., Dysthe, O., & Ludvigsen, K. (2012). Formative assessment and feedback: making learning visible. Studies in Educational Evaluation, 38, 21–27. http://www.qsrinternational.com/nvivo/what-is-nvivo Kvale, S. & Brinkmann, S. (2009) Interview. Introduktion til et håndværk. 2. udgave. Organisation for Economic Co-operation and Development (OECD) København: Hans Reitzels Forlag. Liamputtong, P. (2011). Focus Group Methodology. Principles and Practice. London: Sage Publications Shute, V.J. 2008. Focus on formative feedback. Review of Educational Research 78 (1), 153–89. Zimmerman, B. J. (2002). Becoming a Self-Regulated Learner: An Overview. Theory into Practice, 41(2), 64-70. Wiliam, D. (2011). What is assessment for learning? Studies in Educational Evaluation, 37, 1, 3-14