Students’ perspective on feedback in mathematics in high school

Abstract

The aim of the study is to examine assessment experiences and practices in mathematics in high school from the students’ perspective. To gain insight into the students’ experiences and practices, we used a qualitative approach. The data are based on qualitative focus group interviews with first year students in the general studies education programme. The findings show that the students mostly receive summative feedback on achievements which is expressed through grades. To varying degrees, the students seek feedback during the learning processes, thereby leading to differences in the amount and type of feedback that the students receive as well as the extent to which feedback improves learning and outcomes for all students. The students’ perceived usefulness and active use of feedback is mediated through the teacher’s manner which also influences motivation and effort. The study shows a potential for involving students in assessment and using feedback during a learning process as a significant tool to promote mathematics achievement.

Keywords:

• Feedback
• mathematics
• student perspective
• high school

Reviewing Editor:

• Sammy King Fai Hui, Curriculum & Instruction, The Education University of Hong Kong, Hong Kong

Subjects:

• Classroom Practice
• Assessment & Testing
• Classroom Management & Organisation

Introduction

Feedback is a valuable tool in terms of promoting students’ learning and is a central element in assessment for learning (AFL) (Black & Wiliam, 1998a; Schildkamp et al., 2020; Shute, 2008; Wiliam, 2011). Shute (2008) defines feedback as information provided to the learner to enhance and improve learning. In Hattie’s and Timperleys’ definition (2007), while building on Ramaprasad (1983), feedback relates to performance and aims to reduce the gap between current achievement and the desired outcomes of a learning process. In addition, feedback should have an influence on future performance (Schildkamp et al., 2020; Spooner & Pawlikowska, 2023), and it should be designed for students’ use of the feedback during learning processes (Rakoczy et al., 2019; Spooner & Pawlikowska, 2023). Students’ feedback literacy, such as understanding the feedback and capacity to act upon the feedback, is also a key element for feedback to enhance students’ learning (Carless & Boud, 2018; Esterhazy & Damşa, 2019; Nieminen & Atjonen, 2023). Black and Wiliam (2009) and Henderson et al. (2019) argue that feedback must be integrated in classroom teaching to be effective, which may imply changes in teaching and assessment culture in schools.

Norway has implemented AFL and formative feedback in assessment legislation and curricula since 2006 (Ministry of Education & Research, 2020; Norwegian Directorate for Education & Training, 2017). Students have a legal right to receive formative feedback and be involved in assessment, including self-assessment (Ministry of Education & Research, 2020). The educational authorities have initiated several strategies since 2007 related to the implementation of AFL in both school-based development projects and further education courses and programmes (Norwegian Directorate for Education & Training, 2017; Tveit, 2014).

However, several studies point to challenges in the implementation of AFL (Havnes et al., 2012; Hopfenbeck et al., 2013; Nortvedt et al., 2016; Rambøll Management Consulting, 2020; Tveit, 2014). Gamlem and Smith (2013) argue that students must be provided with sufficient opportunities to use feedback, and several studies refer to the inadequate systematic use of aims and criteria in assessment (Hopfenbeck et al., 2012; 2013; Tveit, 2014). Students’ need for adapted feedback in all phases of a learning process to enhance learning is also stressed as a domain for improvements (Hattie & Gan, 2011; Nortvedt et al., 2016; Nortvedt & Pettersen, 2015; Wisniewski et al., 2019). Havnes et al. (2012) show that teachers regard their feedback to students as useful, while almost half of the students disagree. Havnes et al. (2012) also show that teachers in high schools believe that students use feedback in their learning to a greater extent than reported by the students. The Annual Pupil Survey 2022 (Wendelborg & Hygen, 2022) shows that the students in the programme for general studies report less formative feedback practices than in all the other programmes in high school. The students experience receiving less feedback in mathematics than in subjects such as Norwegian and English (Bueie, 2016; Havnes et al., 2012). Mathematics stands out as a subject in which the students report limited opportunities to engage in discussions about the assessment criteria (Havnes et al., 2012). Gamlem (2019) finds limited evidence of feedback dialogues in mathematics classrooms. Stovner (2021) and Stovner et al. (2021) show that feedback from Norwegian mathematics teachers mostly regarding procedural skills and to a less extent facilitates student agency in feedback. To our knowledge, rather few studies of formative feedback in mathematics in high school have been conducted in the Nordic context (Grevholm, 2021; Nieminen & Atjonen, 2023). Most studies examine teachers’ assessment practices (Nieminen & Atjonen, 2023; Stovner, 2021; Stovner et al., 2021) and even fewer studies have investigated students’ experiences with formative feedback as well as engagement in and use of feedback (Gamlem & Smith, 2013; Nieminen et al., 2021).

In the light of the studies referred to and to address the gap in the literature, this qualitative study examines students’ experiences with feedback in mathematics specialisation in general studies in high school. The aim of the study is to explore feedback practices in mathematics exclusively from the students’ perspective and give students a voice in the feedback discourse (Dawson et al., 2019; United Nations Human Rights, 2002). The research question is What characterises high school students’ experiences with feedback in mathematics? and it is investigated through the themes (a) students’ understanding of the concept feedback, (b) students’ experiences of feedback practice and (c) students’ use of feedback. The study will contribute to the research literature regarding students’ experiences and perceptions of feedback in mathematics in high school.

Theoretical background

Black and Wiliam (2009) discuss AFL as processes of eliciting information about students’ learning, which students and teachers can both use to understand where the students are in their learning process and decide on the next step in a learning process (Black & Wiliam, 2009; Schildkamp et al., 2020). Such assessment activities function as formative feedback when the information is used to adjust the teaching to meet the students’ needs as well as strengthen students’ learning (Black & Wiliam, 1998b; Henderson et al., 2019). The Assessment Reform Group defined formative assessment as ‘the process of seeking and interpreting evidence for use by learners and their teachers to decide where the learners are in their learning, where they need to go and how best to get there’ (Broadfoot et al., 2002, p. 2–3). Consequently, the students’ must be given opportunities to respond to the formative feedback as part of teaching lessons. Therefore, formative feedback should be planned for and integrated in the instructional design (Gamlem & Smith, 2013; Hattie & Gan, 2011; Wiliam & Thompson, 2008). Formative feedback does not by itself generate learning; it must be put into an understandable context that students can relate to; formulated, delivered and framed in a way that allows the students to play an active part in their own learning (Gamlem & Smith, 2013; Havnes et al., 2012; Pippitt et al., 2022). Feedback must also be specific and detailed for students to respond to the feedback and use it in further learning (Henderson et al., 2019; Spooner & Pawlikowska, 2023; Wylie & Lyon, 2015). The usefulness of feedback also depends on the timing of the feedback and how the teacher arranges for and organises learning activities, making opportunities and time for students’ active use of the feedback (Dawson et al., 2019; Gamlem & Smith, 2013; Hattie & Gan, 2011; Jónsson et al., 2018; Schildkamp et al., 2020).

Sadler (1989) and Black and Wiliam (1998b) emphasise three aspects of feedback for enhancing learning: establish a mutual understanding of learning aims and success criteria, provide feedback about the current state in the learning process, and identify the next step in the learning process. Henderson et al. (2019) especially stresses the importance of promoting students’ agency and feedback as a learner-centred process. In line with Black and Wiliam (1998b), Hattie and Timperley (2007) argue that quality feedback must answer three questions: Where am I going?, How am I going? and Where do I go next? These questions are related to four levels in the student’s learning. At the task level, feedback relates to the quality of the student’s work with specific tasks. At the process level, feedback focuses on students’ learning strategies and processing of information. Feedback at the self-regulation level deals with the student’s ability to assess themselves, their ability to organise their work, their motivation, their belief in their own abilities and their willingness. The self-level relates to general feedback that is not specifically addressed, such as praise, encouragement or criticism that is not specific or connected to future achievements (Hattie & Timperley, 2007; Wisniewski et al., 2019). Wiliam and Thompson (2008) refer to Ramaprasad (1983) in their instructional design framework conceptualising AFL in five key strategies: (1) Clarifying and sharing learning intentions and criteria for success; (2) Engineering effective classroom discussions, questions and learning tasks; (3) Providing feedback that moves learners forward; (4) Activating students as instructional resources for one another; and (5) Activating students as the owners of their own learning (Wiliam & Thompson, 2008, p. 15). However, for these key strategies to enhance students’ learning, students’ interpretation and comprehension of feedback information is associated with their understanding of feedback as a source for learning (Hattie et al., 2021; Henderson et al., 2019; Schildkamp et al., 2020).

In Wiliam and Thompson’s framework (2008), an interactive, supportive classroom practice involving students in assessment dialogues is an underlying premise for feedback to function formatively and to promote learning. For formative feedback to be useful, students’ agency in seeking feedback and engagement in mutual dialogues with peers and the teachers is crucial for feedback to promote learning (Boud & Molloy, 2013; Panadero et al., 2018; Winstone & Boud, 2020). Dialogues and discussion in the classroom can promote learning, for example by discussing misunderstandings, different solutions and arguments (Dysthe, 2013; Havnes et al., 2012). However, it can be challenging to engage students in learning dialogues if the students themselves are not active participants. Havnes et al. (2012) argues that learning dialogues can be particularly difficult to steer when it comes to diversity in students’ levels of performance.

The interaction between assessment and students’ motivation can affect the students’ learning (Hattie & Timperley, 2007; Smith et al., 2016), and we relate this to the concepts of self-efficacy and self-regulation (Bandura, 1997; Zimmerman, 2000). Students’ self-efficacy is connected to previous mastery experiences in specific areas, tasks and challenges (Bandura, 1997; Bong & Skaalvik, 2003; Jungert & Andersson, 2013; Smith et al., 2016). Feedback may have an impact on a student’s self-efficacy in terms of setting realistic goals as well as providing verbal support during a task and specific feedback that makes students believe in themselves and their future achievements (Bandura, 1997; Black & Wiliam, 1998b; Hattie & Timperley, 2007). The concept self-regulation refers to the process of setting learning goals, regulating and controlling one’s attention, motivation and work input towards achieving the goal (Pintrich, 2000; Zimmerman, 2000). Self-regulation involves metacognitive skills and the ability to assess own learning. A student’s self-regulation is affected by feedback from fellow students and teachers as well as feedback that promotes the student’s sense of control, competence and belief in their own abilities is a key element of assessment for learning (Smith et al., 2016; Vattøy & Gamlem, 2023; Wiliam, 2011). Whether or not a student will use the feedback they receive depends on their ability to self-regulate as well as their engagement in their own learning process (Smith et al., 2016). Self-efficacy might affect how students interpret feedback, and students’ ability to self-regulate could affect how they use feedback in their further learning (Smith et al., 2016; Zimmerman, 2000). In Hattie and Timperley (2007) feedback model, one aim is to reduce the gap between what the student achieves here and now and the student’s future goals. To reduce the gap, students can increase their effort and change their strategy or goal, while teachers’ adjustments and scaffolding might enhance students’ learning and performances. Teachers can also help students with good learning strategies and by giving feedback on these during a process (Hattie & Timperley, 2007; Smith et al., 2016). The present study was conducted based on these perspectives.

Methods

Study approach

The investigation of students’ perceptions through a qualitative approach, in which the informants are given the opportunity to elaborate and deepen their arguments, might provide valuable information about feedback in mathematics from the students’ perspective (Gill et al., 2008; Kvale & Brinkmann, 2015). Focus group interviews were chosen to illuminate the complexity of students’ experiences by presenting the various aspects of the students’ experiences with feedback in mathematics (Halkier, 2010). Focus group interviews involve group interaction and are commonly used to explore the informants’ attitudes, experiences, perceptions and thoughts (Kitzinger, 1995). The social interaction between the participants in the focus group is a key element in the method. However, the researcher’s role as the moderator is crucial for the quality of the data collection. Steering the discussions by paying close attention to different opinions and perceptions, showing interest in disagreement as well as stimulating the sharing of experiences and attitudes might provide valuable information and quality data (Grønkjær et al., 1970).

Participants

The participants (N = 20) were recruited from two high schools situated in the same region in Norway with approximately five hundred students in each school. The inclusion criteria for the participants were 1^st year students in the Specialisation in General Studies Programme in medium-sized high schools and representing both 1 P mathematics classes (practical mathematics, first year) and 1 T mathematics classes (theoretical mathematics, first year) (Table 1). The learning aims in the subject practical mathematics concerns problem solving, modelling and the practical use of mathematics in society and everyday life. 1 P is a choice for students who do not plan to study natural sciences. The learning aims in theoretical mathematics concern modelling, reasoning and the theoretical use of mathematics and is a basis for studying natural sciences (Utdanning.no, 2024).

Table 1. Informant information.

	Groups	F	M
School 1	Group 1 (1 P + 1T)	1	6
	Group 2 (1 P + 1T)	3	3
School 2	Group 3 (1 P + 1T)	6	1

The potential participants were given written and oral information about the research project, which was organised by researcher two (R2), and twenty students volunteered as informants. The mathematics teachers selected three random groups of participants among the students who volunteered and gave their consent, and organised the students in groups, representing 1 P and 1 T mathematics in each school. Since gender differences were not a topic in this study, the females and males in the three groups were randomly distributed. The information to the participants included information about confidentiality, anonymity and the possibility to withdraw from the study.

Data collection process and analysis

The topics in the focus group interviews were structured in two steps. The first step consisted of open questions and themes for discussion; definitions and experiences of feedback, content in feedback, extent, context and perceived benefits of feedback. To assist the dialogue in the focus groups, we made a scheme for ourselves with keywords to each main question, building on the literature, to use, if necessary. Some examples of keywords to definitions and experiences of feedback: planned dialogues at appointed hours, spontaneous dialogues in lessons/written feedback/oral feedback given by the teacher/requested by the student. In the second step, the students discussed statements based on Hattie and Timperley’s model (2007); task, process, self-regulation, and self. The statements started with ‘After receiving feedback from teachers,’ followed by, for example, ‘I get a good impression and understanding of my process and performances, I learn more and it is easier to ask for help the next time.’ In addition, we asked questions such as: ‘Talk about the last mathematics lesson. Did you receive feedback? How did you receive feedback?’ Each interview lasted approximately 60 minutes and was conducted by using audio recordings and then transcribed.

The data was analysed by both researchers in several steps. In the first step, a deductive analysis of all the statements was conducted by R2, structured according to the topic of discussion in the interview guide. Concept maps were established as a tool for further analysis and provided an overview of the topics and concepts as well as the relationship between them (Butler-Kisber & Poldma, 2010; Rosas & Kane, 2012). The second step focused on meaning condensation based on the concept maps (Kvale & Brinkmann, 2015) and made a framework for establishing the categories: teacher’s role, communication and dialogues, motivation, need for feedback, content of feedback, context, effort, mathematics vs other subjects. In step three, the codes were quantified to study patterns, frequencies and thematic connections between various codes. Based on these steps in the analysis, the findings were organised as categories, constituting the themes in the findings: Conceptual understanding and content of feedback, timing, types and context of feedback, effort and self-regulation, communication and dialogues, motivation and teacher’s role in feedback practice.

Quality criteria

Data analysis by two researchers may strengthen the validity and reliability of the study. Both researchers followed the same steps throughout the analysis but not at the same time. R2 conducted the first analysis process, while researcher one (R1) repeated the analysis using the same steps and framework at a later stage in the research process. The analysis was then compared to ensure consistency in identifying codes and categories. Since all interviews were performed by one researcher (R2), this may ensure consistency in the execution of the interviews, at the same time presenting challenges in terms of consistency in the analysis and interpretation of data. R2 gained an initial understanding of the data by meeting the informants and conducting the interviews. For example, the specific context of the interviews and the interaction in the focus groups, may affect R2’s interpretation of the data. However, R1’s distance to the context for data collection and informants may provide supplementary approaches to the interpretation (Kvale & Brinkmann, 2015; Silverman, 2011). The study followed ethical guidelines in research (National Committee for Research Ethics in the Social Sciences and the Humanities (NESH), 2022).

Findings

The findings are presented according to the categories and themes from the analysis: Conceptual understanding and content of the feedback, timing, types, and context of feedback, effort and self-regulation, communication, dialogues and motivation, and the teacher’s role in feedback practice. Some of the findings are also supplemented with quotes from the informants, as examples of the findings.

Conceptual understanding and content of feedback

The students define feedback in mathematics as both formative and summative, and one student describes feedback as: ‘Response to what I have performed that is okay, and what I can improve or should improve.’ However, it was repeatedly stressed through all the interviews that grades function as evidence of achievements and is the dominating assessment: ‘Grades are a kind of feedback and are the most important feedback. That’s what we have learnt during schooling; you must get high grades.’

When the students describe the content of the feedback from teachers, they stress feedback on the task level and to some degree on the process level and self-regulation level (Hattie & Timperley, 2007). At the task level, the students mostly receive feedback on what is correct and incorrect in their work, as one student expressed:

When we receive feedback on assignments, I only get a grade, but sometimes the teacher writes ‘good’. However, there is no information in the grade about what I should further learn and improve on, and an explanation as to why some answers are wrong.

Another student says:

Generally, you don’t get specific feedback. They say: ‘This is very good, and to just continue like this.’ However, if I must continue, it isn’t good enough, is it? Still, I don’t know what to improve. It is difficult to know what exactly I need to work on.

However, the students express that they receive detailed feedback if they actively seek feedback. Some students report receiving feedback more often in mathematics than in other subjects in school. They argue that since problem-solving strategies are often discussed in class, they seek feedback to complete tasks and the teachers are responding during the learning activity.

Feedback on homework differs between oral feedback related to students’ effort, and written feedback on assignments, followed by a grade. However, there are differences between 1 P- and 1 T-students regarding homework and feedback. 1 T-students do homework every week and the feedback from teachers relate to the academic results at the task level as well as effort and problem-solving strategies. In most 1 P- classes, homework is an optional and individualised activity since the students decide themselves whether they will complete mathematics tasks at home, if they run out of time at school. Homework is seldom followed up on by the teacher, nor do the 1 P- students receive feedback on their optional homework. However, the students argue that homework and feedback on homework have a potential for learning, especially if they drop behind the rest of the class. These findings indicate that there is a difference between 1 P- and 1 T- students as regards receiving feedback on homework, the use of homework and the possibilities to use feedback on homework as a tool for learning.

Timing, types and context of feedback

Feedback in mathematics is given both verbal and written. Verbal feedback is provided in the lessons, but also individually and frequently in the corridor outside the classroom, which is due to the lack of available rooms. Verbal feedback mainly concerns results on assignments and tests and task solving during lessons if the students ask for help. The students express that it is important to receive rapid feedback, both in lessons and after tests. One student spoke about the dilemma in the timing of feedback:

After a test, we usually start on a new topic and chapter in the textbook. And, after three weeks we get the test results and feedback from the teacher, often with grades. And the teacher expects us to go through the test and correct the mistakes. At that time, I have already forgotten what we did three weeks ago. I have even forgotten what the test was about! How can I learn from my mistakes in this way?

As a result, the students find it challenging to use feedback after a test as a resource for further learning. They also express a need for diverse types of feedback during the school year, also related to seasons. In autumn, the students would like to receive specific feedback which also promotes self-efficacy. They argue that when the school year has just begun, their motivation is high, and the students are more eager to receive feedback. One student says: ‘I believe that specific and positive feedback in the beginning of the school year is much more important than receiving such feedback at the end of the year.’ And ‘as the days becomes darker in winter’ as one student says, the feedback should also be motivating: ‘You need the feeling like ‘I can manage this, I will’!’ According to the students, specific feedback in the spring term has little influence on their learning; one student expressed this as ‘it is too late’.

Effort and self-regulation

The students are in their first year in high school and must adjust to the new learning contexts and teaching methods, which has challenged their self-regulation skills. This is particularly manifest in terms of planning their work and the effort put into learning mathematics. The students relate effort to their degree of motivation and to the teachers’ teaching methods. Effort is also linked to mathematics achievement and self-efficacy, which in turn affects the extent to which they use the feedback in further learning. For example, the students state that feedback influences their effort put in mathematics the first week after receiving feedback from the teacher. However, if their continuing work after receiving feedback does not promote progress, their effort tends to decline, according to the students. Consequently, effort is related to mastery experiences in mathematics and a belief in one’s abilities to succeed within a brief time span.

The students also link their own effort to the teacher’s facilitation of learning and the learning environment in the classroom. The students are explicit when arguing that a committed teacher who tries to motivate the students and apparently cares about the students’ progresses and achievements is crucial for students’ effort, motivation and the learning environment in mathematics classrooms. One student says: ‘You easily forget feedback from a teacher if they don’t honestly show that it is important for them as well that I succeed.’ These experiences show students’ sensitivity towards whether the teacher genuinely cares about their academic progress.

Those 1 T and 1 P students who describe themselves as active in the lessons tend to receive more feedback than those who are less active, and the feedback is often directed at the task level. The students in 1 T - classes have also noticed a difference in their achievement level and the degree of feedback received, as one student explained: ‘The students who struggle with understanding mathematics and do not achieve very well do not get as much help as those students who understand and are active in lessons’. The students also discuss that individual differences in the need for feedback and the type of feedback from teachers may influence the teacher’s actions.

Communication, dialogues and motivation

The students underline the reciprocal dialogues between students and teachers as important to the students, as commented on by a student: ‘We listen to the teacher more carefully if she listens to us.’ According to the students, mutual engagement in dialogues between students and teachers will, therefore, also influence their learning. The students also notice the teachers’ choice of words and the way feedback is provided to the students, and the students are sensitive to whether the teachers mean what they say. Constructive criticism can be communicated in a positive manner, and the students who struggle with mathematics and work hard need praise and positive reinforcement with encouraging feedback. One student describes:

You notice when a teacher wishes you well and for you to succeed. When you ask for help, they give specific feedback on my specific mathematics challenge, and they really try to help. And he says ‘Don’t hesitate to ask if you don’t understand’ (…) It won’t take much for the teacher to motivate and build us up with positive words, instead of, for example, ‘this isn’t working, you do not pay attention in lessons’, as a teacher said.’

Some students describe teachers as being biased and critical towards students’ efforts and skills in mathematics. This is interpreted as negative attitudes towards students and it affects the relationship between the students and the teacher. The students are also explicit when saying that if the relationship and trust between the teacher and students is affected negatively, all the feedback will be interpreted negatively, regardless of the content of the feedback. According to the students, the teacher’s attitude and communication skills, therefore, play a vital role in whether the students will benefit from the feedback.

Students who succeed in mathematics find mastery experiences motivating, and they refer to themselves as intrinsically motivated. Students struggling with mathematics learning express a need for frequent support and instant feedback from teachers and become motivated by positive feedback and praise. They express that positive feedback may affect motivation for mathematics, while negative feedback, such as a focus on shortcomings, has a negative effect on motivation. Therefore, positive or negative feedback in mathematics will have an impact on whether students make use of feedback and their efforts in mathematics.

‘The teacher is the most important’—the teacher’s role in feedback practice

The analysis of the focus group interviews identified common experiences among the students related to the teachers’ roles in feedback practice. According to the students, the teacher’s behaviour, manner and attitudes towards the students, their communication skills and the way in which they communicate feedback has a major impact on the students’ motivation. The students had various descriptions of what characterises a good teacher in terms of the provision of feedback. Summarised, the teacher should be knowledgeable, confident in and committed to their subject, adjust their feedback to students’ needs and build close relationships with and between the students. These characteristics and qualities of the teacher are directly apparent in the content of the feedback and the way in which it is given. For example, the students stress that mathematic expertise is a criterion for being able to give academically relevant feedback, and for organising and structuring the students’ learning in classrooms. One student says:

If the teacher is not engaged in mathematics, it is no fun to learn either; maths becomes difficult and complicated. And you notice the difference between a skilful teacher and a teacher who seems uncomfortable in the classroom (…) the teacher is most important; it is motivating and fun to know that we have a good teacher.

The students also state that it is important for the mathematics teacher to be interested in the students’ life outside of school and to get to know them. Knowing their teacher and developing confidence through the teacher’s interest in the students makes it easier for students to seek feedback. The students state that good relationships with the teachers affect how they interpret the feedback and they make it easier to relate to the teachers’ message. One student explains:

If they show that they care and signal that ‘We are going to manage this together. I will help you’, it affects the whole class and there is more energy in the classroom. And it is also important to know the teacher, and that they give of themselves, asking ‘How are you?’ and they show interest.

Summary of the findings

The analysis gave various and complex information about how students perceive formative feedback practice in mathematics, and whether and to what degree the students use the feedback as a basis for further learning. They refer to feedback as a summative action and with a summative aim, but they also report on formative feedback in the mathematic classrooms. One of the main findings is how the various manners in which a teacher meets their students, in terms of dialogues and communication, positive attitudes and timing of feedback, can be a crucial factor for the students to relate to, seek and use the feedback. Looking into the various categories in more detail, it is mainly the teacher’s behaviour and feedback practice that decides whether the students use the feedback and relate to the feedback. According to the students, they want specific feedback which is given by a committed teacher who has a good relationship with the students. Subsequently, to benefit from feedback, the students must be told very specifically the next step in a learning process. They also need to know that their effort will be acknowledged and followed up on by the teacher within a brief time span. The analysis shows that students to a varying degree experience such feedback practice and there are also a few examples of assessment dialogues in the mathematic classrooms.

Discussion

The findings in the study show that the students mostly receive summative feedback in mathematics on results and achievements, which is often expressed by grades. The summative feedback tends to be given after a learning process is completed and as part of the teaching design in the classroom. These experiences might have formed their perceptions of feedback as summative actions and with a summative purpose. The assessment legislation stresses that all assessment during the school year has a formative purpose (Ministry of Education and Research (2020). If grades and summative assessment intend to function as formative assessment, the teacher must plan the timing of feedback and further learning processes as part of the teaching structure and design in the classroom (Carless, 2019; Normann et al., 2023; Pippitt et al., 2022).

The students also report different formative assessment activities. These feedback activities predominantly concern the task, process and self-level (Hattie & Timperley, 2007). Feedback on the task level is mainly directed towards correct or incorrect answers, and to some degree towards problem-solving methods and the process level. The students report of verbal feedback as general and imprecise or given at the end of a learning process when it is difficult for the students to use the feedback in an ongoing learning process. Written feedback also tends to be directed towards the task level, for example on tests, and has a summative function. Havnes et al. (2012) refer to similar findings; feedback in mathematics typically involves responding to correct and incorrect answers as well as correcting mistakes and the findings of Stovner et al. which are related to procedural instructions (2021). If written and verbal feedback from teachers aims to have an impact on further learning, the feedback must be planned for and organised – as part of the teaching and learning in classrooms – as possibilities to use the feedback during learning processes (Boud, 2000; Bueie, 2016; Schildkamp et al., 2020). Although these different feedback activities take place during the students’ learning processes, it is unclear to what extent they function formatively on students’ learning. The analysis shows a few examples of high-quality feedback with references to definitions of quality feedback in previous research (Gamlem & Smith, 2013; Hattie & Timperley, 2007; Sadler, 1989; Schildkamp et al., 2020; Stovner et al., 2021).

The findings also indicate a feedback practice as a unilateral process with the teachers as the providers of feedback and the students as the receivers. However, we have also identified examples of students’ engagement in assessment and thus enhance feedback literacy. Feedback literacy is connected to student agency and facilitating agency in all phases of a feedback process and transform the notion of the teacher as the provider of feedback and the students as passive receivers (Esterhazy & Damşa, 2019; Nieminen et al., 2021). To make sense of feedback and use it in further learning, students’ understanding and judgement of the feedback and possibilities to engage in assessment dialogues and act on the feedback is also a prerequisite for student agency (Carless, 2019; Carless & Boud, 2018; Fiskerstrand & Gamlem, 2023; Pitt et al., 2020). Boud and Molloy (2013, p. 10) elaborate these arguments:

As soon as the active role of learners is acknowledged, then conceptions of feedback need to move from the mechanistic to the responsive. That is, the role of learners as constructors of their own understanding need to be accepted. Feedback then becomes not a control mechanism designed by others to corral the learner, albeit in desirable ways, but a process used by learners to facilitate their own learning.

Boud and Molloy’s arguments (2013) describe some of our findings related to agency and possibilities for the students to use feedback in further learning. Simultaneously, the findings indicate that it is the students’ responsibility to seek feedback during a learning process. The students refer to ‘active students’ who often seek feedback from teachers also receive more feedback than ‘passive students’. They also relate their academic level to their effort and mastery experiences, and thereby how much feedback they receive. Engelsen and Smith (2010) show that teachers gave less and more imprecise feedback to low-achieving students, while the teachers tend to be more involved in dialogues promoting learning with high-achieving students (Engelsen & Smith, 2010). The findings in our study are similar in terms of differences in student engagement in feedback in the classroom. These differences challenge the regulations related to adapted teaching in the curricula (Ministry of Education and Research (2020) and teachers’ responsibility for accomplishing formative feedback at an individual and class level (Engelsen & Smith, 2010; Shute, 2008). The findings also challenge the discourses of learning and assessment dialogues in the classrooms which are supposed to provide students and teachers with information about students’ learning (Ruiz-Primo, 2011; Schildkamp et al., 2020). The teacher is responsible for ensuring that each student can make decisions on their own learning and are given tasks and challenges adapted to their level of performance (Hopfenbeck, 2011; Rønsen, 2013), including promoting student agency (Fiskerstrand & Gamlem, 2023; Pitt et al., 2020).

One reason students find it difficult to use feedback may also be related to the lack of strategies for using feedback or that teachers have not prioritised the development of learning strategies in their teaching (Eriksen, 2017; Gibbs & Simpson, 2004). When the students report receiving feedback at the self-level (Hattie & Timperley, 2007), as praise and positive and appreciative comments, this tends to be directed mainly at their efforts and to some extent their academic work. The students in this study value general praise and interpret general praise as a means for building the relationships between students and teachers. Feedback at the self-level can have a limited effect on the students’ learning due to the lack of information about the quality of the student’s work or the next step in their learning process to a small degree (Boud, 2000; Hattie & Timperley, 2007). However, praise in combination with specific feedback on the student’s progress may have an impact on learning and on student’s outcome expectation (Bandura, 1997; Hattie & Timperley, 2007).

The students state that when the teacher follows up on and promotes learning dialogues, the formative feedback influences their motivation in mathematics and affects their effort in mathematics learning. Furthermore, the students emphasised the teacher’s engagement and competency in mathematics which affects their outcome expectations (Bandura, 1997). This is related to the teacher as a role model: Through the teacher’s engagement in mathematics, the teacher sets a standard that can motivate the students and increase their effort. The students also stated that positive and negative feedback can affect motivation, but with different signs. Feedback is defined as positive when students are provided with specific feedback on mathematics achievement, in addition to appreciating comments on effort. Negative feedback relates to the teacher’s choice of words and what the students interpret as a negative attitude towards students who do not exert themselves. When students sense a negative attitude behind the written and oral feedback, it affects their motivation (Havnes et al., 2012; Straub, 1997). These findings can be related to the emotional aspect of assessment and the emphasis on emotional support, positive climate, teachers’ sensitivity and regard for adolescent perspectives (Pianta et al., 2012).

The distinct characteristics of students’ experiences with feedback in mathematics accentuate the teacher as a mediator for how students relate to feedback in mathematics (Andersson & Palm, 2017). The content of feedback, communication, context and types of feedback influence on students’ response to the feedback and how they benefit from feedback (Gamlem, 2019; Gamlem & Smith, 2013; Rakoczy et al., 2019). The students want comprehensive and relevant feedback to which they can relate. Subsequently, they need to perceive teachers’ positive intentions, which forms a basis for trust. These findings are in line with Hattie’s (2009) argument of teachers as the most crucial factors for learning, and William (2011), arguing that a knowledgeable teacher is vital for students to derive benefit from feedback.

The interaction between the teacher and student may also affect the impact feedback has on a student’s learning (Carless & Boud, 2018; Spooner & Pawlikowska, 2023). Gamlem and Munthe (2014) argue that the interaction quality in classrooms is important as a basis for feedback activities promoting students’ learning, which also emerged in our study. The teacher’s attitudes towards students have an impact on how the students relate to the teacher’s feedback. This shows that the dialogue between the teacher and student is crucial for how the student relates to the feedback (Carless & Boud, 2018; Gamlem & Smith, 2013; Rønsen, 2013). Our findings indicate that students have developed a sensitivity to their teacher’s communication style and that students interpret what the teacher says as an expression of underlying attitudes that the teacher may have towards the students, which was also found in Gamlem (2019) and Henderson et al. (2019).

Conclusion and limitations

The analysis shows that students define assessment as summative, but the students also report diverse types of formative assessment. However, they struggle to make use of the formative assessment. The students want feedback that helps them to improve their performance, but they experience that the methods and opportunities of using feedback are not systematic or part of the teaching design in the classroom. The study shows that the students’ experiences with feedback in mathematics and the use of feedback as a basis for learning is mediated through the teacher’s attitudes and actions in the classroom, and through the quality of their relationships between students and the teacher. The findings may indicate that teacher-controlled mathematics teaching dominates in these classrooms, which might affect the feedback, opportunities for the students to use the feedback in the context in which it was given and students’ agency. The students’ stories of the manner in which feedback is given also may indicate that the teacher expects a high degree of self-regulated behaviour from the students, for example that it is the students’ individual responsibility to follow up on feedback from the teacher.

Studying a small sample of students’ experiences with feedback in mathematics gives a limited insight into the field of assessment. However, by an in-depth analysis of the complex data, this study brings forward important findings related to formative feedback in the mathematics classrooms in Norway, and in line with other studies in this field (Bueie, 2015; Fjørtoft, 2013; Gamlem & Smith, 2013; Havnes et al., 2012; Stovner, 2021). Based on this research, we find it important to conduct further studies which also include teachers in the sample in order to gain a broader picture of feedback in mathematics classrooms in high school.

Disclosure statement

The authors report there are no competing interests to declare. The project is approved by NSD- Norwegian centre for research data.

Additional information

Notes on contributors

Ann Karin Sandal

Ann Karin Sandal is an associate professor/PhD in pedagogy at Western Norway University of Applied Sciences. Her main research interest is assessment in primary and secondary school, and assessment in vocational education and training.

Ann Kristin Sperle

Ann Kristin Sperle is a secondary school teacher with master’s degree, teaching at Sogndal Upper Secondary School. She is working with development of assessment practices in mathematics in upper secondary school.