The question of how to ensure high-quality mathematics experiences for all students that specifically meet their individual needs challenges teachers around the world. This challenge calls for differentiating initiatives that provide “equal opportunities to participate, and engage” (Christenson and Wager, 2012, p. 194). The purpose of differentiation is to tailor instruction so that there are “multiple options for taking in information” (Tomlinson, 2001, p. 1) to achieve an optimal learning experience and to improve self-efficacy in students (Mathiassen, 2009; NOU, 2016, p. 62).

According to Tomlinson (2001), there is a need to differentiate instruction in terms of content (what students learn), process (how they make sense of ideas and information), and product (how students demonstrate what they have learned). Here, we focus on differentiated instruction based on content and readiness by using level-marked mathematics tasks, as in tiered teaching (Pierce and Adams, 2005). We know that level-marked tasks feature in mathematics teachers’ accounts of their teaching (Brändström, 2005; Czeglédy and Szász, 2005; Eriksen et al., 2022) and are used extensively as differentiation initiatives in mathematics classrooms (Grave and Pepin, 2015). In this regard, many mathematics textbooks have a system for marking the difficulty of tasks to help students “find their way” through them (Imsen, 2020, p. 421). Mathematics textbooks have long held a strong position as the main resource for planning and executing the teaching of mathematics (Robitaille and Travers, 1992; Howson, 1995; Stein et al., 2007; Jablonka and Johansson, 2010) and recent studies have confirmed their persistent use (Dolonen et al., 2016).

An appropriate level of difficulty in mathematics is important for ensuring mastery experiences for students, and it is therefore necessary for textbooks and teachers to take differentiated instruction into account (Skaalvik and Fossen, 1995). However, there is a need to examine the interaction between students’ self-efficacy and teachers’ differentiation initiatives more closely (Herset, 2014; McNeill and Polly, 2023; Herset and El Ghami, 2022). To the best of our knowledge, no research has reported on how the extensive use of level-marked tasks affects students’ mathematics self-efficacy. Hence, since self-efficacy – a person’s “beliefs in one’s capabilities to organise and execute the courses of action required to produce given attainments” (Bandura, 1997, p. 3) – is a future-oriented construct that correlates with achievement (Pajares and Miller, 1995; Pajares, 1996), we aimed to report the results from a Norwegian study investigating the effects of level-marked mathematics tasks on students’ mathematics self-efficacy. While previous research has focused on students’ changes in self-efficacy over time, making it hard to say exactly why these changes took place (Street et al., 2022a), the current study investigates how self-efficacy is affected by level-marked tasks within a short time span (allowing no other factors to influence their change in self-efficacy, if present). In this way, this paper sheds new light on tiered teaching according to readiness.

Before we examine previous research on differentiated instruction in mathematics and the role of the textbook and its use of level-marked tasks, we begin this section by providing a more detailed account of self-efficacy, its sources and its importance for mathematics learning in individuals.

To investigate the effect of level-marked tasks on students’ self-efficacy, an online survey with a complex design was developed by the first author for a larger research project. The purpose of the larger project was to investigate the effect of level-marked tasks on students’ self-efficacy and to explore whether and how level marking affects motivational, decisional, cognitive and/or emotional processes. Hence, 11 tasks from the topic “arithmetic and algebra” formed the basis for an online survey. Of these, nine were retrieved from a national test in mathematics (Norwegian Directorate for Education and Training, n.d.), one was chosen, with some adjustment, from a mathematics website (Omtvei, n.d.), and one unsolvable task was created by the first author of this paper. The difficulty level of task A-I follows from the national test, and the difficulty level of Task J was marked as “hard” since only 17% of the students in a pilot study solved it correctly (Herset and El Ghami, 2022). Figure 1 illustrates the difficulty level of each of the 11 included tasks.

Our research question and associated hypotheses were formulated on the basis of the reviewed literature. Taken together, if both hypotheses held, we would have an argument for the effect of level-marked mathematics tasks on students’ self-efficacy. Descriptive statistics related to tasks A, B and C are presented in Table 2.

When comparing the two “mean” columns (columns 4 and 8) and the two “median” columns (columns 3 and 7) in Table 2, we see how reported self-efficacy declines as tasks go from no level marking to being marked as difficult.

Because of the way in which this study was designed, all students in the EGs received the three similar tasks twice. This means that all students, regardless of which EG they were in, received three tasks in Set 2 with different level markings: easy, medium and difficult (see Figure 2 in the methods section). Hence, we had 259 student responses (i.e., one response from each of the [94 + 74 + 91] students in all three EGs) to easy-marked tasks, medium-marked tasks and difficult-marked tasks. This enabled us, in hypothesis testing, to examine the differences in self-efficacy of the responses between no level marking and easy-level marking, between no level marking and medium-level marking, and between no level marking and difficult-level marking. We found that the effect of difficult-level marking was the largest, as illustrated in Table 3.

As the same students’ in the EGs answered Sets 1 and 2, the sample is dependent, and the Wilcoxon test was used because the data were not normally distributed (Cohen et al., 2018). As shown in Table 4, a Wilcoxon test revealed that students’ self-efficacy was significantly lower when tasks were marked as difficult, z = −4.033, p < 0.001. There was no significant difference between no level marking and medium-level marking (z = −0.930, p = 0.353) or between no level marking and easy-level marking (z = −0.233, p = 0.824).

To test H2—that is, to determine whether the differences highlighted in Table 3 were statistically significant—Friedman tests were carried out (see Table 5). This revealed a significant effect of the level marking on students’ self-efficacy, χ² (2, n = 259) = 11.413, p = 0.003, <0.01. The medians indicated that students’ differences in self-efficacy were highest when the tasks were marked as difficult, followed by medium- and easy-level marking.

Further analyses with Friedman tests were conducted to follow up pairwise comparisons. These pairs were set up in the following manner: Pair 1 compared x and y, where x is the difference in median between “self-efficacy with no level marking” and “self-efficacy with easy-level marking” and y is the difference in median between “self-efficacy with no level marking” and “self-efficacy with medium-level marking.” In the same manner, Pair 2 dealt with students’ responses to medium- and difficult-level marked tasks and Pair 3 with easy- and difficult-marked tasks (see Table 6).

Overall, the results in Table 6 show that the effect on students’ self-efficacy was significant when testing Pair 2 (going from no level marking to difficult-marked tasks, compared to going from no level marking to medium-marked tasks; p = 0.046), and Pair 3 (going from no level marking to difficult-marked tasks, compared to going from no level marking to easy-marked tasks; p = 0.006). The trend also applied in testing Pair 1 (going from no level marking to medium-marked tasks, compared to going from no level marking to easy-marked tasks), but this difference was not significant (p = 0.455). However, the effect on students’ self-efficacy was significantly larger when going from no level marking to difficult-marked tasks, compared to going from no level marking to easy- and medium-marked tasks. Taken together, this shows that the gap between students’ self-efficacy when encountering the same tasks with and without level marking expands going from easy- to difficult-marked tasks and from medium to difficult-marked tasks.

When encountering a mathematics task, most people are affected by additional information, such as information about the task’s level of difficulty. The most striking result from our analysis was the extent to which tasks marked as difficult had a negative effect on students’ self-efficacy. We found that students reported a significantly lower level of self-efficacy when encountering tasks marked as difficult compared to when they encountered the same task without level marking. Further, the difference in students’ self-efficacy when solving tasks with and without level marking became larger when the markings denoted increasing difficulty levels. Here, we discuss what this finding means for students in terms of their mathematics learning and what it means for mathematics teachers’ differentiation initiatives and for future mathematics textbooks.

Whether a student perceives a given task as being easy or difficult is a matter of personal opinion. This affects the student’s level of self-efficacy, which in turn influences the strength of their self-efficacy (Bandura, 1997). The negative effect of difficult-level markings on students’ self-efficacy highlights that even when all students receive the same task, the expectation of mastery becomes lower when a task is marked as difficult. This is consistent with Street et al.’s (2017) finding that students’ perceptions of difficulty could be different from the actual difficulty level. When tasks were marked as easy, this did not affect students’ self-efficacy, which suggests that the students did not perceive the tasks to be any easier than when no level markings were given. Keeping in mind that the first author designed the study using easy tasks—at mastery level 2 of 5 (Björnsson, 2016)—an effect for easy marking might have arisen if the focus had been on tasks with a higher difficulty level. More research is required to determine how level markings affect different levels of actual difficulty.

Although the sources of self-efficacy were not directly measured in this study, the results of our study apply to this body of research. As reported in previous research, mastery experience is the most powerful source of self-efficacy (Bandura, 1997; Stevens et al., 2006; Usher and Pajares, 2009; Joët et al., 2011; Butz and Usher, 2015), and this is a good reason for believing that some of the students’ previous mastery experiences with difficult-marked tasks had affected their self-efficacy negatively. This is in line with Skaalvik and Skaalvik (2018, p. 197), who claimed that mastery experiences are necessary for students to develop and preserve expectations of mastery. A possible interpretation of this finding is that level marking affects students’ perceptions of the level of difficulty, and if their mastery experience has previously been low when solving tasks marked as difficult, their level of self-efficacy may decrease. This resonates with Bandura (1997), Chen and Zimmerman (2007), and Street et al. (2022b), who suggested that students’ opinions about whether tasks are easy or difficult affect their self-efficacy.

Our results can also be attributed to students’ physiological and affective states, in that their self-efficacy beliefs are informed by anxiety, mood, stress and fatigue (Bandura, 1997). When told that a task is difficult, some draw on this comparatively weak source of self-efficacy, with detrimental results. This could explain some of the negative effects we found. No positive effects of level marking were found, which seems to indicate that level marking does not improve students’ physical or emotional well-being. However, previous studies are inconsistent in their conclusions on this point; for example, Stevens et al. (2006) and Usher and Pajares (2009) found significant correlations between self-efficacy and physiological and affective states, while Joët et al. (2011) did not. In terms of the last two sources of self-efficacy—social persuasion and vicarious experiences—we could only speculate about how they may have affected our results. Qualitative research is required to investigate this in greater detail.

Surprisingly, no positive effect of level marking on students’ self-efficacy was found. However, the present study did not investigate how level marking affects students with different self-efficacy strengths. It is likely that the effect of level marking is different for groups of students with high and low self-efficacy. This was supported by Schunk (1991), who claimed that a person with a high sense of self-efficacy would be more motivated, persist longer and be willing to expend a higher degree of effort. Further research is required to determine exactly how the effect of level marking on students’ self-efficacy varies by strength of self-efficacy, as well as how the effect of level marking varies between groups of students (e.g., according to gender, grade, motivational factors and mastery experiences).

We are aware that our research may have some limitations related to the voluntary nature of participation in the survey, sample size and data collection taking place via the schools’ principals. We attempted to select schools randomly, but because several schools withdrew due to COVID-19, we had to choose several schools in one district to obtain sufficient data. Moreover, in Norway, there are ~113,700 students in grades 8 and 9, and our data collection consists of n = 436 students. On the one hand, according to the sample size table (Cohen et al., 2018, p. 207), a sample of 383 students is recommended, which is lower than the number of participants in our study (n = 436). On the other hand, the participants were divided into different groups and there were missing data, so the sample size might be a limitation. Moreover, due to COVID, surveys were distributed to students by their teacher, which limited our opportunities to ensure sufficiently good and purposeful data collection. These limitations highlight the difficulty of collecting data, especially during COVID.

In reviewing the literature, we found that some countries, such as England and Germany, utilise mathematics textbooks that are adapted to different levels of ability (Pepin and Haggerty, 2003), indicating that level-marked tasks may not appear consistently in English and German mathematics classrooms. However, the use of level-marked tasks is extensive in Norwegian mathematics textbooks (Grave and Pepin, 2015) and classrooms (Eriksen et al., 2022). Although Skaalvik and Fossen (1995) claimed that textbooks require differentiation, our finding that the level marking of tasks negatively affects students’ self-efficacy suggests that there is a need to investigate this in more detail. Brändström (2005) raised questions regarding the level marking of tasks in Swedish mathematics textbooks nearly two decades ago, and to our knowledge, nothing has changed since then.

Glasnović Gracin (2014) highlighted the need for research on the content and structure of textbooks. We add to this call by pointing the research path in the direction of level-marked tasks, specifically in terms of the number of such tasks in textbooks, their stated purpose as specified by textbook authors and how they are intended to contribute to better learning. The findings of the current study show that the level marking of tasks appears to have a detrimental effect on students’ beliefs in their own ability to accomplish the tasks. Finding that difficult-level-marked mathematics tasks may result in reduced self-efficacy in students may indicate that marking tasks as difficult has consequences for students’ learning. The level marking of tasks may result in students’ avoidance of difficult tasks and lead to low and inaccurate self-efficacy judgements, which can in turn affect their achievement. This negative effect on students’ self-efficacy is the opposite of what level marking is intended to achieve.

Our results contribute to a new understanding of level-marked tasks in mathematics textbooks as a differentiation initiative. The results indicate that level marking does not improve self-efficacy, which contradicts the purpose of differentiation (Mathiassen, 2009; NOU, 2016, p. 62). The finding that difficult-level marking of tasks reduces students’ self-efficacy has implications for mathematics teachers in terms of their choice of differentiation initiatives. This study adds new insights to the body of research reporting on how self-efficacy affects task choice, effort, persistence, self-evaluation, resilience and achievement (Zimmerman and Martinez-Pons, 1990; Pajares and Miller, 1995; Pajares, 1996; Ramdass and Zimmerman, 2008; Schunk and Mullen, 2012; Zakariya, 2021), and may have implications for how teachers use level-marked tasks in the classroom. If teachers allow students to choose between level-marked tasks, a negative consequence might be that some students avoid tasks marked as difficult. However, considering that the present study investigated only three tasks, more research is required to determine how level-marked tasks affect students’ cognitive, affective, selective and motivational processes. In addition, we recommend that future research include more than one mathematics task per level to measure the internal consistency of students’ self-efficacy. We are currently in the process of investigating the effect of level-marked tasks on students’ performance, persistence and choice of tasks, for a future examination of how level-marked tasks affect students’ learning of mathematics.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

The studies involving human participants were reviewed and approved by NSD – Norwegian centre for research data. Written informed consent to participate in this study was provided by the participants’ legal guardian/next of kin.

All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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