Formative Assessment and Self-Regulated Learning in Lower Secondary Mathematics: Students’ and Teachers’ Perceptions

Abstract

Formative assessment is widely seen as a key teaching strategy to support student learning; however, evidence about its connection with self-regulated learning and the alignment between teachers’ and students’ perceptions remains mixed. This study explored the role of formative assessment in promoting self-regulated learning in lower secondary mathematics by incorporating both students’ and teachers’ viewpoints. From a co-regulatory perspective, formative assessment is considered a process developed through ongoing interactions between teachers and students and shared views of assessment practices. The sample included 305 students from Grades 5–9 and 39 mathematics teachers. Students reported their perceptions of formative assessment practices and self-regulated learning, while teachers reported their own practices. Analyses included Pearson correlation and multiple regression at the student level, along with class-level comparisons of teacher–student perceptions and analyses of perceptual agreement. Results revealed that students’ perceptions of formative assessment were positively linked to cognitive, metacognitive, behavioral, and motivational dimensions of self-regulated learning. Multiple regression results showed that different aspects of formative assessment significantly predicted students’ self-regulation, with the greatest explained variance in behavioral self-regulation. Teachers believed they used more formative assessment practices than students perceived. Additionally, higher levels of perceptual agreement between teachers and students, especially in clarifying learning goals and gathering evidence of learning, were associated with increased behavioral regulation and motivational independence among students. These findings emphasize formative assessment in mathematics as a relational and co-regulatory process that relies on shared understanding between teachers and students.

1. Introduction

Formative assessment (FA) has been increasingly recognized as a central component of effective teaching and learning, particularly when conceptualized as a process enacted with students rather than merely for them (Andrade et al., 2021). In contrast to summative assessment, which primarily serves to certify learning outcomes, FA aims to generate information to adapt instruction and support students’ learning processes in real time (Black & Wiliam, 2009). Within this perspective, alignment between teachers’ and students’ perceptions of assessment practices has emerged as a critical condition for assessment quality and instructional effectiveness, as it shapes how assessment information is interpreted and used for learning (Balbi et al., 2025; Veugen et al., 2024).

Formative assessment has been widely recognized as a powerful approach for supporting student learning and improving classroom instruction (Black & Wiliam, 1998; Wiliam, 2011).

Beyond its instructional function, FA has been consistently linked to the development of students’ self-regulated learning (SRL). SRL refers to learners’ capacity to plan, monitor, and adapt their cognitive, motivational, and behavioral processes in order to achieve academic goals (Brandmo et al., 2020; Zimmerman, 2002). Prominent theoretical models conceptualize SRL as a multidimensional process involving cognitive and metacognitive strategies, motivational beliefs, and behavioral engagement (Wolters et al., 2005). A growing body of research highlights the close conceptual and empirical relationship between FA and SRL, suggesting that formative practices create conditions that enable students to regulate their learning more effectively through clearer goal orientation, the proactive use of feedback, and structured opportunities to evaluate and adjust their study strategies (Panadero et al., 2018).

This relationship is particularly salient in mathematics education, a domain characterized by cumulative knowledge structures, high cognitive demands, and persistent student difficulties. Successful learning in mathematics requires sustained engagement in problem-solving, strategic planning, monitoring solution processes, and persistence in the face of errors. Empirical studies indicate that FA practices can support these processes by promoting meaningful feedback, instructional adaptation, and student engagement (Rakoczy et al., 2019). In parallel, SRL has been consistently associated with improved mathematical learning and achievement, underscoring its importance in this subject area (Dignath & Büttner, 2008; Özcan, 2016).

In the Portuguese educational context, data from PISA 2022 (Duarte et al., 2023) indicate a decline in students’ average performance in mathematics. Moreover, over the past decade, mathematics has consistently had the highest failure rate among students in the second and third cycles of basic education (ages 10–15) (DGEEC, 2023a, 2023b). From a motivational perspective, the TIMSS 2023 (Duarte et al., 2024) report further shows that a substantial proportion of Portuguese eighth-grade students (ages 13–14) report disliking learning mathematics. These indicators persist despite educational policy initiatives aimed at improving pedagogical practices and promoting formative assessment, most notably the MAIA Project (Monitoring, Support, and Research in Pedagogical Assessment) (Fernandes et al., 2021). Implemented nationwide by the Directorate-General for Education in 2019, the MAIA Project sought to integrate the formative function of assessment more coherently within the curriculum. However, the mismatch between efforts to improve teaching practices and students’ learning outcomes suggests that changes in teachers’ practices alone are insufficient, highlighting the need for students’ active involvement in the teaching and learning process.

Recent research suggests that the effectiveness of FA does not depend solely on the presence or frequency of formative practices, but critically on how students perceive and interpret these practices. Several studies have documented systematic discrepancies between teachers’ self-reports of FA practices and students’ perceptions, with teachers often perceiving their practices as more formative than students do (Pat-El et al., 2015; van der Kleij, 2019). Such perceptual incongruence may weaken the regulatory function of assessment, limiting students’ ability to use feedback to guide their learning and self-regulation (J. Hattie & Timperley, 2007; Sadler, 1989). These findings are consistent with contemporary views of FA as a relational, dialogic, and interpretive practice, whose impact depends on shared teacher–student sense-making rather than on technical implementation alone (Carless & Winstone, 2023).

Despite these advances, few studies have jointly examined formative assessment, multiple dimensions of self-regulated learning, and teacher–student perceptual congruence within the specific context of lower secondary mathematics. Existing research has often focused on either students’ perceptions or teachers’ practices in isolation, or on FA-SRL relations without explicitly considering the alignment between teachers’ intentions and students’ interpretations. Addressing this gap, the present study integrates students’ and teachers’ perspectives to examine how perceived formative assessment practices relate to different dimensions of SRL in mathematics, and whether congruence between teachers’ and students’ perceptions is associated with students’ regulatory functioning.

This body of research suggests that formative assessment may support self-regulated learning not only through instructional design, but through students’ perceptions and shared sense-making with teachers, an assumption tested in the present study.

Conceptually, the present study advances the literature by integrating three strands of research that have often been examined separately: (a) the multidimensional structure of self-regulated learning, (b) students’ and teachers’ parallel perceptions of formative assessment practices, and (c) multilevel modeling of teacher–student perceptual congruence in a mathematics-specific context. By simultaneously examining global formative assessment effects, dimensional patterns, and congruence indices at the classroom level, this study moves beyond simple association models and offers a more relational, system-oriented account of how formative assessment operates in authentic instructional settings. In doing so, it contributes empirical evidence to ongoing debates about the role of perceptual alignment in activating the regulatory potential of formative assessment.

2. Theoretical Background

To frame the present study, the following sections review the literature on formative assessment practices in mathematics education, their relationship with students’ self-regulated learning, and the importance of teacher–student perceptual congruence in formative assessment processes.

Learning mathematics goes beyond the simple memorization of disconnected concepts and procedures (Hodgen & Wiliam, 2006); it involves students becoming capable of manipulating mathematical elements and deciding which representation is most appropriate for each problem situation (Ollerton, 2009). Thus, mathematics teaching should enable students to create their own meaning in relation to the content (Suurtamm et al., 2016) and actively engage in developing deep understanding and connecting mathematical ideas to real-world contexts (Hodgen & Wiliam, 2006). To achieve these outcomes, given the central role that assessment practices play in the teaching and learning process, it is important that assessment practices in mathematics education adopt a more formative than summative perspective (Kilpatrick & Swafford, 2002).

2.1. Formative Assessment in Mathematics

Formative Assessment encompasses a wide range of approaches that have demonstrated positive effects on both teaching practices and student learning in general education and, more specifically, in mathematics education. FA enables teachers to gather evidence of student learning to inform subsequent instructional actions (Andrade & Heritage, 2017; Kilpatrick & Swafford, 2002; Schneider & Meyer, 2012), while supporting students in monitoring their progress and adjusting their learning strategies (Panadero et al., 2018). Conceptualizations of FA have evolved from teacher-centered views focused on the provision of feedback (Sadler, 1989) toward dialogic perspectives that involve teachers, students, and peers.

In this study, FA is grounded in the definition proposed by Black and Wiliam (2009), which considers classroom practice formative to the extent that evidence of student learning is elicited, interpreted, and used by teachers, students, or peers to make decisions about next steps in teaching and learning.

In mathematics education, this formative assessment (FA) perspective can occur in both informal moments within everyday classroom routines and in more formal moments aimed at assessing students’ current state of knowledge through activities designed to elicit complex processes such as problem solving, justification, and the development of reasoning (Suurtamm et al., 2016). This is particularly important because standardized tests typically assess only elementary mathematical knowledge, failing to capture the problem-solving competencies central to students’ development in the modern world (Kilpatrick & Swafford, 2002). Therefore, for mathematics teachers to understand what students have comprehended, they need to challenge them with activities that encourage them to think and talk about their ideas (Hodgen & Wiliam, 2006).

Building on earlier work on formative assessment (Black & Wiliam, 1998), Wiliam (2007) proposed five interrelated strategies that structure formative assessment practices in the classroom. These strategies have been widely used as a conceptual framework for analysing formative assessment practices across subject domains, including mathematics education.

The first strategy focuses on clarifying and collaboratively sharing learning goals and assessment criteria, using language accessible to students (J. A. C. Hattie, 2009; Leahy et al., 2005). Making learning intentions and success criteria explicit helps the teacher anticipate students’ potential mathematical difficulties and, consequently, structure possible future actions to support more consistent mathematics learning (Stein & Smith, 2011). For students, this strategy helps them understand what is expected of them, identify quality standards for performance (Wolterinck-Broekhuis et al., 2024), and recognize gaps between their current understanding and the learning goals (J. A. C. Hattie, 2009; Hodgen & Wiliam, 2006).

From a cognitive perspective, such transparency supports students in aligning their study strategies with learning objectives and enables evaluative discussions around exemplars and different levels of quality in the mathematical task (Hodgen & Wiliam, 2006). From a socio-emotional perspective, clarity of goals and criteria has been associated with enhanced self-regulation, reduced anxiety and fear of failure, strengthened perceptions of competence, and increased trust and fairness in the assessment process (Panadero et al., 2017; Santos & Pinto, 2014).

Once learning goals and criteria are clarified, the second strategy involves engineering effective classroom discussions and tasks to elicit evidence of student learning. In mathematics education, this strategy relies on the systematic use of questioning, dialogue, observation, open-ended questions with multiple possible solution paths, and analysis of student work to gather information about what students know and can do during the learning process (Hodgen & Wiliam, 2006; Ollerton, 2009; Stein & Smith, 2011; Suurtamm et al., 2016).

Ongoing evidence collection helps teachers identify students’ learning needs and adjust instruction accordingly, by supporting struggling students and providing cognitively challenging tasks to those who already show understanding (Schneider & Meyer, 2012; Suurtamm et al., 2016; Wiliam, 2011).

From a cognitive perspective, mathematical discussions encourage students to recognize different approaches to the same problem and identify patterns in solution strategies (Baumert et al., 2010; Ponte, 2017; Stein & Smith, 2011). These interactions support monitoring and the development of metacognitive awareness. Socio-emotionally, they also value student participation, foster a sense of belonging, and contribute to a positive and inclusive classroom climate.

The third strategy concerns providing feedback that advances learning. Unlike summative assessment, which focuses on classifying final performance, formative feedback is embedded in the learning process, through valuing errors as opportunities for learning, and may be provided by teachers, peers, or technological tools (Andrade & Heritage, 2017; Carless & Boud, 2018; Hodgen & Wiliam, 2006). Effective feedback addresses three key questions—Where am I going? How am I doing? What are the next steps?—at the levels of task, process, and self-regulation, thereby reducing the gap between current performance and intended goals (J. Hattie & Timperley, 2007; Leahy et al., 2005). Research further indicates that feedback is most effective when it is dialogic and involves shared interpretation and meaning making, rather than unidirectional correction (Carless, 2012). Especially in mathematics, dialogue is an effective strategy for promoting understanding of different forms and representations of concepts (Hodgen & Wiliam, 2006). For feedback to support learning, students must understand its purpose and know how to use it to regulate their learning (Carless & Boud, 2018). Different types of feedback contribute to SRL in complementary ways: praise and corrective feedback influence motivation and knowledge acquisition (Nakata et al., 2025); peer feedback supports co- and self-regulated learning (Veugen et al., 2024); confirmatory feedback enhances confidence and self-efficacy; and transformative feedback supports time management and strategic adaptation by providing explicit guidance on how to improve (Bellhäuser et al., 2023). Across these processes, trust emerges as a key condition for effective use of feedback, as supportive classroom climates encourage students to engage with critique and articulate uncertainties (Carless, 2012).

Building on dialogic feedback processes, the fourth strategy involves activating students as learning resources for one another through peer assessment and peer feedback (Leahy et al., 2005). Engaging students in evaluating one another’s work promotes critical thinking, internalization of assessment criteria, and collaborative learning skills (Ponte, 2017; Wiliam, 2007).

From a regulatory perspective, these practices align with co-regulation frameworks, in which learning regulation emerges through social interaction and shared responsibility (Andrade et al., 2021). Cognitively, peer assessment during mathematics lessons fosters evaluative judgment and metacognitive reflection on quality and performance (Hodgen & Wiliam, 2006). Socio-emotionally, it supports the development of empathy, motivation, and SRL strategies (Panadero et al., 2019; Weldmeskel & Michael, 2016).

Empirical evidence suggests that self-assessment and peer feedback are more strongly associated with SRL development than feedback provided exclusively by teachers (Makkonen & Jaquet, 2020).

Finally, the fifth strategy emphasizes activating students as owners of their own learning by fostering autonomy in monitoring performance and determining subsequent learning steps (Wiliam, 2007). Practices such as self-assessment and the use of rubrics are particularly effective in supporting student engagement and self-regulation (Andrade & Heritage, 2017; Hodgen & Wiliam, 2006; Wiliam, 2011). Aligned with the second strategy, opportunities for students to express their ideas and reasoning not only support the development of mathematical language but also place them in a more active role in the learning process (Hodgen & Wiliam, 2006; Ollerton, 2009). Furthermore, when students clearly understand learning goals and assessment criteria, they are better able to reflect critically on their work and use feedback independently to manage their learning progress. Cognitively, this strategy consolidates metacognitive processes and the capacity to learn how to learn, while socio-emotionally it promotes autonomy, self-confidence, and self-efficacy, key foundations of intrinsic motivation (Ryan & Deci, 2020).

When implemented systematically and coherently, these five formative assessment strategies contribute to instructional improvement and student learning in mathematics.

Empirical studies show that formative practices promote student-centered teaching and enhance students’ confidence and perceptions of assessment usefulness, particularly through progress-oriented feedback (Rakoczy et al., 2019).

Reviews of mathematics education research further indicate that formative assessment positively affects academic achievement through instructional adaptation, process-focused feedback, and self-assessment practices (Palm et al., 2017). Evidence from proportional reasoning instruction demonstrates that the integrated use of the five strategies can improve both mathematical performance and metacognitive awareness among lower-achieving students (Wafubwa & Csíkos, 2022). More recently, personalized feedback approaches have been shown to enhance learning of mathematical concepts and support the development of self-regulated learning (Huang et al., 2024), reinforcing the relevance of formative assessment for mathematics teaching and learning.

From this perspective, formative assessment in mathematics functions not as a collection of isolated techniques but as a coherent pedagogical approach in which instructional decisions, feedback interactions, and student engagement are continuously aligned to support learning. Importantly, such an integrated enactment foregrounds the relational and interactive nature of assessment processes, directing attention to how regulation of learning is distributed and negotiated between teachers and students during classroom activity. In this way, beyond the construction of knowledge, a supportive environment is created for the development and use of self-regulated learning strategies, which are essential for students to actively engage in learning mathematics.

2.2. Self-Regulated Learning

Self-regulated learners are characterized by personal initiative, perseverance, and the ability to adapt to new situations, qualities that are essential for lifelong learning (Zimmerman, 2002). From a cognitive perspective, self-regulated learning (SRL) refers to the processes through which learners actively monitor, control, and manage their cognitive activities and learning behaviors (Pintrich, 2002). More specifically, Zimmerman (2002) conceptualizes SRL as an active, constructive process in which learners transform their cognitive abilities into academic skills to achieve learning goals, rather than merely reacting to instructional techniques.

SRL extends beyond the acquisition of isolated skills and involves a coordinated set of processes related to self-awareness, self-motivation, and behavioral control during task engagement. Empirical research consistently shows that SRL is a strong predictor of academic achievement, as self-regulated learners are able to set their own learning goals, select effective strategies, regulate effort and time use, monitor progress, remain motivated, and adapt plans or seek help when facing difficulties (Andrade & Heritage, 2017).

Over time, several theoretical models have been developed to explain how learners regulate their learning, including those proposed by Zimmerman (1989); Boekaerts (1997); Pintrich (2000); Efklides (2011); and Hadwin et al. (2017). Despite their differences, these models share core assumptions, such as the active role of the learner, learners’ potential control over learning activities, the centrality of goal setting and success criteria, and the interaction between personal and contextual factors in shaping performance (Pintrich, 2004; Wolters et al., 2005). Among these frameworks, Zimmerman’s cyclical model is the most widely used in educational research (Panadero et al., 2017; van der Linden et al., 2023). This model conceptualizes SRL as a dynamic process unfolding across three interrelated phases: forethought (planning), performance (monitoring), and self-reflection. The forethought phase involves cognitive processes activated prior to task engagement, such as task analysis, goal setting, strategy selection, and planning. The performance phase occurs during task execution and includes metacognitive monitoring of progress, strategy implementation, and self-control. Finally, the self-reflection phase involves evaluating both task outcomes and the effectiveness of strategies used, leading to adaptive inferences that inform subsequent learning cycles (Andrade & Heritage, 2017; De Smul et al., 2019; Wolters et al., 2005; Zimmerman, 2002).

Although Zimmerman’s model primarily adopts an individual perspective, contemporary research increasingly emphasizes the social and collaborative nature of learning regulation. In this regard, Hadwin et al. (2017) distinguish between self-regulation, co-regulation, and socially shared regulation of learning. Self-regulation refers to individual regulation processes, whereas co-regulation involves the temporary support of regulation through interaction with others, and socially shared regulation refers to collective regulation processes emerging during group work. From this perspective, co-regulation functions as a critical mechanism through which learners progressively develop SRL strategies through social interaction (Andrade et al., 2021).

To operationalize SRL across its phases, Wolters et al. (2005) identify three core dimensions of regulation: cognitive/metacognitive, motivational, and behavioral. The cognitive dimension encompasses strategies for processing information and performing tasks, while the metacognitive component includes monitoring, evaluating, and regulating these cognitive processes. The motivational dimension refers to the degree of self-determination of motivation, that is, the type of regulation that explains why a learner engages in a behavior. The behavioral dimension reflects learners’ effort, persistence, time management, and help-seeking behaviors. Together, these dimensions provide a comprehensive framework for analyzing how learners regulate their learning processes.

In mathematics education, SRL plays a particularly critical role given the subject’s cumulative and cognitively demanding nature. Empirical studies indicate that strengthening metacognitive aspects of SRL, such as planning solution strategies, monitoring reasoning processes, and validating results, positively affects students’ mathematical performance, particularly in domains such as proportional reasoning (Wafubwa & Csíkos, 2022). Planning-related SRL strategies have also been shown to support mathematics learning, as students who proactively organize their study using advanced access to materials demonstrate stronger content mastery and improved assessment preparedness (Miller & Bernacki, 2019). Moreover, interventions targeting SRL strategies have been found to enhance both mathematics-related motivation and academic achievement, underscoring the relevance of SRL for sustaining engagement and success in mathematics learning (Granello et al., 2025).

These theoretical premises support the analysis of mathematics learning through the cognitive/metacognitive, motivational, and behavioral dimensions of SRL. Understanding this multidimensional structure of SRL provides a necessary foundation for examining how formative assessment practices can create classroom conditions that foster students’ self-regulated learning, which is addressed in the following section.

2.3. Formative Assessment as a Catalyst for Self- and Co-Regulation

The relationship between formative assessment (FA) and self-regulated learning (SRL) has received increasing attention in educational research over recent years. Scholars have emphasized that FA extends beyond continuous assessment practices and contributes to structuring classroom environments that actively promote the development and use of SRL strategies (Andrade & Heritage, 2017; Panadero et al., 2018), as well as to processes of co-regulation (Andrade et al., 2021).

Accordingly, this section examines how FA practices support the development of SRL and co-regulation, with particular emphasis on evidence from mathematics education. FA and SRL are closely interconnected, as both theoretical frameworks address core elements such as the use of learning goals and standards, students’ proactive engagement, goal setting, and sustained effort in everyday classroom practice (Brandmo et al., 2020).

Despite these shared foundations, the two perspectives differ in emphasis: SRL focuses primarily on the individual learner’s regulatory processes, whereas FA seeks to optimize teaching and learning through the joint actions of teachers and students (Brandmo et al., 2020; Li & Gu, 2024). Moreover, FA in classroom contexts involves multiple sources of regulation beyond the learner, including teachers, peers, assessment tasks, and instructional materials, making it a key mechanism for supporting co-regulation of learning (Andrade et al., 2021).

When implemented effectively, FA stimulates both cognitive and motivational aspects of learning by orienting students toward learning goals and providing feedback that supports the refinement of learning strategies (Panadero et al., 2018; van der Linden et al., 2023; Weldmeskel & Michael, 2016; Xiao & Yang, 2019). Empirical evidence suggests that students’ behaviors during FA practices align closely with the phases of SRL. Specifically, during the planning phase, students set learning goals and select appropriate strategies based on shared assessment criteria; during the performance phase, they implement and adapt strategies while monitoring progress; and during the reflection phase, they critically evaluate their learning processes and outcomes in order to make necessary adjustments and advance to subsequent learning tasks (Xiao & Yang, 2019). In this sense, formative practices not only support conceptual understanding but also foster metacognitive awareness and learner autonomy (Li & Gu, 2024).

From the students’ perspective, recognizing the formative purpose of assessment increases their sense of responsibility and promotes active engagement in learning (Weldmeskel & Michael, 2016). Such positive perceptions are influenced by the clarity of learning goals and by how feedback is communicated and framed (Panadero et al., 2018). When students perceive feedback as constructive and useful for improvement, they are more likely to adopt proactive learning behaviors and engage in SRL strategies (He et al., 2023; Nicol & MacFarlane-Dick, 2006).

Conversely, developing awareness of the importance of SRL enables students to take increasing ownership of their learning processes and to assume greater responsibility for regulating their progress (Panadero et al., 2017). Mathematics instruction provides particularly favorable conditions for the development of SRL through FA. As Ollerton (2009) argues, mathematics teaching goes beyond the transmission of content and involves aligning teaching with learning in ways that support students’ organization, analysis, and generalization skills.

Sharing and clarifying learning goals and success criteria, often through co-constructed rubrics or exemplars of mathematical work with varying levels of quality, helps students understand the reasoning processes underlying final answers and shapes their expectations about learning (Andrade & Heritage, 2017; Ollerton, 2009). Regarding the design of activities to elicit evidence of mathematical learning, tasks that promote hands-on work, collaboration, discussion, exploration, problem solving, creativity, autonomy, and positive attitudes toward mathematics have been shown to support both engagement and regulation (Ollerton, 2009).

Furthermore, cognitively activating mathematical tasks that encourage diverse solution strategies and explicitly probe reasoning processes not only facilitate conceptual understanding but also strengthen students’ metacognitive awareness of their own problem-solving strategies (Baumert et al., 2010). Considered together, the relationship between FA and SRL is shaped by multiple theoretical and practical factors.

When the formative assessment strategies proposed by Wiliam and Thompson (2007) are implemented coherently, they support students’ progression through the phases and dimensions of SRL, cognitive/metacognitive, motivational, and behavioral, while simultaneously creating opportunities for co-regulation within collaborative learning contexts (Wolters et al., 2005; Zimmerman, 2002). Accordingly, formative assessment can be understood as a key mechanism through which self-regulation is scaffolded and co-regulation emerges in classroom interaction.

In the present study, co-regulation is not examined as a directly measured construct, but as an interpretive mechanism through which formative assessment practices and teacher–student perceptual congruence are expected to support the development of students’ self-regulated learning in mathematics. This perspective underpins the present study’s focus on formative assessment as a relational and co-regulatory process, rather than as a set of isolated instructional techniques. Nevertheless, the effectiveness of this collaborative approach depends critically on the quality of implementation and on the alignment between teachers’ instructional intentions and students’ perceptions of formative practices, an issue addressed in the following section.

2.4. Teacher–Student Congruence in Perceptions of Formative Assessment

The effectiveness of formative assessment (FA) depends not only on teachers’ implementation of specific assessment strategies, but also on how students perceive and interpret these practices (Carless & Winstone, 2023; Pat-El et al., 2015). A growing body of research has documented significant incongruences between teachers’ reports of formative assessment practices and students’ actual perceptions of those practices, suggesting that such discrepancies may moderate the effects of FA on learning outcomes and self-regulated learning (SRL) (Mäkipää, 2021; Pat-El et al., 2015, 2024; Šimić Šašić & Atlaga, 2024; van der Kleij, 2019). This section examines the concept of teacher–student perceptual congruence in FA, synthesizes empirical evidence on congruence and incongruence, and discusses contextual factors that influence these dynamics.

Perceptual congruence refers to the degree of alignment between teachers’ perceptions of their formative assessment practices and students’ perceptions of those same practices (Pat-El et al., 2015). This alignment is commonly examined using mirrored instruments, in which teachers and students respond to parallel items describing the teacher’s formative practices, allowing for direct comparison of perceptions (Balbi et al., 2025; Pat-El et al., 2013; Veugen et al., 2021). In contrast, perceptual incongruence can manifest in at least two distinct forms. The first concerns implementation incongruence, in which teachers report implementing formative practices that students do not perceive (Mäkipää, 2021; Pat-El et al., 2015). The second concerns interpretive incongruence, in which both teachers and students recognize the presence of a practice but attribute different meanings or purposes to it (Mäkipää, 2021; Šimić Šašić & Atlaga, 2024; van der Kleij, 2019). Regardless of its form, perceptual incongruence has been shown to undermine the effectiveness of formative assessment practices (Pat-El et al., 2024).

Empirical studies indicate that perceptual congruence is more frequently observed in collaborative practices, such as peer assessment and peer feedback, whereas discrepancies become more pronounced in practices that require higher levels of metacognitive engagement, such as self-assessment (Balbi et al., 2025; Veugen et al., 2024). More broadly, research suggests that teachers tend to overestimate the formative nature of their assessment practices relative to students’ perceptions (Pat-El et al., 2015). This overestimation may stem from communication breakdowns or from teachers’ emphasis on instructional planning without sufficient consideration of how students experience and interpret assessment practices (van der Kleij, 2019).

Within this context, Mäkipää (2021) highlights that students do not always perceive oral feedback as such, or interpret it merely as error correction, in contrast to teachers’ beliefs that such feedback is frequent and supportive. This misalignment is particularly problematic for SRL, as it may prevent students from using feedback effectively to monitor their learning progress and regulate subsequent actions. When students do not recognize or understand the intentions behind feedback, the regulatory function of formative assessment is substantially weakened.

Several contextual factors have been identified as influencing the convergence of teachers’ and students’ perceptions of formative practices. Professional development plays a key role in helping teachers develop greater clarity about their own practices and integrate formative approaches more coherently into classroom routines (Balbi et al., 2025). Research further suggests that changes in assessment practice tend to occur gradually and are more likely to be sustained when professional development includes extended duration, practical application, and opportunities for reflection (Veugen et al., 2021). Another important factor concerns the visibility of formative strategies in classroom practice. Higher levels of congruence have been observed with more explicit strategies, such as clarifying assessment criteria and peer assessment, whereas practices such as feedback, particularly oral feedback, are more prone to perceptual divergence (Balbi et al., 2025; Mäkipää, 2021; van der Kleij, 2019).

In sum, these findings underscore the importance of students’ perceptions of classroom assessment for learning outcomes and SRL development. While teachers’ formative intentions are essential, they are not sufficient on their own; explicit communication and visible enactment of assessment practices are necessary for these intentions to translate into meaningful student engagement. Investigating points of convergence and divergence between teachers’ pedagogical intentions and students’ perceived experiences is, therefore, a fruitful avenue for understanding how formative assessment can be optimized to support learning and self-regulation. Accordingly, formative assessment can be understood as a key mechanism through which self-regulation is scaffolded, and co-regulation emerges in classroom interaction. This perspective underpins the present study’s focus on formative assessment as a relational and co-regulatory process, rather than as a set of isolated instructional techniques.

Against this theoretical and empirical background, the present study aimed to examine the role of formative assessment practices in fostering self-regulated learning in lower secondary mathematics by integrating students’ and teachers’ perspectives. Specifically, the study addressed three sets of research questions:

RQ1. Are students’ perceptions of formative assessment (FA) practices in mathematics, both at the global level and across specific dimensions, positively associated with cognitive and metacognitive self-regulation, behavioral self-regulation, and motivational autonomy?

H1. 

Students’ perceptions of formative assessment (FA) practices, both globally and across its specific dimensions (Clarification and Elicitation, Feedback, and Shared Regulation), are positively associated with cognitive and metacognitive self-regulation, behavioral self-regulation, and motivational autonomy.

RQ2. To what extent do various aspects of formative assessment practices, such as clarification and elicitation, feedback, and shared regulation, independently predict students’ cognitive, metacognitive, behavioral, and motivational self-regulated learning?

H2. 

Different dimensions of formative assessment are expected to differentially predict students’ self-regulated learning.

RQ3. Do teachers’ and students’ perceptions of formative assessment (FA) practices differ, and is teacher–student perceptual congruence across FA dimensions associated with class-level motivational, behavioral, cognitive, and metacognitive self-regulated learning outcomes?

H3a. 

At the classroom level, teachers report significantly higher levels of formative assessment practices than students perceive, both globally and across formative assessment dimensions.

H3b. 

Teacher–student perceptual congruence in formative assessment is expected to show a cross-level association, such that classroom-level congruence is positively related to student-level self-regulated learning outcomes.

Taken together, this body of research indicates that formative assessment practices can support students’ self-regulated learning both directly and via shared teacher–student understandings of assessment processes.

3. Materials and Methods

3.1. Participants

Participants were 305 students enrolled in lower secondary education (Grades 5–9). This level was selected because it encompasses the transition to upper secondary education, during which students are expected to demonstrate more advanced self-regulated learning competencies (Meusen-Beekman et al., 2016), and because few studies cover this level of schooling.

The sample included 161 girls (52.8%) and 144 boys (47.2%). Students were distributed across Grades 5 to 9, with 7.5% in Grade 5 (n = 23), 40.1% in Grade 6 (n = 123), 26.6% in Grade 7 (n = 81), 14.1% in Grade 8 (n = 43), and 11.5% in Grade 9 (n = 35). It is important to note that the higher concentration of Grade 6 students was not intentional but resulted from the availability of classes in the schools where data collection took place. This asymmetry will be duly considered in the study’s discussion and limitations.

Regarding grade retention, 91.1% of students (n = 278) reported no history of grade repetition, while 8.9% (n = 27) indicated having repeated at least one school year.

Data were collected in two public schools in the Greater Lisbon region (NUTS III sub-region), in a predominantly low- to middle-socioeconomic context. The questionnaires were administered during regular school hours. Depending on the school organization, in one school, data collection took place in the library without teachers present; in the other, it occurred in the classroom, with teachers present but remaining at their desks and not intervening in the completion of the questionnaires.

The teacher sample consisted of 39 mathematics teachers. Regarding sex, most participants were female (n = 29), while ten were male (n = 10). Teachers’ ages ranged from 27 to 62 years, with a mean age of 48.21 years (SD = 7.55), indicating a predominantly mid- to late-career teaching workforce. Regarding teaching experience, participants reported 3 to 36 years of professional experience. On average, teachers had 22.41 years of experience (SD = 7.67), reflecting a sample composed mainly of experienced professionals. The teacher sample was evenly distributed across age and experience groups and was predominantly female and experienced.

3.2. Instruments

Detailed psychometric analyses of all instruments used in this study, including exploratory and confirmatory factor analyses and reliability indices, are reported in the Supplementary Materials.

The instruments were adapted from previous research, with specific adjustments, including adding new items to the formative assessment scale and reorganizing items in the self-regulated learning scales to optimize their psychometric properties. In this section, we present the final versions of the scales used in the data analysis, along with psychometric evidence supporting the reliability of the findings. A comprehensive description of the original scales as administered to participants, including the full item pool and the step-by-step validation process, is provided in the Supplementary Material.

Instruments that had not been previously adapted or validated were first subjected to exploratory factor analyses (EFA) to examine their latent structure, followed by confirmatory factor analyses (CFA) to test the adequacy of the proposed measurement models (Brown, 2015; Kline, 2016). Model fit was evaluated using commonly reported fit indices and established decision guidelines. Internal consistency reliability was assessed using both Cronbach’s alpha and McDonald’s omega. Omega was reported alongside alpha because it provides a less restrictive and often more accurate estimate of reliability when the assumption of tau-equivalence is violated (Dunn et al., 2014).

The internal consistency of the scales was evaluated using the guidelines proposed by George and Mallery (2003), which provide conventional benchmarks for interpreting Cronbach’s alpha coefficients. The interpretation of the CFA models was conducted in accordance with the recommendations and fit index guidelines proposed by Hair et al. (2019).

1. Self-Regulated Learning in Mathematics

The scale used in this study to assess students’ self-regulated learning is a composite of three scales, each reflecting how the individual regulates the specific dimensions proposed by Wolters et al. (2005): Strategies for the Regulation of Academic Cognition, Strategies for the Regulation of Academic Behavior, and Strategies for the Regulation of Academic Motivation.

1.1. Strategies for the Regulation of Academic Cognition

The scale evaluating strategies for regulating academic cognition included items that measured students’ use of cognitive and metacognitive strategies in mathematics learning. Cognitive self-regulation consisted of 14 items reflecting rehearsal, elaboration, and organization strategies, while metacognitive self-regulation comprised 12 items assessing students’ planning, monitoring, and regulation of their learning processes. All items were rated on a five-point Likert scale, with higher scores indicating more frequent use of self-regulated learning strategies.

A confirmatory factor analysis supported a two-factor structure distinguishing Cognitive Self-Regulation (14 items) and Metacognitive Self-Regulation (12 items), with acceptable model fit (CFI = 0.919, TLI = 0.906, SRMR = 0.044, RMSEA = 0.046). Internal consistency was good for both dimensions (Cognitive Self-Regulation: α = 0.857, ω = 0.859; Metacognitive Self-Regulation: α = 0.817, ω = 0.822), and the overall scale demonstrated excellent reliability (α = 0.911, ω = 0.912).

1.2. Strategies for the Regulation of Academic Behavior

Behavioral self-regulation strategies were assessed using a unidimensional model adapted from the original two-factor self-report scales developed by Wolters et al. (2005), as detailed in the Supplementary Material. The unidimensional model combines all 12 items into a single Behavioral Self-Regulation dimension (e.g., “I try to do my math assignments on my own, even if I need help”), reflecting an integrated process in which students manage both their persistence and their study conditions simultaneously. The behavioral regulation instrument was rated on a five-point Likert scale, with higher scores indicating greater use of behavioral self-regulation strategies. Scores for each dimension were computed by averaging the corresponding item responses, with higher values reflecting more effective regulation of time, study environment, and effort.

The unidimensional scale was subjected to confirmatory factor analysis. This model showed acceptable fit, χ²(48) = 106, p < 0.001, CFI = 0.932, TLI = 0.907, SRMR = 0.049, RMSEA = 0.063, 90% CI [0.047, 0.080]. Standardized loadings ranged from 0.218 to 0.709 and were statistically significant.

Internal consistency was adequate (α = 0.809; ω = 0.817), supporting retention of the unidimensional structure for subsequent analyses.

1.3. Strategies for the Regulation of Academic Motivation

Motivational self-regulation strategies were evaluated using the Academic Self-Regulation Questionnaire (SRQ-A), the Portuguese validated version developed by Gomes et al. (2019), based on Self-Determination Theory (Ryan & Deci, 2000). The instrument measures students’ reasons for participating in academic activities and captures various forms of motivational regulation along a spectrum of self-determination.

The version used in this study included 16 items divided into four categories (four items each): External Regulation, which reflects motivation driven by external demands or rewards; Introjected Regulation, representing behavior influenced by internal pressures such as guilt or contingent self-worth; Identified Regulation, referring to engagement based on the personal significance of the activity; and Intrinsic Regulation, indicating motivation driven by interest and enjoyment. All items were rated on a five-point Likert scale, with higher scores showing a stronger endorsement of each regulatory style.

Internal consistency coefficients ranged from acceptable to good across the four dimensions (α = 0.699–0.856; ω = 0.707–0.859).

In addition, a Relative Autonomy Index (RAI) was computed to provide a global indicator of motivational self-regulation, reflecting the extent to which students’ motivation was relatively autonomous rather than controlled (Grolnick & Ryan, 1989).

2. Formative assessment scale

2.1. Students’ version

Students’ and teachers’ perceptions of formative assessment practices were evaluated using a 27-item self-report scale. Although the instrument was initially designed to align with Wiliam and Thompson’s (2007) five formative assessment strategies, the psychometric analyses presented in the Supplementary Materials supported a simpler three-dimensional structure: Clarification and Elicitation (11 items), Feedback (12 items), and Shared Regulation (4 items).

Clarification and Elicitation evaluate how clearly learning goals and criteria are communicated and how teachers use activities and classroom interactions to gather evidence of students’ understanding. Feedback measures how effectively teachers offer improvement-focused feedback that enhances students’ learning. Shared Regulation involves practices that encourage student involvement in managing their learning, including self-assessment and peer assessment.

All items were rated on a five-point Likert scale, with higher scores indicating a stronger perceived presence of formative assessment practices. A confirmatory factor analysis supported the three-factor structure with good model fit (CFI = 0.933, TLI = 0.925, SRMR = 0.049, RMSEA = 0.050). Internal consistency was good to excellent across the dimensions (α = 0.706–0.925; ω = 0.712–0.925), with excellent reliability for the overall formative assessment score (α = 0.931; ω = 0.931).

2.2. Teachers’ version

To examine the psychometric properties of the teacher version of the instrument, a confirmatory factor analysis was conducted using the same three-dimensional structure identified in the student sample. The results indicated weak model fit, likely due to the small sample size of teachers (N = 39), which can affect the stability of CFA estimates. Nonetheless, internal consistency estimates were acceptable across dimensions (α = 0.70–0.77; ω = 0.75–0.76).

Given the model’s theoretical coherence and the acceptable reliability of the dimensions, the teacher version of the scale was kept to allow comparisons between students’ and teachers’ perceptions of formative assessment practices.

3.3. Data Analysis Procedures

The data analysis proceeded in three consecutive stages aligned with the study hypotheses: (1) student-level correlational analyses (H1), (2) student-level multiple regression analyses evaluating the predictive contributions of formative assessment dimensions (H2), and (3) classroom-level analyses examining teacher–student perceptual discrepancies and agreement (H3).

Perceived formative assessment was operationalized using both a global score and dimensional scores. The global score reflected students’ overall perceptions of formative assessment practices and was used in correlational analyses, while dimensional scores, clarification and elicitation, feedback, and shared regulation were used to examine the specific contributions of these practices to different components of self-regulated learning.

Hypothesis H1 was tested using Pearson correlation analyses at the student level to explore links between students’ perceptions of formative assessment and indicators of self-regulated learning.

Hypothesis H2 explored whether different dimensions of formative assessment predicted specific aspects of self-regulated learning. In these analyses, the three formative assessment dimensions were entered simultaneously as predictors in multiple regression models. Four models were estimated, with cognitive self-regulation, metacognitive self-regulation, behavioral self-regulation, and motivational autonomy (Relative Autonomy Index) designated as dependent variables. Standardized regression coefficients (β), coefficients of determination (R²), and 95% confidence intervals were reported. Multicollinearity among predictors was evaluated using Variance Inflation Factors (VIFs) and tolerance statistics.

Because teacher–student congruence was calculated using class-aggregated student perceptions, the adequacy of this aggregation was assessed. ICC (1) values for the student-reported formative assessment ranged from 0.17 to 0.32, indicating significant between-class variability. With an average class size of (k = 7), ICC (2) values ranged from 0.59 to 0.76, supporting the reliability of the classroom means used as Level 2 predictors.

Hypothesis H3a was tested at the classroom level using matched teacher–class pairs. Student perception scores were combined at the class level and compared with teacher self-reports using paired-sample t-tests.

Hypothesis H3b was examined using multilevel linear models with random classroom intercepts to account for the hierarchical data structure, with students (Level 1) nested within classrooms (Level 2). For each self-regulated learning outcome (cognitive, metacognitive, behavioral, and motivational regulation), an unconditional (intercept-only) model was first fitted to calculate the intraclass correlation coefficient (ICC), which measures the proportion of variance due to differences between classrooms. ICC values ranged from 0.068 to 0.145, indicating significant between-class variance and justifying the use of multilevel modeling.

Teacher–student perceptual agreement in formative assessment practices was measured using classroom-level discrepancy scores. Absolute differences were calculated between teachers’ self-reported formative assessment scores and the corresponding class-aggregated student perception scores for each formative assessment dimension (clarification and elicitation, feedback, and shared regulation). Lower values indicate closer teacher–student perceptual alignment, while higher values reflect greater perceptual divergence.

These discrepancy indices were entered as Level 2 fixed predictors in the multilevel models, while students’ self-regulated learning outcomes were specified at Level 1. This modeling approach allowed examination of whether variation in teacher–student perceptual alignment across classrooms was linked to differences in students’ self-regulated learning, while accounting for the non-independence of observations within classrooms.

For interpretative purposes, approximate standardized coefficients were calculated by rescaling the unstandardized fixed effects using the ratio of the predictor and outcome standard deviations (β_std ≈ b × SD_X/SD_Y). This transformation does not influence statistical inference but makes it easier to compare effect sizes across different outcomes.

Before interpreting the regression and multilevel models, diagnostic procedures were performed to evaluate underlying assumptions. For the single-level regression models, linearity and homoscedasticity were checked through visual inspection of standardized residuals plotted against predicted values, and normality was assessed using histograms and normal P–P plots of standardized residuals. No significant violations were detected. Influential observations were examined using Cook’s distance and standardized residuals; Cook’s distance values stayed below 0.14, and standardized residuals did not exceed |2.07|. Multicollinearity diagnostics showed no problematic collinearity (VIF < 2.12; tolerance > 0.47).

For the multilevel models, examining Level 1 residuals plotted against fitted values showed no serious violations of linearity or homoscedasticity. Considering the Level 1 sample size (N = 305), the estimation methods are deemed robust to small deviations from normality. Overall, no significant violations of model assumptions were found that would threaten the validity of the reported results. All statistical analyses were carried out using Jamovi software (version 2.5.3) and IBM SPSS Statistics (version 31.01.0 (49)).

4. Results

4.1. Associations Between Formative Assessment and Self-Regulated Learning

To test H1, Pearson correlation analyses were conducted at the student level to examine the relationships between students’ perceptions of formative assessment practices and various indicators of self-regulated learning (SRL). As shown in Table 1, results indicated that Global FA was positively and significantly associated with all major dimensions of self-regulated learning. Higher perceived levels of formative assessment were moderately associated with cognitive SRL, metacognitive SRL, and behavioral SRL, as well as with students’ Relative Autonomy Index (RAI).

Table 1. Pearson correlations between formative assessment perceptions and self-regulated learning dimensions.

Formative Assessment	CG	MC	BS	RAI
Global FA	0.38 ***	0.41 ***	0.46 ***	0.31 ***
Clarification and Elicitation	0.45 ***	0.48 ***	0.52 ***	0.34 ***
Feedback	0.29 ***	0.33 ***	0.27 ***	0.18 *
Shared Regulation	0.70 ***	0.83 ***	0.58 ***	0.46 ***

Note. CG = Cognitive self-regulation; MC = Metacognitive self-regulation; BS = Behavioral self-regulation; RAI = Relative Autonomy Index; Global FA = Global Formative Assessment. * p < 0.05. *** p < 0.001.

As reported in Table 1, some correlations among self-regulated learning dimensions were relatively high, particularly between shared regulation and metacognitive self-regulation. This pattern likely reflects the conceptual proximity between these constructs, as both involve processes of monitoring, reflection, and regulation during learning activities. Because both variables were assessed via student self-report, shared method variance may also have contributed to the magnitude of these associations. Accordingly, these correlations were interpreted as indicative of strong alignment rather than as evidence of construct redundancy.

All three dimensions of formative assessment were positively and significantly associated with cognitive, metacognitive, behavioral, and motivational aspects of SRL. The strongest associations were observed for Shared Regulation, especially with metacognitive (r = 0.83, p < 0.001) and cognitive self-regulation (r = 0.70, p < 0.001). Theoretically, this pattern is coherent: shared regulation practices involve dialogue, joint monitoring, and collaborative evaluation, processes that externalize regulatory thinking and may support the development of individual metacognitive control.

Clarification and Elicitation also showed consistent positive associations across SRL dimensions, particularly with behavioral regulation (e.g., effort and time management). Feedback demonstrated positive, though comparatively smaller, relationships with SRL indicators. In addition, all three formative assessment dimensions were positively related to students’ Relative Autonomy Index, suggesting links between formative classroom practices and motivational autonomy.

These results indicate that while formative assessment operates as a coherent global construct, its components relate differentially to specific self-regulatory processes.

4.2. Predictors of Self-Regulated Learning Dimensions

To test Hypothesis 2, a series of multiple linear regression analyses was performed at the student level to evaluate the specific contributions of different formative assessment dimensions to students’ self-regulated learning (SRL). In these analyses, three formative assessment dimensions, clarification and elicitation, feedback, and shared regulation, were included simultaneously as predictors, and each SRL dimension was analyzed as a separate outcome variable.

Results indicated that the regression model predicting cognitive self-regulation was statistically significant, F(3, 301) = 17.55, p < 0.001, accounting for 14.9% of the variance (R² = 0.149). Both clarification and elicitation (β = 0.16, p = 0.022) and feedback (β = 0.17, p = 0.030) emerged as significant positive predictors, while shared regulation showed a marginal association (β = 0.13, p = 0.057).

The overall model for metacognitive self-regulation was also significant, F(3, 301) = 22.30, p < 0.001, accounting for 18.2% of the variance (R² = 0.182). In this model, clarification and elicitation was the only significant predictor (β = 0.38, p < 0.001), while feedback and shared regulation did not show significant effects.

The model predicting behavioral self-regulation was significant, F(3, 300) = 43.48, p < 0.001, explaining 30.3% of the variance (R² = 0.303). Clarification and elicitation again emerged as the only significant predictor (β = 0.54, p < 0.001), while feedback and shared regulation were not significantly linked to behavioral regulation.

Finally, the regression model predicting motivational autonomy (Relative Autonomy Index) was also significant, F(3, 297) = 15.24, p < 0.001, explaining 13.3% of the variance (R² = 0.133). Clarification and elicitation significantly predicted higher levels of autonomous motivation (β = 0.33, p < 0.001), while feedback and shared regulation were not significant predictors.

Across models, multicollinearity diagnostics showed no issues, as Variance Inflation Factor (VIF) values stayed well below standard thresholds.

These findings suggest that different formative assessment dimensions display distinct predictive patterns across SRL outcomes. Specifically, practices related to clarifying learning goals and gathering evidence of student understanding stand out as the most reliable predictors across cognitive, metacognitive, behavioral, and motivational aspects of self-regulated learning.

4.3. Discrepancies Between Teachers’ and Students’ Perceptions of Formative Assessment

To test Hypothesis H3a, paired-samples t-tests were conducted at the teacher/class level (N = 39) to compare teachers’ self-reported use of formative assessment (FA) practices with students’ class-aggregated perceptions. In addition to dimensional analyses, a paired-samples t-test was also conducted using a global formative assessment score (Global FA) to provide an overall synthesis of teacher–student perceptual differences. Because the teacher version of the FA measure did not show ideal psychometric properties (see Section 3.2), these comparisons should be interpreted cautiously as contrasts between parallel observed perceptions rather than between psychometrically equivalent latent constructs.

Results based on the global score indicated that teachers reported significantly higher overall levels of formative assessment than students perceived, t(38) = −10.45, p < 0.001, with a very large effect size (Cohen’s d = −1.67). Dimensional analyses revealed the same pattern across all FA components. Teachers reported significantly higher levels of Clarification and Elicitation (M = 4.49, SD = 0.34) than students perceived (M = 3.65, SD = 0.43), t(38) = −11.32, p < 0.001, d = −1.81. Teachers’ reports of Feedback (M = 3.68, SD = 0.35) also exceeded students’ perceptions (M = 2.67, SD = 0.63), t(38) = −10.10, p < 0.001, d = −1.62. Finally, teachers reported higher levels of Shared Regulation (M = 2.53, SD = 0.69) than students did (M = 1.90, SD = 0.53), t(38) = −5.04, p < 0.001, d = −0.81. Overall, these findings provide strong support for H3a, indicating large and systematic discrepancies between teachers’ self-reports and students’ perceptions, both globally and across dimensions.

In addition to mean differences, Pearson correlations between teachers’ and class-aggregated students’ perceptions were examined. These correlations were small to moderate across dimensions (rs ranging from 0.19 to 0.30; r = 0.23 for the global score), indicating partial but limited convergence between teachers’ and students’ views of formative assessment practices.

4.4. Perceptual Congruence and Student Self-Regulation

To investigate whether teacher–student perceptual consistency across formative assessment areas relates to students’ self-regulated learning (SRL), a series of multilevel models was used to account for the nested structure of students within classrooms. Null (intercept-only) models showed meaningful variability between classes for SRL outcomes, with intraclass correlation coefficients (ICC) ranging from 0.068 (motivational autonomy; RAI) to 0.145 (cognitive regulation), indicating that between 6.8% and 14.5% of the variance in students’ self-regulated learning was due to classroom membership. These results demonstrate significant between-class differences and justify using multilevel modeling.

Perceptual congruence was operationalized as absolute difference scores between teachers’ self-reports and class-aggregated student perceptions for each FA dimension. Because both measures were assessed on five-point Likert scales, discrepancy scores could theoretically range from 0 (perfect alignment) to 4 (maximum divergence). In the present sample, observed discrepancy scores were substantially lower, with standard deviations ranging approximately from 0.65 to 0.75, indicating moderate variability across classrooms. Accordingly, lower discrepancy values indicate greater teacher–student alignment, whereas higher values reflect greater perceptual divergence. Because congruence was modeled using absolute difference scores, negative regression coefficients indicate that smaller discrepancies (i.e., greater alignment) are associated with higher SRL outcomes.

Multilevel models were estimated to examine the association between teacher–student perceptual congruence and students’ self-regulated learning outcomes.

To improve transparency and enable a comprehensive evaluation of the analyses, Table 2 displays the full set of multilevel regression models, including both significant and non-significant effects, along with standard errors, standardized coefficients (where applicable), and p-values.

Table 2. Multilevel regression models predicting self-regulated learning outcomes from teacher–student perceptual congruence in formative assessment practices (unstandardized coefficients).

Outcome	Predictor	b	SE	t	p
Cognitive	IndCongru_Clarification and Elicitation	−0.336	0.058	−5.80	<0.001
	IndCongru_Feedback	−0.294	0.057	−5.20	<0.001
	IndCongru_Shared Regulation	−0.166	0.062	−2.69	0.008
Metacognitive	IndCongru_Clarification and Elicitation	−0.422	0.053	−7.96	<0.001
	IndCongru_Feedback	−0.278	0.054	−5.17	<0.001
	IndCongru_Shared Regulation	−0.080	0.059	−1.35	0.178
Behavioral	IndCongru_Clarification and Elicitation	−0.501	0.048	−10.40	<0.001
	IndCongru_Feedback	−0.244	0.052	−4.69	<0.001
	IndCongru_Shared Regulation	−0.058	0.058	−1.01	0.311
Motivational (RAI)	IndCongru_Clarification and Elicitation	−2.01	0.283	−7.09	<0.001
	IndCongru_Feedback	−1.21	0.288	−4.21	<0.001
	IndCongru_Shared Regulation	−0.219	0.313	−0.70	0.484

Note 1. IndCongru_Clarification and Elicitation = teacher–student perceptual incongruence in clarification and elicitation; IndCongru_Feedback = teacher–student perceptual incongruence in feedback; IndCongru_Shared Regulation = teacher–student perceptual incongruence in shared regulation. b = unstandardized fixed-effect coefficient; SE = standard error. Note 2. Standardized coefficients (βstd) are reported in the text for interpretative purposes. Because motivational autonomy was operationalized using the Relative Autonomy Index (RAI), which has a wider scale range than the Likert-type formative assessment measures, unstandardized coefficients greater than 1 may occur and do not indicate estimation problems.

For cognitive self-regulation, congruence in Clarification and Elicitation significantly predicted outcomes (β = −0.34, SE = 0.06, t = −5.80, p < 0.001; β_std ≈ −0.32). Congruence in Feedback was also significant (β = −0.29, SE = 0.06, t = −5.20, p < 0.001; β_std ≈ −0.30). In this outcome only, congruence in Shared Regulation showed a small but statistically significant association (β = −0.17, SE = 0.06, t = −2.69, p = 0.008; β_std ≈ −0.16).

For metacognitive self-regulation, congruence in Clarification and Elicitation was a significant predictor (β = −0.42, SE = 0.05, t = −7.96, p < 0.001; β_std ≈ −0.43), as was congruence in Feedback (β = −0.28, SE = 0.05, t = −5.17, p < 0.001; β_std ≈ −0.30). Congruence in Shared Regulation was not statistically significant (β = −0.08, SE = 0.06, p = 0.178; β_std ≈ −0.08).

A similar pattern was observed for behavioral self-regulation. Congruence in Clarification and Elicitation showed a strong association (β = −0.50, SE = 0.05, t = −10.40, p < 0.001; β_std ≈ −0.53), representing the largest standardized effect across models. Congruence in Feedback was also significant (β = −0.24, SE = 0.05, t = −4.69, p < 0.001; β_std ≈ −0.27), whereas congruence in Shared Regulation was not significant (β = −0.06, SE = 0.06, p = 0.311; β_std ≈ −0.06).

For motivational autonomy (RAI), congruence in Clarification and Elicitation emerged as a significant predictor (β = −2.01, SE = 0.28, t = −7.09, p < 0.001; β_std ≈ −0.42). Congruence in Feedback was also significant (β = −1.21, SE = 0.29, t = −4.21, p < 0.001; β_std ≈ −0.25). In contrast, congruence in Shared Regulation did not significantly predict RAI (β = −0.22, SE = 0.31, p = 0.484; β_std ≈ −0.04).

In addition to the fixed effects reported in Table 2, the marginal and conditional R² values in Table 3 indicate the proportion of variance explained by the models. Marginal R² values, reflecting variance explained by the fixed effects alone, ranged from 0.002 to 0.272 across outcomes, indicating modest to moderate explanatory power, depending on the formative assessment dimension considered. The largest marginal R² values were observed for behavioral self-regulation predicted by Clarification and Elicitation (R²m = 0.272) and for metacognitive regulation predicted by Clarification and Elicitation (R²m = 0.178). Conditional R² values, which incorporate both fixed and random effects, ranged from 0.074 to 0.339, suggesting that between-class variability accounted for an additional proportion of variance across outcomes. Overall, these indices indicate that perceptual congruence in core formative assessment practices explains a meaningful, though not exhaustive, share of classroom-level differences in self-regulated learning.

Table 3. Marginal and conditional R² for multilevel models predicting self-regulated learning from teacher–student perceptual incongruence.

Outcome (DV)	Predictor	R2 Marginal	R2 Conditional
Cognitive	Clarification/Elicitation	0.100	0.267
Cognitive	Feedback	0.087	0.247
Cognitive	Shared Regulation	0.024	0.184
Metacognitive	Clarification/Elicitation	0.178	0.285
Metacognitive	Feedback	0.087	0.209
Metacognitive	Shared Regulation	0.060	0.111
Behavioral	Clarification/Elicitation	0.272	0.339
Behavioral	Feedback	0.074	0.167
Behavioral	Shared Regulation	0.004	0.111
Motivational (RAI)	Clarification/Elicitation	0.150	0.209
Motivational (RAI)	Feedback	0.061	0.153
Motivational (RAI)	Shared Regulation	0.002	0.074

Note: R² marginal represents variance explained by fixed effects. R² conditional represents variance explained by the full model including random intercepts (class level).

These findings suggest that although some effects operate primarily at the individual level, task–objective incongruence exhibits a more stable class-level pattern. Importantly, the multilevel mixed-effects models reported above already accounted for clustering by class, reinforcing the robustness of the main results.

The pattern of findings provides strong but dimension-specific support for H3b. Across outcomes, greater teacher–student alignment in Clarification and Elicitation showed the most consistent and strongest associations with cognitive, metacognitive, behavioral, and motivational regulation, followed by moderate and stable associations for Feedback. Congruence in Shared Regulation showed generally weak or nonsignificant associations, except for a small association with cognitive regulation.

5. Discussion

The present findings indicate that students’ perceptions of formative assessment (FA) practices in mathematics are positively associated with cognitive, metacognitive, behavioral, and motivational dimensions of self-regulated learning (SRL). At a global level, FA showed moderate correlations with all SRL components, suggesting that students who perceive their classroom as more formative also report engaging more frequently in regulatory processes.

Rather than merely replicating accounts that position formative assessment as inherently linked to self-regulated learning (Black & Wiliam, 2009; Nicol & MacFarlane-Dick, 2006; Panadero et al., 2018), these findings align with a growing body of work conceptualizing FA as a contextual mechanism that structures and sustains regulatory processes (Brandmo et al., 2020; van der Linden et al., 2023; Li & Gu, 2024). Within this perspective, formative assessment operates not as an isolated feedback event but as an integrated instructional ecology in which goals, evidence, and feedback are continuously aligned. When students experience mathematics classrooms as environments where expectations are transparent, evidence of understanding is actively elicited, and feedback informs subsequent action, regulatory processes are embedded within instructional interaction (Clark, 2012; Heritage & Wylie, 2023).

Clarification and elicitation practices showed moderate-to-strong associations with cognitive, metacognitive, and behavioral regulation. This pattern is theoretically coherent. In Zimmerman’s (2000) cyclical model, the forethought phase involves task analysis and strategic planning. When teachers make learning intentions and success criteria explicit, students gain access to the standards against which performance is evaluated (Andrade & Heritage, 2017). Clarity reduces ambiguity about quality and supports anticipatory alignment between task demands and strategy selection. In mathematics, where effective problem solving requires coordination between procedural execution and conceptual justification, transparent criteria may facilitate deliberate strategy choice and ongoing monitoring of reasoning processes. Empirical research examining students’ perceptions of assessment transparency further indicates that clarity of goals and criteria is associated with stronger engagement and regulatory behavior (Wolterinck-Broekhuis et al., 2024; Šimić Šašić & Atlaga, 2024).

Exposure to criteria also supports the development of evaluative judgment, defined as the capacity to appraise the quality of one’s own work (Panadero & Broadbent, 2018). Evaluative judgment inherently activates metacognitive processes, particularly comparisons between current performance and explicit standards. Evidence from studies on self- and co-regulated learning suggests that evaluative processes serve as a bridge between formative assessment practices and metacognitive activation (Panadero et al., 2019; van der Linden et al., 2023). Accordingly, the observed association between clarification practices and metacognitive SRL reflects theoretical alignment rather than incidental covariance. These findings do not imply causal direction but suggest that classrooms characterized by transparent goal communication are also those in which students report greater engagement in planning and monitoring processes.

Formative feedback was positively associated with all SRL dimensions, although effect sizes were smaller. Feedback has long been conceptualized as information that reduces the discrepancy between current and desired performance (Nicol & MacFarlane-Dick, 2006). However, its regulatory potential depends on learners’ capacity to interpret, internalize, and act on it. Research on feedback literacy emphasizes that feedback functions formatively only when it is meaningfully processed and translated into strategic adjustment (Carless & Winstone, 2023; He et al., 2023). The more moderate correlations observed may therefore reflect the conditional nature of feedback use. Although feedback may be present in classroom practice, its impact varies depending on whether students perceive it as dialogic, actionable, and relevant to improvement. In mathematics contexts, where feedback often targets procedural correctness, its influence on deeper metacognitive processes may be attenuated if it is experienced as corrective rather than developmental.

The strongest correlations emerged between shared regulation of learning and both metacognitive and cognitive self-regulation. This finding aligns with frameworks that distinguish individual, co-regulated, and socially shared regulation (Hadwin et al., 2017). Socially shared regulation involves joint planning, monitoring, and evaluation enacted through dialogue. In assessment contexts, regulatory processes may be externalized in classroom discourse before being internalized at the individual level (Allal, 2013; Andrade et al., 2021). Classroom-based research further indicates that co-regulated and socially shared practices are associated with increased engagement and strategic participation in secondary education settings (Veugen et al., 2024; Fernández-Ferrer et al., 2025). In shared regulation environments, monitoring and evaluation are made visible and collectively negotiated, which may normalize metacognitive engagement. At the same time, given that both constructs were assessed via self-report and involve conceptually overlapping activities, part of the magnitude of these correlations may reflect shared method variance. The results, therefore, suggest strong functional alignment rather than construct equivalence.

All FA dimensions were positively associated with motivational autonomy (RAI), though effect sizes were more moderate. Formative assessment may support adaptive motivation by shifting the evaluative focus from normative comparison to personal improvement (Panadero et al., 2018). When goals are transparent and feedback emphasizes progress, students may experience enhanced perceived competence and clearer expectations. Empirical evidence indicates that students who perceive assessment as constructive and improvement-oriented report higher levels of intrinsic motivation and engagement (Pat-El et al., 2024; van der Linden et al., 2023).

Nevertheless, motivational regulation is shaped by multiple interacting influences. Situated Expectancy-Value Theory posits that prior achievement contributes recursively to the development of competence beliefs and task values (Eccles & Wigfield, 2020; Marsh et al., 2012). Self-Determination Theory similarly conceptualizes autonomy as the outcome of progressive internalization processes supported by satisfaction of competence, autonomy, and relatedness needs (Ryan & Deci, 2000, 2017, 2020). Evidence further suggests that perceptions of feedback influence regulatory engagement, in part, through motivational mediators such as self-efficacy and goal orientation (He et al., 2023). The comparatively modest effect sizes observed are therefore theoretically coherent: formative assessment may facilitate motivational internalization, but it operates within a broader motivational ecology shaped by prior experiences, identity-related meanings, and classroom climate.

We also examined whether different dimensions of students’ perceived formative assessment practices predict variance in various self-regulated learning (SRL) dimensions (H2). Conceptualizing formative assessment as a system of interconnected practices suggests that its different elements may contribute in distinct ways to students’ regulatory processes rather than functioning as a single undifferentiated construct (Wiliam & Thompson, 2007). Therefore, the analyses considered the simultaneous contribution of three formative assessment dimensions, clarification and elicitation, feedback, and shared regulation, to multiple SRL outcomes.

The results showed different predictive patterns across SRL dimensions. In particular, practices involving clarifying learning goals and gathering evidence of student understanding emerged as the most consistent predictors across regulatory domains. This dimension significantly predicted cognitive, metacognitive, behavioral, and motivational aspects of SRL, suggesting that classrooms where expectations are made clear and evidence of understanding is regularly collected may offer stronger support for students’ learning processes. This pattern aligns with theories that see clarifying learning goals and collecting evidence as key parts of formative assessment (Wiliam & Thompson, 2007; Panadero et al., 2018). When students know what quality work looks like and are often asked to show their understanding through tasks and discussions, they can better monitor their progress, evaluate their strategies, and adjust their learning accordingly.

Clarification and elicitation practices were especially strongly linked to behavioral self-regulation, which accounted for the largest portion of variance among the SRL outcomes. Behavioral regulation reflects the active side of self-regulation, including effort, persistence, time management, and strategic follow-through. In math learning, where tasks often demand sustained reasoning and repeated problem-solving, these active regulatory processes are particularly important. Practices that clarify next steps, create opportunities for revision, and make progress visible may thus directly impact students’ behavioral engagement with math tasks.

This pattern is especially meaningful in mathematics education. Mathematical understanding develops through cumulative, conceptually structured processes that integrate procedural fluency, conceptual understanding, and strategic competence (Kilpatrick & Swafford, 2002). Empirical research also shows that successful mathematical problem solving depends on metacognitive monitoring and persistence when facing difficulties (Özcan, 2016; Wafubwa & Csíkos, 2022). In such contexts, formative practices that make learning goals explicit and regularly gather evidence of understanding can help students regulate effort, revise strategies, and stay engaged during cognitively demanding tasks.

In contrast, formative feedback demonstrated more limited predictive effects once the other formative dimensions were considered together. Although feedback has long been recognized as a key mechanism linking assessment and learning, its regulatory influence may depend on the extent to which it is integrated into broader cycles of clarification, evidence collection, and revision (Nicol & MacFarlane-Dick, 2006; Panadero et al., 2018). When combined with practices that clarify expectations and gather evidence of understanding, feedback alone might only cover part of the regulatory processes through which formative assessment supports learning.

Clarification and elicitation practices also predicted motivational autonomy, although the proportion of explained variance was smaller than that for cognitive, metacognitive, and behavioral regulation. Within Self-Determination Theory, autonomy refers to the extent to which regulatory processes have been internalized and integrated into the self (Ryan & Deci, 2020). Formative assessment practices that clarify expectations and emphasize improvement may support students’ perceptions of competence and reduce controlling evaluative pressures, thereby fostering autonomous regulation (Ryan & Deci, 2000, 2017, 2020; Jang et al., 2010). At the same time, motivational internalization typically develops gradually within sustained need-supportive environments rather than as an immediate result of individual instructional practices (Ryan & Deci, 2017, 2020). From a Situated Expectancy-Value perspective, prior achievement experiences and evolving beliefs about competence also significantly influence motivational pathways (Eccles & Wigfield, 2020; Marsh et al., 2012). Therefore, formative assessment may serve as one of several contextual factors affecting students’ motivational regulation.

These findings highlight that formative assessment practices do not contribute equally to students’ regulatory processes. Instead, practices related to clarifying learning goals and eliciting evidence of understanding seem to play a particularly central role in supporting multiple aspects of self-regulated learning. This varied pattern emphasizes the importance of viewing formative assessment not only as a unified instructional approach but also as a collection of practices that can influence different facets of students’ regulatory engagement with learning.

Interestingly, the pattern observed in the congruence analyses partially mirrors the student-level results reported for Hypothesis 2. In the regression models examining students’ perceptions of formative assessment practices, clarification and elicitation emerged as the most consistent predictors across several self-regulated learning dimensions. A similar pattern is observed in the congruence analyses, where alignment between teachers and students in this dimension shows the strongest and most stable associations with classroom-level self-regulated learning outcomes.

Hypothesis 3a was tested using both the global Formative Assessment (FA) score and its specific dimensions (Clarification and Elicitation, Feedback, and Shared Regulation), enabling both a synthetic and a differentiated analysis of teacher–student discrepancies. The results revealed a clear and consistent pattern: teachers reported significantly higher levels of formative assessment practices than students perceived, both at the global level and across all assessed dimensions. Effect sizes were large to very large, indicating that the discrepancy is not marginal but structural and systematic.

This pattern aligns with the literature on perceptual incongruence in formative assessment. Studies by Pat-El et al. (2013, 2015) show that teachers report higher levels of Assessment for Learning practices than students recognize, highlighting systematic discrepancies between pedagogical intention and student experience. These authors distinguish between implementation incongruence (a practice is reported by the teacher but not clearly perceived by students) and interpretative incongruence (both parties recognize the practice but attribute different meanings to it). While the present study does not allow us to determine which of these mechanisms may be operating, the observed discrepancies are compatible with the types of incongruence described in prior research.

The particularly large discrepancies observed in the dimensions of Clarification, Elicitation, and Feedback suggest that practices teachers consider central to formative assessment may not be experienced by students as regulatory tools. As argued by Panadero et al. (2018), mere exposure to criteria does not guarantee the development of evaluative judgment; students must appropriate those criteria as tools for monitoring and self-regulation. Similarly, the feedback literature emphasizes that its formative function depends on how learners interpret and use it (Nicol & MacFarlane-Dick, 2006; Carless & Winstone, 2023). Thus, the observed discrepancy may reflect differences in how the purpose and nature of feedback are perceived, particularly when feedback is experienced as corrective rather than developmental.

Although smaller in magnitude, the discrepancy in Shared Regulation remained statistically significant. Given that this dimension involves interactive, socially visible practices (Hadwin et al., 2017), it may be more readily recognized by students than less explicitly collaborative practices. Nevertheless, the results suggest that opportunities teachers interpret as co-regulatory may not always be experienced by students as genuine moments of joint monitoring and negotiation. Beyond mean differences, correlations between teachers’ perceptions and aggregated student perceptions were small to moderate, indicating partial but limited convergence. This pattern suggests that both informants capture related aspects of the formative classroom climate, but not in equivalent ways. The literature consistently shows that multiple informants provide complementary perspectives and that the absence of strong convergence does not invalidate either source but rather reflects the relational and interpretative nature of assessment practices (Pat-El et al., 2015).

The interpretation of these findings should be considered, considering the psychometric limitations of the teacher-reported scale. As described in the instruments section, the relatively small number of teacher participants constrained the stability of psychometric estimates and limited the robustness of factor-analytic procedures at the teacher level. Although the pattern of discrepancies is consistent and theoretically plausible, the magnitude of the differences should be interpreted with caution, acknowledging potential measurement-related constraints.

The results of H3a confirm the presence of large, systematic discrepancies between teachers’ self-reported formative assessment practices and students’ perceptions, both globally and across dimensions. Hypothesis 3b examined whether teacher–student perceptual congruence across specific formative assessment (FA) dimensions was associated with student-level SRL outcomes, estimated using multilevel models that accounted for classroom-level clustering. Congruence was operationalized as the absolute difference between teachers’ reports and class-level student perceptions for each FA dimension. Importantly, analyses were conducted at a dimensional level rather than using a global FA score. This decision was theoretically motivated, as prior research suggests that discrepancies between teachers’ and students’ perceptions may vary across specific formative practices (Pat-El et al., 2013, 2015), and aggregating across dimensions could obscure differentiated patterns of alignment.

Importantly, the current analyses were conducted using multilevel models with student-level SRL outcomes nested within classrooms. Therefore, the results should be viewed as cross-level associations between classroom-level perceptual congruence and students’ self-regulated learning, rather than as solely classroom-aggregated effects.

The results provided dimension-specific support for H3b. Across outcomes, greater teacher–student alignment in Clarification and Elicitation showed the most consistent and substantial associations, followed by moderate associations for Feedback. Congruence in Shared Regulation was generally weak or non-significant, except for a small association with cognitive regulation.

At the cognitive level, congruence in Clarification and Elicitation and in Feedback was significantly associated with higher class-level cognitive self-regulation, with a smaller but significant effect also emerging for Shared Regulation. Cognitive regulation refers to the strategic processing and organization of information; thus, alignment in how learning goals, criteria, and evidence-eliciting tasks are perceived may strengthen students’ understanding of what constitutes adequate mathematical reasoning and solution strategies. Formative assessment frameworks emphasize that learning intentions and criteria serve as regulatory anchors when students meaningfully understand and use them (Panadero et al., 2018). When teachers and students share similar interpretations of these practices, the transparency of expectations may facilitate strategic engagement with mathematical tasks. Importantly, however, given the correlational and multilevel nature of the analyses, these findings indicate association rather than directional influence.

A similar pattern emerged for metacognitive regulation, with congruence in Clarification and Elicitation, and in Feedback, showing stable, substantial associations, whereas Shared Regulation did not reach significance. Metacognitive regulation involves monitoring and evaluating one’s understanding and strategies. If teachers perceive that criteria and questioning practices are clearly articulated, but students do not recognize or interpret them similarly, the metacognitive potential of these practices may be attenuated. The present findings are consistent with the idea that a shared understanding of learning goals and success criteria may enhance the extent to which students engage in reflective monitoring processes at the classroom level. At the same time, caution is warranted: these data do not allow conclusions about whether perceptual alignment enhances metacognitive engagement or whether classrooms characterized by stronger metacognitive climates foster more aligned perceptions.

For behavioral self-regulation, congruence in Clarification and Elicitation again showed the strongest association, followed by Feedback, while Shared Regulation was non-significant. Behavioral regulation reflects effort management, persistence, and sustained engagement, processes particularly salient in mathematics learning. When teachers and students converge on their understanding of what is expected and how evidence of learning is elicited, students may be better positioned to translate goals and feedback into observable effort and persistence on tasks. Feedback, when perceived similarly by teachers and students, may function as actionable guidance that supports strategic adjustment. These findings align with prior work suggest that discrepancies in how feedback practices are perceived may weaken their formative function (Pat-El et al., 2015). Nonetheless, as with clarification practices, the present results remain associational.

Finally, for motivational autonomy (RAI), congruence in Clarification and Elicitation and in Feedback showed significant associations, whereas Shared Regulation did not. This pattern suggests that alignment in core formative practices, such as transparent expectations and improvement-oriented feedback, may coexist with stronger classroom-level motivational internalization. When students recognize assessment practices as coherent and aligned with teachers’ intentions, they may experience greater clarity and perceived competence, which are theoretically linked to autonomous motivation. However, the present design does not permit claims about motivational mechanisms, and these associations should not be interpreted causally.

In contrast, perceptual congruence in Shared Regulation was associated with SRL outcomes only to a limited extent. At first glance, this may appear inconsistent with H1, which predicted that students’ perceptions of shared regulation would be strongly correlated with individual SRL. However, the constructs and levels of analysis differ. H1 examined student-level associations between perceived shared regulation and individual SRL, whereas H3b examined whether teacher–student alignment in that perception predicted class-level outcomes. The weaker congruence effects observed here, therefore, do not contradict earlier findings; rather, they suggest that alignment between teacher and student perceptions of shared regulation may be less strongly related to aggregated regulatory outcomes than alignment in clarification and feedback practices.

One possible interpretation, consistent with frameworks that distinguish individual, co-regulated, and socially shared regulation (Hadwin et al., 2017), is that students may experience socially shared regulation in ways that do not necessarily depend on symmetrical perceptions between teachers and students. Shared regulation is inherently distributed and interactional; thus, students may experience collaborative regulation even when teachers conceptualize those practices differently. However, the present design does not allow conclusions regarding underlying mechanisms. The weaker associations may also reflect measurement characteristics, contextual variability in collaborative practices, or the inherently distributed nature of shared regulation processes. Further research using observational or longitudinal designs would be needed to clarify how perceptual alignment interacts with socially mediated regulation in mathematics classrooms.

Measurement constraints must also be acknowledged. As noted in the Instruments section, the teacher-reported formative assessment scale did not demonstrate optimal psychometric stability, largely due to the relatively small number of teacher participants. Difference scores are inherently sensitive to measurement error in both component variables, and instability in the teacher measure may attenuate the effects of congruence. Consequently, although the overall pattern of results is theoretically interpretable and statistically robust for certain dimensions, the magnitude of associations should be interpreted with caution.

Despite these limitations, the findings extend prior work on perceptual discrepancies in Assessment for Learning (Pat-El et al., 2013, 2015) by examining, through multilevel modeling, whether perceptual congruence is associated with classroom-level SRL in mathematics. While few studies have applied similar multilevel difference-score approaches in subject-specific contexts, the present results suggest that teacher–student alignment in core formative practices, particularly those related to goal clarification and feedback, may be meaningfully associated with collective regulatory functioning. At the same time, the differentiated pattern across dimensions underscores that not all formative practices rely equally on perceptual alignment to relate to self-regulated learning outcomes.

6. Conclusions

The present study examined how students’ and teachers’ perceptions of formative assessment relate to students’ self-regulated learning in lower secondary mathematics. This study shows that formative assessment plays an important role in supporting students’ self-regulated learning in lower secondary mathematics. Students who perceived a stronger formative assessment environment reported higher levels of cognitive, metacognitive, behavioral, and motivational regulation. More specifically, among the formative assessment dimensions, clarification and elicitation emerged as the most consistent predictor across all SRL domains.

Simultaneously, the findings showed consistent differences between teachers’ reported practices and students’ perceptions, emphasizing that the effectiveness of formative assessment relies on how students interpret and apply assessment information. Significantly, greater teacher–student perceptual alignment, especially in clarifying learning goals and gathering evidence of learning, was linked to improved behavioral regulation and increased motivational autonomy. These findings support viewing formative assessment as a relational and co-regulatory process with important implications for both instructional practice and assessment policy.

From a pedagogical perspective, the findings carry important implications for mathematics teaching. First, the particularly strong associations between formative assessment and behavioral regulation suggest that formative practices in mathematics may be especially effective when they structure visible cycles of revision, persistence, and strategic adjustment. Mathematics learning often requires sustained engagement with complex, multi-step tasks in which errors serve as opportunities for refinement rather than as final evaluations. Teachers may therefore enhance students’ self-regulated engagement by explicitly framing feedback and success criteria as tools for iterative improvement, making the revision process visible and expected rather than optional.

Second, the robust effects of teacher–student congruence in Clarification and Elicitation underscore the importance of a shared understanding of learning goals and success criteria. In mathematics classrooms, where conceptual coherence and procedural justification are central, clarifying what counts as a valid strategy, a complete explanation, or a mathematically sound argument may strengthen students’ capacity to plan, monitor, and evaluate their work. Importantly, the findings suggest that clarity must not only be provided but also perceived as meaningful by students. This underscores the need for dialogic negotiation of criteria, the use of exemplars, and opportunities for students to articulate their understanding of expectations.

Third, the weaker and less consistent effects observed for shared regulation congruence suggest that collaborative practices alone may not guarantee regulatory impact unless their purpose and function are made explicit. Teachers may benefit from making the regulatory intentions behind peer discussion and group problem-solving visible, helping students recognize these moments as opportunities for joint monitoring and strategy development rather than as routine classroom interaction.

The findings suggest that in mathematics education, formative assessment practices are most likely to foster self-regulated learning when they are coherent, transparent, and explicitly linked to students’ regulatory processes. Professional development initiatives may therefore prioritize not only implementing formative techniques but also strategies that enhance perceptual alignment between teachers and students regarding the purpose and function of assessment practices.

Despite its contributions, the present study has several limitations that should be considered when interpreting the findings and that point to directions for future research.

First, the study relied on self-reported measures of formative assessment and self-regulated learning. Although students’ perceptions are theoretically central to understanding the regulatory function of formative assessment (Pat-El et al., 2013), self-report data may be influenced by social desirability and shared method variance. Future studies would benefit from combining self-reports with classroom observations, analysis of instructional artifacts, or process-oriented measures of self-regulation (Panadero et al., 2018).

Second, the cross-sectional design limits causal inference. While the findings are consistent with theoretical models proposing that formative assessment supports the development of self-regulated learning (Clark, 2012; Meusen-Beekman et al., 2016), reciprocal relations are also plausible. Longitudinal and intervention studies are needed to examine how changes in formative assessment practices and perceptual alignment over time influence students’ self-regulation and motivation.

Third, interpreting teacher–student discrepancies and perceptual congruence requires caution. Although the student version of the formative assessment scale demonstrated a robust factor structure and strong reliability, the teacher version showed limited structural validity and was therefore treated as a descriptive observed measure. Consequently, the discrepancy and congruence indices represent associations between parallel perceptions rather than comparisons between psychometrically equivalent constructs. This limitation may have attenuated the magnitude of congruence effects and highlights the need for further refinement and validation of teacher-reported measures of formative assessment. Accordingly, findings related to H3a and H3b should be interpreted as indicative patterns of perceptual alignment and misalignment rather than precise estimates of latent agreement.

Fourth, because the study relied on self-reported measures, common method bias cannot be fully ruled out. Future studies could complement questionnaire data with classroom observations or performance-based measures.

Another limitation involves the relatively small number of classrooms included in the multilevel analyses (N = 39). Simulation studies show that cluster-level sample sizes of this size have limited statistical power to detect small effects at Level 2. Therefore, some non-significant results should be interpreted carefully, as the analyses may have been underpowered to identify small but potentially meaningful classroom-level relationships.

Finally, future studies could extend the present work by examining mediating and moderating mechanisms, such as whether the effects of formative assessment on motivational autonomy are mediated by cognitive or behavioral self-regulation, or whether perceptual congruence operates differently across subject domains, age groups, or instructional contexts. Such research would further refine the understanding of how formative assessment can be effectively leveraged to support the development of self-regulated learners (Pat-El et al., 2024).

These findings contribute to the growing body of research examining how formative assessment practices operate within subject-specific contexts, particularly in mathematics education. They highlight the importance of fostering shared understandings of assessment processes in classrooms, suggesting that the effectiveness of formative assessment depends not only on teachers’ instructional intentions but also on how students perceive and engage with these practices during learning.