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In the present study we investigate one 7th-grade mathematics teacher’s eight-month long implementation of a comprehensive multi-approach formative assessment practice. Based on an analysis of classroom observations, interviews and written teacher logbooks, this classroom practice is described in detail to illustrate how multi-approach formative assessments may be enacted in practice. Furthermore, based on the same data, we identify characteristics of formative assessment practices that have been argued to influence student motivational characteristics that affect motivation manifested as behavioural engagement and autonomous types of motivation. We also demonstrate that while the students in the two control classes (n = 9 in both classes) decreased their engagement in learning activities and became less autonomous in their motivation during this period, the students in the intervention class (n = 14) became more engaged and did not become less autonomous in their motivation.

It is well-known that a key to promoting students’ mathematics learning is to provide opportunities for problem solving and reasoning, but also that maintaining such opportunities in student–teacher interaction is challenging for teachers. In particular, teachers need support for identifying students’ specific difficulties, in order to select appropriate feedback that supports students’ mathematically founded reasoning without reducing students’ responsibility for solving the task. The aim of this study was to develop a diagnostic framework that is functional for identifying, characterising, and communicating about the difficulties students encounter when trying to solve a problem and needing help from the teacher to continue the construction of mathematically founded reasoning. We describe how we reached this aim by devising iterations of design experiments, including 285 examples of students’ difficulties from grades 1–12, related to 110 tasks, successively increasing the empirical grounding and theoretical refinement of the framework. The resulting framework includes diagnostic questions, definitions, and indicators for each diagnosis and structures the diagnostic process in two simpler steps with guidelines for difficult cases. The framework therefore has the potential to support teachers both in eliciting evidence about students’ reasoning during problem solving and in interpreting this evidence.

Understanding teachers’ conceptions of assessment is a key objective in supporting assessment practices that lead to improved learning outcomes. Thus, inventories capable of identifying teachers’ assessment conceptions are important. The Teachers Conceptions of Assessment (TCoA) inventory was an early and influential measure of teacher assessment conceptions, but replication studies have shown that the model may be affected by policy and practice context. In the present study, a Swedish adaptation of the TCoA was administered twice, 18 months apart. A sample of 249 teachers were matched across the 2 time-points and their self-reported scores were analysed with confirmatory factor analysis and invariance testing. With good correspondence to the data, six of the nine factors in the TCoA were completely replicated and one factor was partially replicated. The model had sufficient similarity between time points to permit mean score comparisons, which were largely equivalent between times. The study indicates that the Swedish Teacher Conceptions of Assessment adaptation can be used reliably in Swedish primary and lower secondary schools as measure of teacher conceptions of the uses of assessment.

Research has shown that students’ learning gains in mathematics are greater when they work with problems rather than routine tasks. These learning gains from problem-solving activities may be enhanced by providing feedback that does not give away the solutions to the problems, but helps students construct their solution methods themselves and anchor their reasoning in intrinsic properties of the mathematical components involved in the reasoning. However, in order to use feedback, students would need to perceive it as useful, and not all students may find such feedback useful. In this study, we investigate how students’ ability and motivational beliefs affect how useful they perceive feedback aimed at supporting mathematical reasoning to be. In the study, students worked with mathematical problems and received metacognitive and heuristic feedback when they needed help. We used structural equation modeling (SEM) to analyze the effects. The results show that students’ mastery goals had a direct effect on the perceived usefulness of the feedback, but no such effects were found for students’ national test grades, self-efficacy beliefs, performance goals, or intrinsic or extrinsic forms of motivation. The proportion of successful use of feedback did not mediate the effects.

Research has shown that formative assessment can have large positive effects on student achievement, but the effects vary substantially and are not always positive. In addition, the underlying mechanisms responsible for the learning effects are not well understood. We present a framework developed to support research efforts to identify these mechanisms. The framework includes formative assessment processes as well as students’ learning processes, defines and exemplifies the term mechanisms in relevant contexts, indicates possible mechanisms, and identifies aspects that require further research to characterise and explain the mechanisms through which formative assessment affects student achievement. Finally, we exemplify how the framework may be used to design studies capable of providing the robust evidence required for drawing conclusions about the mechanisms.

Introduction: Teacher conceptions of feedback ideally predict their feedback practices, but little robust evidence identifies which beliefs matter to practices. It is logical to presume that teacher conceptions of feedback would align with the policy framework of an educational jurisdiction. The Teacher Conceptions of Feedback (TCoF) inventory was developed in New Zealand which has a relatively low-stakes, formative policy framework. Methods: This study surveyed 451 Swedish teachers working in Years 1-9, a policy context that prioritises teachers using multiple data sources to help students learn. The study used a translated version of the TCoF inventory, but isolated six items related to formative feedback practices from various factors. Results: A six-factor TCoF was recovered (Praise, Improvement, Ignore, Required, PASA, and Timely), giving partial replication to the previous study. A well-fitting structural equation model showed formative practices were predicted by just two conceptions of feedback (i.e., feedback improves learning and students may ignore feedback). Discussion: This study demonstrates that the TCoF inventory can be used to identify plausible relations from feedback beliefs to formative feedback practices.

Research has shown that formative assessment can enhance student learning. However, it is conceptualised and implemented in different ways, and its effects on student achievement vary. A need has been identified for experimental studies to carefully describe both the characteristics of implemented formative assessment practices and their impact on student achievement. We examined the effects on student achievement of changes in formative assessment of a random sample of 14 secondary school mathematics teachers after a professional development programme. This study describes practices implemented and students’ achievement as measured by pre-tests and post-tests. We found no significant differences in achievement on the post-test, after controlling for pre-test scores, between the intervention group and control group, and no significant correlation between the number of formative assessment activities implemented and the post-test scores (controlled for the pre-test scores). We discuss characteristics of formative assessment implementations that may be critical for enhancing student achievement.

Behavioral engagement is a key determinant of students’ learning. Hence, knowledge about mechanisms affecting engagement is crucial for educators and stakeholders. Self-determination theory (SDT) offers a framework to understand one of these mechanisms. However, extant studies mostly consider only parts of SDT’s theoretical paths from basic psychological need satisfaction via regulations to student engagement. Studies that investigate the full model are rare, especially in mathematics, and results are inconclusive. Moreover, constructs are often merged in ways that may preclude detailed understanding. In this study, we used structural equation modeling to test several hypothesized paths between the individual variables that make up higher-order constructs of need satisfaction, regulations, and behavioral engagement. Satisfaction of the need for competence had a dominating effect on engagement, both directly and via identified regulation. Similarly, satisfaction of the need for relatedness predicted identified regulation, that in turn predicted engagement. Satisfaction of the need for autonomy predicted intrinsic regulation as expected but, in contrast to theory, was also positively associated with controlled motivation (external and introjected regulation). Neither intrinsic nor controlled regulation predicted engagement. Theoretical and method-related reasons for this unexpected pattern are discussed, as well as implications for research and teaching.

The study investigates one mathematics teacher’s implementation of formative assessment and its effects on students’ self-regulated learning (SRL). A questionnaire administered before and after the eight-month long intervention shows a significant effect, compared to two control classes, on students’ motivational beliefs involved in SRL. Qualitative data shows a notable enhancement of the students’ SRL behavior in the classroom. Analysis of the teacher’s implemented formative assessment shows a practice integrating several aspects of formative assessment, and provides empirical evidence of what formative assessment with large effects on students’ SRL may look like and how it fits with models of SRL development.