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The potential of using formative assessment is well demonstrated, but studies about the use of formative assessment from a special education perspective are lacking. This study adds to this gap by investigating the view of formative assessment in a group of 39 special education teachers in mathematics (SETMs) who had learned about formative assessment within the SETM-program 2–6 years earlier. Five respondent interviews were used to design a questionnaire answered by the rest of the group. The SETMs had perceived formative assessment beneficial and useful in all their common sub-responsibilities and reported experiences of benefits as well as challenges. The article discusses the importance of reaching an inclusive formative assessment practice in mathematics education.

This theoretical paper is based on an empirical study where the framework of formative assessment by Wiliam and Thompson was used to analyze teachers' use of formative assessment in their mathematics classroom practice. The paper argues for treating a component named Adjusted Teacher Instruction (ATI) as a key strategy in complement to the five key strategies in the original framework. ATI is a significant component in formative assessment, but also particularly challenging for teachers to implement in their classroom practice. Treating ATI as a key strategy could facilitate the analysis of teachers' use of formative assessment activities and enhance the understandings about what kind of ATIs are most useful for whom under what conditions. Extended understandings about effective formative assessment activities are important in decisions about what formative assessment to include in teacher education and in-service training for teachers.

Visst använder lärare formativ bedömning i sin matematikundervisning, men … Resultaten från det forskningsprojekt som beskrivs i denna artikel visar att elevernas lärande påverkas när lärare låter bedömningar ligga till grund för förändringar av undervisningen. Hur påverkas elevernas lärande då? Jo, de lär sig – mer och bättre.

The potential of formative assessment, evident in several research reviews, has raised the interest in many countries to invest in reform initiatives to develop its use. However, implementation of formative assessment is not straightforward and there is a lack of knowledge about how to design appropriate professional development. The intervention study presented in this thesis aimed to see if a random selection of teachers, participating in a professional development program with many contact hours and substantial support of an expert, implemented formative assessment in a way that increased their students’ learning in mathematics. It also aimed to examine the reasons for the teachers’ changes in their classroom practice.

The twenty-two year 4 teachers attended a professional development program in formative assessment in mathematics. A mixed methods approach used classroom observations, teacher interviews, questionnaire surveys and student mathematics tests to investigate the effects on teacher classroom practice and student achievement.

It was found that the teachers trained in formative assessment built on their previous formative classroom practice and added new formative assessment activities into their mathematics classroom practice to a level that had significant impact on student achievement in mathematics (p = .036, d = .66). The teachers developed their formative assessment practice in three dimensions: key processes in teaching and learning, agents in the classroom, and the length of the formative assessment cycle.

The reasons for teachers ́ implementation of new formative assessment activities were well explained by the expectancy-value theory of achievement motivation. Important aspects of the professional development program were: (1) A formative and process-oriented character; (2) Activities directly useable in classrooms; (3) Experience of using formative assessment activities; (4) Connection between theory and practice; (5) Time; and (6) Knowledgeable support.

The thesis shows that it was possible to provide sufficient support to a random selection of teachers for them to develop their formative assessment practice in a way that improved student achievement. However, this thesis also indicates that it can be expected that teachers would need substantial time and support to achieve such developments in their classroom practice.

The potential of using Assessment for Learning (AfL) is well established, but studies of AfL practice in groups of students with intellectual disabilities (ID) are rare. The respondents in this study were assistants and teachers working in compulsory school for students with ID. In a two-year project they had worked with translating five AfL key strategies (KSs) to fit their context. The study aimed at exploring this translation to depict the use of AfL KSs in the classes of students with ID and reveal opportunities and challenges. The AfL KSs were used to structure interviews and classroom observations, and an ensuing thematic data analysis. The overall conclusion confirms the potential of using AfL in this context. Three themes depict the overall use of AfL: a whole-class focus, a team approach, and the integrated use of the AfL KSs. Various themes characterise the implementation of each KS, and the opportunities and challenges. The findings implicate benefits for the students, and advantages as well as concerns for the staff. The findings are expected to be of value inside and outside the study’s context. The study demonstrates how contextual variation can contribute to new insights and questions for the AfL research field.

Using formative assessment has woken interest in many countries because of the potential effect on student achievement. To investigate Swedish teachers' use of formative assessment in mathematics, this study used classroom observations and teacher interviews of 38 mathematics teachers. The teachers used formative assessment, but additional formative activities could support teachers to better take advantage of the potential in using formative assessment

Research shows that substantial learning gains are possible through the use of formative assessment. However, little is known about Swedish mathematics teachers’ use of formative assessment, and thus about the possible value of professional development programmes. This study uses teacher interviews and classroom observations to examine the classroom practice of 38 randomly selected primary and secondary school teachers in a mid-sized Swedish municipality. A framework of formative assessment comprising one big idea and five Key strategies structured the analysis. The study identifies characteristics of current formative assessment practices. The results show that the teachers do use a variety of formative assessment activities, but also that there is much room for development towards a more effective formative classroom practice. 

In this case study, we follow the career of one student teacher (Ellen) from her pre-service training to her first year as a mathematics teacher. As part of a research project about what it means to become a mathematics teacher, the aim of the study was to gain insight into the development of formative assessment competence. To accomplish this, we used data from video-recorded lessons and audio-recorded conversations to depict changes in classroom practice and reflections on that practice during the study. Our findings show that Ellen made incremental changes in her classroom practice and that these had an impact on classroom interaction, formative assessment processes, and student involvement in those processes. Corresponding changes were identified in Ellen's reflections, which also indicated that she increased her insight into formative assessment. We discuss our findings in relation both to what it means to become a mathematics teacher and to the development of formative assessment competence.

Students with intellectual disabilities (ID) risk leaving school without having the opportunity to develop their independence to become less reliant on others. This study aims to gain insights into how formative assessment as a teaching design can support self-regulated learning (SRL) among students with ID. Two experienced Swedish special school teachers, using formative assessment to support students’ SRL competence, participated in this study. Data consisted of the teachers’ written teaching descriptions, classroom observations, and teacher interviews. The analysis showed that the teachers managed to implement a formative classroom practice aiming to support the students to develop subject-matter knowledge as well as SRL skills. Three themes of challenges were identified: Low expectations and caretaking, Experiences of shortcomings, and Learning difficulties. Overcoming such challenges is discussed. The study shows promising examples of the use of theories and principles of formative assessment to promote SRL competence among students with ID and also incentives for doing so.

This paper focuses a mathematics teacher’s implementation of formative assessment (FA) when helping students solve mathematics tasks. Such FA practice has great potential, but is non-trivial, and teachers will need substantial support for developing their beliefs and practices. We have studied why an engaged and experienced mathematics teacher who had participated in a comprehensive professional development program made certain changes but not others and how additional support helped her overcome obstacles she experienced. The study exemplifies the significance of first-hand information from teachers' classroom practices together with adapted feedback when providing professional development support for their FA development.

An earlier study showed that the changes in teachers’ classroom practice, after participation in a professional development program in formative assessment, significantly improved student achievement in mathematics. The teachers in that study were a random selection of Year 4 teachers in a Swedish mid-sized municipality. In the present study, we analyse and describe the characteristics of these changes in classroom practice, which were based on a combination of various strategies for formative assessment. Data were collected through teacher interviews and classroom observations. The teachers implemented many new activities that strengthened a formative classroom practice based on identifying student learning needs and modifying the teaching and learning accordingly. The characteristics of the changes the teachers made reveal the complexity of this formative assessment practice and why such developments of practice are likely to require major changes in most teachers’ practices. We also discuss how such changes in practice afford new learning opportunities.

Formative assessment has been shown to have the potential to significantly enhance student achievement, but a strong research base about how to support teachers to implement such a practice is lacking. This is particularly so for a conceptualisation of formative assessment as a unity of integrated formative assessment strategies. The aim of this study is to investigate why the mathematics teachers who participated in a successful professional development programme in formative assessment developed their formative classroom practice to such an extent that it had a significant impact on student achievement. An analysis of data from teacher questionnaires and interviews shows that the teachers' actions can be explained by expectancy-value theory of achievement motivation. Characteristics of the professional development programme that the teachers experienced as important for their development of a formative classroom practice are identified, and the characteristics' affordances for the development of the teachers' expectancy and value beliefs are discussed.

A random sample of 22 Year 4 teachers in mathematics from a middle-sized Swedish municipality participated in a teacher professional development programme in formative assessment. The content ofthe programme was formative assessment conceptualised as a unity of different, integrated strategies.The study examines the effects on student achievement of the changes in the teachers’ formative classroom practice that followed the professional development input. Results show that, after controlling for pretest scores, the classes in the intervention group significantly out performed the classes in thecontrol group in a posttest administered one school year after the end of the programme (p = 0.036, d = 0.66). The study contributes to the understanding of under-studied areas of the impact of professional development in formative assessment, and the impact of teacher practice based on formative assessment conceptualised as a unity of different formative assessment strategies.

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.

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.

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.

Motivation is a prerequisite for students’ learning, and formative assessment has been suggested as a possible way of supporting students’ motivation. However, there is a lack of empirical evidence corroborating the hypothesis of large effects from formative assessment interventions on students’ autonomous forms of motivation and motivation in terms of behavioral engagement in learning activities. In addition, formative assessment practices that do have an impact on students’ motivation may put additional requirements on teachers than more traditional teaching practices. Such requirements include decisions teachers need to make in classroom practice. The requirements on teachers’ decision-making in formative assessment practices that have a positive impact on students’ autonomous forms of motivation and behavioral engagement have not been investigated. This study describes one teacher’s formative assessment practice during a sociology course in upper secondary school, and it identifies the requirements for the teacher’s decision-making. The teacher had participated in a professional development program about formative assessment just prior to this study. This study also investigated changes in the students’ motivation when the teacher implemented the formative assessment practice. The teacher’s practice was examined through observations, weekly teacher logs, the teacher’s teaching descriptions, and an interview with the teacher. Data on changes in the students’ type of motivation and engagement were collected in the teacher’s class and in five comparison classes through a questionnaire administered in the beginning and the end of the course. The students responded to the questionnaire items by choosing the extent to which they agreed with the statements on a scale from 1–7. The teacher’s formative assessment practice focused on collecting information about the students’ knowledge and skills and then using this information to make decisions about subsequent instruction. Several types of decisions, and the knowledge and skills required to make them that exceed those required in more traditional teaching practices, were identified. The students’ in the intervention teacher’s class increased their controlled and autonomous forms of motivation as well as their engagement in learning activities more than the students in the comparison classes.

This paper outlines the research program for the formative assessment group at Umeå Mathematics Education Research Centre. The program was presented in a symposium at the conference, and focuses on the study of the development and impact of formative assessment. The main purpose of the research carried out by the research group is to provide research results that will be used outside the research community for educational decisions on systemic level, or as support for improved teaching and learning at classroom level. The paper outlines the fundamental ideas of the program, current studies, and examples of completed studies.

Research reviews show that formative assessment has great potential for raising student achievement in general, but there is a need for reviews of formative assessment in individual subjects. This review examines its impact on student achievement in mathematics through an assessment of scientific journal articles published between 2005 and 2014 and indexed in Web of science. Through the use of search terms such as ”formative assessment”, ”assessment for learning” and ”self-regulated learning”, different approaches to formative assessment were included in the review. While varying in approach, they all share the defining characteristic of formative assessment: agents in the classroom collect evidence of student learning and, based on this information, adjust their teaching and/or learning. The results show positive relations between student achievement in mathematics and the ways of doing formative assessment included in the review.

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.

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.

The current project focuses on mathematics education, and is partitioned into three subprojects mapping research on formative assessment, classroom teaching, and curriculum programs in mathematics. The rationale for focusing on these three areas is that they are all highly relevant for understanding and improving Swedish mathematics education and students’ knowing of mathematics. Therefore, the aim of the project is to map research on formative assessment, classroom teaching, and curriculum programs in mathematics education.

The methodology of the literature review has been inspired by Gough, Oliver, and Thomas (2013), and we have focused on the mapping on journal articles published on Web of Science (WoS).

The results from the sample of articles on formative assessment show that strategies of formative assessment in mathematics are positively correlated to students’ performance in mathematics with medium and large effect sizes. However, based on the current mapping it is difficult to specify aspects of how the formative strategies are to be implemented in order to promote students’ knowing of mathematics.

Despite the change in perspective of what constitutes knowledge in mathematics to also include reasoning, problem-solving and communication, the map shows that research is mainly focused on examining teaching methods and their effects on students’ skills in mathematics. A closer examination of the studies that do focus on teaching for supporting students in developing competencies like reasoning and problem-solving shows that connections between and comparison of students’ solutions, as well as teachers’ ways of asking questions to support students in explaining their solutions clearly and in detail, are important for students’ learning of these competencies.

A central finding stemming from this review of curriculum programs is the complexity involved in how the programs can support teachers in establishing classroom practices. Curriculum resources and teacher resources, as well as other influencing factors, impact the quality of instruction, and studies have begun to point out how curriculum resources and teacher resources uniquely and jointly impact classroom practices. Multiple research articles have expressed the need for teacher support in implementing curriculum programs, by means of professional development, teacher education and support provided by the curriculum programs themselves. Interesting in this regard is the state of the research field concerning the design of educative curriculum programs, and how teachers make use of such support. Studies have proposed design approaches, regarding both the actual development of educative curriculum programs as well as how to use them in teacher education to support prospective teachers’ development of knowledge. Further, although research has revealed that it is important to prepare for teaching in certain ways, we found very little research that explicitly analyzed how teachers actually prepare for teaching a mathematics lesson.

Limitations of the project include: (1) the lack of searching in potentially relevant databases, (2) the fact that a relatively small proportion of articles found in the search have been coded, (3) that we have not engaged in deep considerations as to whether and in what ways results from international research are relevant in the Swedish context, and (4) that we therefore have not been able to synthesize the results of the study. In relation to the Swedish context (Hemmi & Ryve, 2014; Boesen et al., 2014), international research (Hattie, 2009; Smith & Stein, 2011), and the current project’s findings, we recommend that Skolforskningsinstitutet focus on two aspects of great importance for developing students’ knowing of mathematics. First, Skolforskningsinstitutet should synthesize research that supports actors, such as teachers and principals, in acting within school practices. In the case of teachers, support is needed to engage them in actively anticipating students’ thinking, using curriculum programs effectively, introducing mathematical content, acting in group work, formatively assessing students’ learning, and orchestrating whole-class mathematical discussions. Secondly, actors within school practices need support not only in initiating and implementing developments but also in institutionalizing such developments. Skolforskningsinstitutet should specify the kind of support needed in order to ensure that material, routines, competences, and organizations become integral and permanent features of Swedish school practice. 

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.