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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. 

Research reviews have shown that the use of formative assessment in classroom practice can substantially improve student achievement. However, a strong research base about how to support teachers’ implementation of such formative classroom practice is lacking. In this thesis, I investigate the effects of a comprehensive professional development programme (PDP) in formative assessment on teachers’ classroom practice and students’ achievement in mathematics. In addition, I identify reasons for the changes made in the teachers’ formative classroom practice. Fourteen randomly selected year - 7 mathematics teachers participated in the PDP. The teachers’ formative classroom practice before and after attending the programme was analysed and described, and reasons for their change in practice were explored. The effect of the changes in formative classroom practice on students’ mathematics achievement was examined using pre- and post-tests administered to both the intervention group and a control group. A mixed methods approach with classroom observations, teacher interviews, questionnaires and student achievement tests in mathematics was used in the studies included in the thesis.

The results show that the teachers used aspects of formative assessment in their classroom practice before the PDP, but that there was plenty of room for development towards a more effective formative assessment practice. Several possibilities for developing the practice were identified. After the PDP the teachers believed in the idea of formative assessment and were motivated to make changes towards a more formative classroom practice. The teachers included new formative assessment activities in their classroom practice, but in different ways and to different degrees. The characteristics of these changes were identified, and also the characteristics of the PDP that the teachers found to be influential for their development of the formative classroom practice. Results also show that the teachers’ motivational beliefs held after the PDP was an explanatory factor for their changes in practice. However, the formative assessment practice the teachers implemented did not have a significant effect on their students’ achievement compared to the control group. In addition, there was no correlation between the number of formative assessment activities implemented by the teachers and their students’ achievement gains. Reasons for these non-effects on student achievement, and for the teachers’ degree and type of implementation of formative assessment in the classroom practice, are discussed in the thesis.

This study is a sub study in a project about a comprehensive professional development program (PDP) for mathematics teachers in formative assessment (FA). My aim is to investigate in which ways the participating teachers’ classroom practice change, due to the delivered PDP, and also to identify reasons for the changes and the variation in changes. Fourteen randomly chosen mathematics teachers in secondary school participated in the PDP. The teachers were interviewed and their classroom practice observed before and after the PDP. They have also answered two questionnaires. Preliminary results show that all teachers were motivated to change and did change their practice, but to varying degrees. Factors that were important for the change to take place have been identified.

This is a substudy in a project about a comprehensiveprofessional development program (PDP) in formative assessment (FA) formathematics teachers. My aim is to investigate in which ways the teachers’classroom practice change, with respect to FA, after participating in the PDP andwhat some of the reasons may be for these changes. Fourteen randomly chosenmathematics teachers in secondary school participated in the PDP. The teachers wereinterviewed and their classroom practice observed before and after the PDP.They have also answered two questionnaires. The PDPand the analysis about the teachers’ change is based on Dylan Wiliam and his colleagues’framework of FA. Preliminary results showthat all teachers were motivated to change and did change their practice, butto varying degrees.

This study is part of a larger research project about a comprehensive professional development program (PDP) in formative assessment for mathematics teachers. The aim of the study is to investigate in which ways the teachers' classroom practice change, with respect to formative assessment, after participating in the PDP, and which some of the reasons may be for these changes. Fourteen randomly chosen grade-seven mathematics teachers participated in the PDP. The teachers were interviewed and their classroom practices observed, before and after the PDP. They also answered two questionnaires about the PDP. Preliminary results show that all teachers were motivated to change and did change their practice, but to varying degrees.

Formative assessment has been shown to have the power to positively affect student achievement, but support for teachers to substantially develop their formative classroom practices have been frequently unsuccessful. In this study, a random selection of year-7 teachers participated in a professional development programme (PDP) in formative assessment. The PDP was designed in accordance with many of the characteristics known to be important for teachers’ possibilities to develop their practice. Classroom observations, questionnaires and interviews are used to investigate the changes made in the teachers’ classroom practices after the PDP, and the conditions and barriers they perceived to have been important in their endeavours to developing a formative classroom practice. The results show how all teachers developed their practice, but to different degrees, and that a majority of the implemented activities focus on the teacher as the responsible agent for the formative assessment process. The teachers were satisfied with most of the conditions provided during the PDP, but experienced barriers for change from the teaching conditions at their schools after the PDP. A comparison is made with a parallel PDP for year-4 teachers that resulted in large teacher changes and significant effects on student achievement.

Research has identified characteristics of professional development programmes (PDPs) that are important for accomplishing change in teachers’ practice and student achievement. However, these characteristics do not predict and guarantee the outcomes of a specific PDP. In the present study the authors investigated whether the expectancy-value theory of achievement motivation can be used to explain teachers’ change of practice. Through teacher interviews and questionnaires the authors investigated why randomly selected year-7 teachers, after participating in a PDP on formative assessment, changed their practice in ways identified in an earlier study, and why these changes differed from those of year-4 teachers participating in a similar PDP. The results show that expectancy-value theory can be used to explain both the schoolyear-7 teachers’ changes in practice, and why the PDP for the year-7 teachers produced different outcomes in teacher practice than the parallel PDP, with the same general design features, did for the year-4 teachers.

Research has identified characteristics of professional development programmes (PDPs) which are successful inchanging teachers practice and improving student achievement. However, these characteristics do not predict and guarantee the outcomes of a specific PDP. Through teacher interviews and questionnaires, we investigated why randomly selected teachers in schoolyear-7, after participating in a PDP on formative assessment, changed their practice in ways identified in an earlier study and why these changes differed from those of teachers in schoolyear-4 participating in a similar PDP. The results show that the teachers’ motivational beliefs held after the PDP is an explanatory factor for their changes in practice. We discuss how differences in these beliefs may have developed by connecting characteristics of the teachers, the school, and the PDP to the mechanisms of change identified in a model of teacher growth.

Formative assessment has been shown to have the power to positively affect student achievement, but professional-development initiatives for teachers to substantially develop their formative assessment practices have been frequently unsuccessful. In this study, a random selection of Year-7 teachers participated in a professional-development programme (PDP) in formative assessment. Classroom observations, questionnaires, and interviews were used to investigate the changes made in the teachers’ classroom practices after the PDP, and the conditions and barriers they perceived to have been important in their endeavours to develop a formative classroom practice. The results show how all teachers developed their practice, but to different degrees, and that a majority of the implemented activities focused on the teacher as the responsible agent for the formative assessment process. The teachers were satisfied with most of the conditions provided during the PDP, but experienced barriers for change from the teaching conditions at their schools after the PDP.

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.

Research has shown that formative assessment can enhance student learning. However, there is a great variety in how formative assessment is conceptualized and implemented, and in the size of the effects found on student achievement. A need has been identified for experimental studies both carefully describing the characteristics of the implemented formative assessment practice and its impact on student achievement. This study examines the effects on student achievement of the changes in a random sample of 14 secondary school mathematics teachers’ formative classroom practice that followed a professional development input. The practices were described, and student achievement were measured with pre-tests and post-tests. Results show that there were no significant differences in learning gains between the classes in the intervention group and the control group. The results also show no significant correlation between the number of formative assessment activities implemented by the teachers and the change in students’ achievement

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.

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.