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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.

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 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.

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.

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 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.

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. 

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.

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