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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. 

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.

This study investigates the impact of a national reform in Sweden introducing mathematical competency goals. Data were gathered through interviews, classroom observations, and online surveys with nearly 200 teachers. Contrasting to most studies of this size, qualitative analyses were conducted. The results show that teachers are positive to the message, but the combination of using national curriculum documents and national tests to convey the reform message has not been sufficient for teachers to identify the meaning of the message. Thus, the teachers have not acquired the functional knowledge of the competence message required to modify their teaching in alignment with the reform. The results indicate that for complex reform messages, such as the competency message, to have intended impact on classroom practice, special attention needs to be put on the clarity of the message. To have high-stakes tests, for example, does not alone seem to be sufficient. 

Internationally, education reform has been directed towards describing educational goals that go beyond topic and content descriptions. The idea of mathematical competencies describes such goals. National tests have been seen as one way of communicating these goals and influence teaching. The present study analyses Swedish national tests in mathematics, and seeks evidence about the extent to which they represent these competencies and may play a role in reforming teaching. The results show that the national tests assess all competencies. However, the study also shows a limited focus on the competencies’ interpretation and evaluation aspects. Thus, the tests do not fully capture the complex nature of the competencies. This may cloud the reform message and restrict the possibilities for the tests to function as levers for reform.

The relation between types of tasks and the mathematical reasoning used by students trying to solve tasks in a national test situation is analyzed. The results show that when confronted with test tasks that share important properties with tasks in the textbook the students solved them by trying to recall facts or algorithms. Such test tasks did not require conceptual understanding. In contrast, test tasks that do not share important properties with the textbook mostly elicited creative mathematically founded reasoning. In addition, most successful solutions to such tasks were based on this type of reasoning.

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

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.

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.

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.

 Performance assessment and authentic assessment are recurrent terms in the literature on education and educational research. They have both been given a number of different meanings and unclear definitions and are in some publications not defined at all. Such uncertainty of meaning causes difficulties in interpretation and communication and can cause clouded or misleading research conclusions. This paper reviews the meanings attached to these concepts in the literature and describes the similarities and wide range of differences between the meanings of each concept.

In this paper the issue of the authenticity of applied mathematical school tasks is discussed. The paper includes a description of a framework for reflection, analysis and development of authentic tasks. Its possible uses are exemplified by two studies. One of the studies is an analysis of in what way and to what extent the applied tasks included in the national assessments in Finland and Sweden are, or are not, authentic. In the second example the framework is used in a study of the impact of authenticity on the students' sense making in word problem solving.

Mathematical communication, oral and written, is generally regarded as an important aspect of mathematics and mathematics education. This implies that oral mathematical communication also should play a part in various kinds of assessments. But oral assessments of subject matter knowledge or communication abilities, in education and elsewhere, often display reliability problems, which render difficulties with their use. In mathematics education, research about the reliability of oral assessments is comparably uncommon and this lack of research is particularly striking when it comes to the assessment of mathematical communication abilities. This study analyses the interrater reliability of the assessment of oral mathematical communication in a Swedish national test for upper secondary level. The results show that the assessment does suffer from interrater reliability problems. In addition, the difficulties to assess this construct reliably do not seem to mainly come from the communication aspect in itself, but from insufficiencies in the model employed to assess the construct.

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.

We investigate the mathematical reasoning required to solve the tasks in the Swedish national tests and a random selection of Swedish teacher-made tests. The results show that only a small proportion of the tasks in the teacher-made tests require the students to produce new reasoning and to consider the intrinsic mathematical properties involved in the tasks. In contrast, the national tests include a large proportion of tasks for which memorization of facts and procedures are not sufficient. The conditions and constraints under which the test development takes place indicate some of the reasons for this discrepancy and difference in alignment with the reform documents.

This study focuses on gender differences in the extent to which students take real-world considerations into account when working with word problems in mathematics. Previous studies have found that students have a tendency to neglect an appropriate use of real-world knowledge in their word-problem solving, which leads to solutions that are inconsistent with the ‘real' situations described in the tasks. Research has also shown that the authenticity of the word problems can influence students' activation of their knowledge of the ‘real' situations described in the tasks, as well as their use of this real-world knowledge in order to provide ‘realistic' solutions. The study reported here investigates whether there are gender differences in the students' activation and use of real-world knowledge when working with word problems in mathematics. In addition, it investigates whether task authenticity influences boys and girls differently with respect to these real-world considerations. The results show that even though some of the tasks used in the study affected boys and girls differently, across all tasks and students no evidence of gender differences with respect to real-world considerations were found.

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.