Implementation and outcomes of inquiry-based learning in mathematics content courses for pre-service teachers

This mixed-methods study describes classroom characteristics and student outcomes from university mathematics courses that are based in mathematics departments, targeted to future pre-tertiary teachers, and taught with inquiry-based learning (IBL) approaches. The study focused on three two-term sequences taught at two research universities, separately targeting elementary and secondary pre-service teachers. Classroom observation established that the courses were taught with student-centred methods that were comparable to those used in IBL courses for students in mathematics-intensive fields at the same institutions. To measure pre-service teachers' gains in mathematical knowledge for teaching, we administered the Learning Mathematics for Teaching (LMT) instrument developed by Hill, Ball and Schilling for in-service teacher professional development. Results from the LMT show that pre-service teachers made significant score gains from beginning to end of their course, while data from interviews and from surveys of learning gains show that pre-service teachers viewed their gains as relevant to their future teaching work. Measured changes on pre-/post-surveys of attitudes and beliefs were generally supportive of learning mathematics but modest in magnitude. The study is distinctive in applying the LMT to document pre-service teachers' growth in mathematical knowledge for teaching. The study also suggests IBL is an approach well suited to mathematics departments seeking to strengthen their pre-service teacher preparation offerings in ways consistent with research-based recommendations.     

Inquiry-based learning in mathematics and science: a comparative baseline study of teachers’ beliefs and practices across 12 European countries

In the European educational context, reports by expert groups have identified the necessity of a renewed pedagogy in schools to overcome deficits in science and mathematics teaching and to raise the standards of scientific and mathematical literacy. Inquiry-based learning (IBL) is considered the method of choice. However, it remains open to what extent IBL is actually used in day-to-day teaching. In the study presented here we elaborate—from the perspective of teachers—the current status of IBL in day-to-day teaching. Further, we explore what problems teachers anticipate when implementing IBL. In order to gain insight into the wide spectrum of practices in mathematics and science teaching in relation to IBL, a baseline study using teacher questionnaires was carried out in the 12 participating countries. We present selected results from this study that for the first time provides an overview of teachers’ beliefs and their reports on the current use of IBL practices in a European context. The results facilitate a cross-cultural comparison on the potentials and challenges of implementing IBL from the perspective of practicing teachers. Furthermore, the study reveals considerable differences between the teaching of mathematics and science subjects. The findings of the baseline study can serve as a reference line against which the impact of interventions to improve the quality of teaching and learning can be evaluated.     

Implementation of inquiry-based learning in day-to-day teaching: a synthesis

This synthesis is designed to provide insight into the most important issues involved in a large-scale implementation of inquiry-based learning (IBL). We will first turn to IBL itself by reflecting on (1) the definition of IBL and (2) examining the current state of the art of its implementation. Afterwards, we will move on to the implementation of IBL and look at its dissemination through resources, professional development, and the involvement of the context. Based on these theoretical reflections, we will develop a conceptual framework for the analysis of dissemination activities before briefly analyzing four exemplary projects. The aim of our analysis is to reflect on the various implementation strategies and raise awareness of the different ways of using and combining them. This synthesis will end with considerations about the framework and conclusions regarding needed future actions.     

Re-sourcing teachers’ work and interactions: a collective perspective on resources, their use and transformation

This paper reviews the literature on the theme of mathematics teachers’ work and interactions with resources, taking a particular perspective, the so-called ‘collective perspective’ on resources, their use and transformation. The review is presented under three headings: (1) theoretical frameworks commonly used in this area of research; (2) teachers’ interactions with resources in terms of their design and use; and (3) teachers’ interactions with resources in terms of teacher learning and professional development. From the literature, and the collection of papers in this issue, we argue that the collective dimensions play an important role in mathematics teachers’ work with resources and in their professional learning/development. Further empirical investigations are likely to be needed on: how teachers may work in collectives and with resources, and in which ways ‘productive’ collectives may form and work together; which roles particular resources can play in these delicate constellations and how particular resources may support teachers in their work and learning; and which kinds of resources offer opportunities for community building.     

Sociocultural perspectives in research on and with mathematics teachers: a zone theory approach

Sociocultural theories view teacher learning as changing participation in social practices that develop their professional identities rather than as acquisition of new knowledge or beliefs that are internal to the individual. Although sociocultural research on mathematics teacher education has tended to focus on understanding teachers’ learning, this article argues that sociocultural perspectives can also guide more interventionist research involving changing classroom practice. The approach illustrated here uses an adaptation of Valsiner’s zone theory to analyse teacher learning and development in two separate research studies. In one study the aim was to understand how teachers incorporated digital technologies into their practice, while the other study helped teachers implement an investigative approach to working mathematically consistent with a new syllabus. In both studies, productive tensions between teachers’ beliefs, contexts, and goals were a trigger for learning and development.     

A US perspective on the implementation of inquiry-based learning in mathematics

This paper discusses issues related to the potential adoption of inquiry-based learning (IBL) projects in mathematics in the United States. To explain the challenges faced in making a place for IBL in the mathematics curriculum, we describe the historical demands of working with a diverse, highly distributed educational system (that is, a system that does not have a central educational decision-making agency with the authority to mandate nation-wide changes), the impact of high-stakes tests to either open or limit the potential for curricular changes, and the changing context in the United States owing to the emergence of the Common Core State Standards in Mathematics (CCSS-M) and nationwide high-stakes assessments designed to be consistent with the CCSS-M. We identify a number of dimensions along which there would be challenges for the implementation of IBL in US school mathematics, including: perceived societal needs; schooling traditions; the specific framing of CCSS-M goals pertaining to problem solving, communicating and reasoning, and modeling and data analysis; and the readiness of the US teaching force to implement IBL. We then consider the issue of scaling up interventions such as IBL, and the politics involved therein.     

Mathematics teacher educators’/researchers’ collaboration with teachers as a context for professional learning

This paper describes our joint activity as mathematics teacher educators and academic researchers in collaborating with both experienced and novice teachers in two contexts: an emergent community of inquiry into mathematics teaching and its development; and a research methods course, offered as part of a mathematics education Master’s program, aspiring to initiate participating teachers into research practice through inquiry. Adopting an Activity Theory (AT) perspective, we analyse our activity, identifying its nature and transformations that frame our professional learning. The results indicate that our professional learning is the outcome of a continuous process of becoming aware of our own activity and its transformation in relation to that of the teachers.     

Inquiry-based learning for students, teachers, researchers, and representatives of educational administration and policy: reflections on a nation-wide initiative fostering educational innovations

International comparative studies such as TIMSS and PISA have had a considerable influence on the national educational policy in many countries. In Austria, as a reaction to the disappointing TIMSS 1995 results at the upper secondary level, a national initiative with the aim to foster mathematics and science education was launched in 1998: the IMST project. Due to specific challenges of the Austrian educational system, it has undergone several adaptations, but is still running. One of the project’s basic interventions is to promote teachers’ investigation into their own work. It is assumed that this supports the teachers’ critical stance towards innovation and inquiry, which in turn is an important basis for disseminating inquiry-based learning. A general look at the whole project and a specific look into one research project of IMST are used as opportunities to reflect on the complex interconnection and natural tension between the goal of promoting students’ IBL and its sustainable dissemination on a large scale. The paper introduces the project’s theoretical framework and genesis, provides exemplary research results, and reflects on its impact. The paper finishes with five “lessons learnt” from IMST.     

Response to key issues raised in the Post-14 mathematics inquiry

This article is a detailed response to the issues raised by the Post-14 Mathematics Inquiry in the UK. It aims to debate some of the central issues in mathematics teaching in the UK, including recruitment and retention of mathematics teachers, the curriculum content, national assessment, teaching resources (including ICT) and national strategies and policy (including inspection). Throughout, we have tried to base our recommendations on evidence and experience from the many teachers and tutors we work with as well as on our own experience. We have not hesitated to make what could be seen as controversial recommendations, but we believe a fundamental rethink of education policy and practice is needed if mathematics teaching and learning is to improve. We have also considered the impact that a proposed ‘National Centre for Excellence in Mathematics Education’ might have on the situation, although we doubt that it can have a marked long-term impact in the current UK situation.     

Pre‐Service Teachers and Mathematics: The Impact of Service‐Learning on Teacher Preparation

In spite of repeated reform efforts, there is research and data that suggest that teachers lack the needed knowledge to successfully teach elementary mathematics. Some argue that teachers lack the needed content knowledge while other argue that a lack of confidence and practice are impacting teachers’ ability to successful teach mathematics. As a result of these issues, this paper looks at the impact of a service‐learning experience on pre‐service teachers’ confidence and preparation in the area of mathematics. The service‐learning experience had a number of intended and unintended outcomes. As a result of the service‐learning experience, pre‐service teachers noted increased understanding, innovation and confidence in the area of mathematics.     

Developing a reform mathematics curriculum program in Sweden: relating international research and the local context

This paper reports on a research-based mathematics curriculum program development project in Sweden, whose educational context is currently characterized by multiple reform initiatives. Current reforms include a repositioning of the teacher as central for students’ learning, but also a trend toward initiatives and teacher resources that are more directive than has been the case in the past 30 years. Collecting data from multiple sources, such as teacher log books, lesson observations and feedback meetings, we build on input from 11 elementary school teachers trying out our materials, including student texts and a teachers’ guide, during four trial rounds. We analyze how international research about curriculum programs and teachers’ use of these programs are interpreted and operationalized within the Swedish context. In particular, the two research questions guiding the study are: (1) “How do Swedish teachers interact with and reason about the reform-based classroom practices promoted by the curriculum program?” and (2) “How do Swedish teachers interact with and reason about their use of a teachers’ guide?” From our experiences in the Swedish educational context, we suggest the following contextual aspects to take into account when designing a curriculum program whose design is grounded in international research literature: characteristics of current classroom practices, teachers’ role in classrooms, the level of explicit/implicit support teachers are used to receiving, and teachers’ experiences using a teachers’ guide.     

Toward professional development for teachers grounded in a theory of decision making

There is now robust evidence that teachers’ and others’ in-the-moment decision making can be modeled and explained as a function of the following: their knowledge and other intellectual, social, and material resources; their goals; and their orientations (their beliefs, values, and preferences). The role of beliefs as they affect teachers’ behavior can thus be described at a level of mechanism—but of necessity in interaction with resources and goals. This paper outlines and exemplifies how resources, goals, and orientations shape teachers’ behavior. It indicates how they are interconnected, and why their evolution is necessarily slow. It then suggests how these understandings can be used as a foundation for mathematics teachers’ professional development, and describes how they are being used to shape a course of participatory professional development for middle school mathematics teachers.     

A teacher’s learning process in dual design research: learning to scaffold language in a multilingual mathematics classroom

In this paper, we argue that dual design research (DDR) is a fruitful way to promote and trace the development of a mathematics teacher’s expertise. We address the question of how a teacher participating in dual design research can learn to scaffold students’ development of the language required for mathematical learning in multilingual classrooms. Empirical data were collected from two teaching experiments (each with 8 lessons, and 21 and 22 students, aged 11–12 years), for which lesson series about line graphs were co-designed by the researchers and the teacher. The teacher’s learning process was promoted (e.g. by conducting stimulated recall interviews and providing feedback) and traced (e.g. by carrying out 5 pre- and post-interviews before and after the teaching experiments). An analytic framework for teachers’ reported and derived learning outcomes was used to analyse pre- and post-interviews. The teacher’s learning process was analysed in terms of changes in knowledge and beliefs, changes in practice and intentions for practice. Further analysis showed that this learning process could be attributed to the characteristics of dual design research, for instance the cyclic and interventionist character, the continuous process of prediction and reflection that lies at its heart, and the process of co-designing complemented with stimulated recall interviews.     

Enhancing the pedagogy of mathematics teachers (EPMT) project: a hybrid model of professional development

Enhancing the pedagogy of mathematics teachers (EPMT) project is a hybrid model of professional development (PD) that reflects a gradual shift in the centre of gravity away from the University-based, “supply-side”, “off-line” forms of knowledge production conducted by university scholars for teachers towards an emergent school-based, demand-side, on-line, in situ forms of knowledge production conducted by teachers with support from university scholars. The aims of the EPMT project were threefold: to provide teachers with training, to facilitate teachers’ work (practice and feedback) at the school level and to enthuse and support teachers to contribute towards the development of fellow teachers. This paper examines two project participants’ infusion of their learning in classroom practice. From the lessons enacted by the two teachers it was apparent that both teachers were able to apply their learning in their lessons. The teachers also manifested changes in their perception of teaching mathematics.     

Middle School Mathematics Teachers’ Perceptions of the Common Core State Standards for Mathematics and Its Impact on the Instructional Environment

This study examines Middle School Mathematics Teachers’ (MSMTs') (N = 1,241) perceptions of the Common Core State Standards for Mathematics (CCSSM) and its impact on the instructional environment. A total of eight factors appear in the data. These factors include professional support, teachers’ use of district‐adopted and non‐district‐adopted curricular resources, influence of CCSSM assessment and teacher evaluation on the instructional environment, influence of the CCSSM on classroom instruction, teachers’ planning practices, and perceived rigor of the CCSSM. The data suggest that teachers’ use of digital resources located online was disconnected from their district‐adopted resources suggesting a lack of curricular coherence. MSMTs note that the CCSSM had caused them to incorporate more reform‐oriented practices such as exploration and productive struggle into their daily instruction. MSMTs also perceive that the CCSSM includes new content that is more rigorous than previous state standards. Sampled MSMTs state that while state assessments will measure CCSSM content, they are less likely to include more complex problems or the standards for mathematical practice. Teachers are more likely to read teacher resources than student textbook activities online and to use digital resources for remediation instead of inquiry activities. Over one‐third of MSMTs wanted more CCSSM professional development.     

Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching

This paper sets the scene for a special issue of ZDM—The International Journal on Mathematics Education—by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers’ and didacticians’ engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice.     

Teaching mathematics to lower attainers: dilemmas and discourses

This article draws on Foucault’s concepts of power and discourse to explore the issues of teaching mathematics to low attainers in primary schools in England. We analyse a data set of interviews, from a larger study, with the mathematics teachers of one child across three years, showing how accountability practices, discourses of ability and inclusion policies interrelate to regulate both teachers and student. We demonstrate the impact of neoliberal policy discourses on teachers’ practices and how they are caught up in conflicting ways by an accountability regime that subverts inclusive pedagogies, requiring teachers to monitor, label and assign within-child deficits. In spite of these regulatory technologies we identify contradictory fault lines between mathematics education policy discourses which we argue provide the potential for developing critical awareness of accepted practices and opportunities for change.     

Research evidence on the benefits of IBL

This paper describes the current state of knowledge of empirical studies in the broader sense dealing with inquiry-based learning (IBL) of mathematics and science subjects in schools and universities. The advantages, disadvantages, and effects on relevant outcomes that students can achieve in IBL classrooms are discussed from the aspect of further developing teaching quality. First, the conceptual aspects of IBL are considered briefly to show the background of the studies and the results are categorized. Secondly, references are given with explanations or possible reasons for the results that are not always consistent and, at times, even contradictory. Finally, conclusions from current studies including this overview are drawn with respect to open scientific questions.     

Capitalizing on Emerging Technologies: A Case Study of Classroom Blogging

The challenge many teachers face is how to incorporate new technology into their classrooms that strengthens classroom learning by capitalizing on students’ media literacies. Blogs, a new and innovative technological tool, can be used in math and science classrooms to support student learning by capitalizing on students’ interests and familiarity with on‐line communication. This study explores the emerging blogging practices of one high school mathematics teacher and his class to explore issues of intent, use, and perceived value. Data sources for this case included one year's worth of blog content, an interview with the facilitating teacher, and students ‘perceptions of classroom blogging practices. Findings indicate that (1) teachers’ intentions focused on creating additional forms of participation as well as increasing student exposure time with content; (2) blogs were used in a wide variety of ways that likely afforded particular benefits; and (3) both teacher and students perceived the greater investment to be worthwhile. The findings are used to critically consider claims made in the literature about the potential of blogging to effectively support classroom learning.