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REMATH: Researching Practice-Based Mathematics Teacher Education. A national graduate school

The doctoral programme REMATH has nine doctoral students across the universities of Stockholm, Kristianstad, Mälardalen and Dalarna. It operates from the guiding question of what it takes for student teachers to learn the mathematical work of teaching needed to engage in deliberate and equitable practice.

Practice-based teacher education addresses what it takes to learn in and from practice, how high-leverage practices can be transformed into university settings making the work of teachers visible for student teachers and how programme components can contribute to a stronger research-based education.

The graduate school will engage the following three foci:

  1. Studies on current implementations of elements of practice-based mathematics teacher education across teacher education environments in Sweden and abroad
  2. Research on alternative implementations of practice-based mathematics teacher education in Swedish and international contexts,
  3. Research on teaching for equity and social justice in mathematics teacher education.

It is expected that addressing these foci, through elaborating key-concepts theoretically and through critically engaging desired mathematics education practices, the doctoral projects will collectively contribute to further the understanding and characterisation of the mathematical work of teaching, and how teacher education can facilitate learning these components of practice.

 

Project description

Objective

… professional education must help novices attend to the complexities of interaction, whether in a classroom, congregation, or therapist’s office, and to respond in the moment under conditions of uncertainty. (Grossman et al. 2009: 2060).

The proposed graduate school will analyse, develop and pilot approaches to practice-based mathematics teacher education, that is, approaches addressing what it takes to learn in and from practice. The question guiding this work is: what does it take for student teachers to learn the mathematical work of teaching needed to engage in deliberate and equitable practice? As a result of this work, the graduate school will strengthen, consolidate and expand Swedish mathematics teacher education research. The main contribution will be to consolidate the young field of subject-specialised teacher education research in Sweden. In particular, the doctoral projects and research carried out within REMATH will generate important insights into the interplay between the content, structure, and pedagogy of teacher education. Through studying practices across a range of institutions in Sweden, with very different histories, and contrasting with practices across the world (see international collaboration), REMATH will both utilise and extend existing research on mathematics teacher education. In addition, REMATH will strengthen the research foundation of Swedish mathematics teacher education practices.

The problematique

The organisation and pedagogy of teacher education can gain much form being informed by research, international studies suggest. In professional programmes, learning in and from practice is crucial, and here we refer to approaches to facilitating such learning under the umbrella term of practice-based teacher education. A core point in practice-based teacher education is that learning in and from practice is a complex endeavour.


Research suggests the importance of making the work of teachers visible to student teachers. However, making the work of teachers visible for student teachers requires more than participating and engaging in classroom practices, it requires explicit teaching (e.g., Kleickmann et al. 2013; Nilssen 2010). Yet several studies point to the relative invisibility and inaccessibility of constituting factors of good teaching, consequently leaving the work of connecting theory and practice up to student teachers (see Asami-Johansson et al. 2020; UKÄ, 2020; Österling 2021). In mathematics teacher education in particular, substantial parts of the mathematical work of teaching (Ball 2017) typically need explicit teaching—for instance choice of representations, the substantiations of theorems, definitions and procedures, the engagement with learner thinking, and leading mathematical classroom discussions, and of which are informed by both mathematics and mathematics education. Not doing so constitutes hurdles to student teachers’ learning, often resulting in inequitable access for student teachers from different backgrounds (Skog, 2014).


Reports on interventions aimed at teaching student teachers aspects of deliberate practice are plentiful in the international research. Many of these interventions aim to bridge the proclaimed gap between theory and practice in teacher education (e.g., microteaching, Basturk 2016; video-based teaching of noticing, Santagata & Yeh 2014; joint post-lesson reflections, Amador & Carter 2016; lesson study, Amador et al. 2016; and research during practicum, Kazemi & Wæge 2015). Yet, as these examples suggest, the interventions are often researched as singular pedagogies, not as part of a complete teacher education programme. To inform teacher education comprehensively, we need more research on how pedagogies interact, and the opportunities to learn across a programme they offer (e.g., Grossman 2018).


Methodologically, research on mathematics teacher education has been characterised by “small scale qualitative studies (how); teacher educators studying their own contexts (who); and a predominance of publications from countries where English is a national language” (Adler et al. 2005: 375). Later reviews have largely confirmed this picture, demonstrating the need for a methodological shift (Potari & Stouraitis 2019; Stahnke et al. 2016). Larger and more coherent research programmes are needed, up-scaling of tested interventions must be considered, an increased distance between researchers and researched practices is necessary, and more principled perspectives on practices are vital to moving the field forward. REMATH will respond to this call.


These gaps in focus and methodology are equally prevalent in our context. Research in mathematics teacher education in Sweden is best described as sporadic. A review of Nordic research in the field confirms this picture (Mosvold 2017), though the field is expanding (see e.g., Klette et.al. 2017). Which teacher competencies Swedish mathematics teacher education covers, to what extent, and how, has not been given sufficient attention in research. In addition, the existing studies are generally too few and too small in scale to give an accurate picture of the pedagogies utilised and the aspects of mathematics teaching and learning it addresses (e.g., Asami-Johansson et al. 2020; Ryve et al. 2012).

The proposed graduate school as a response to the problematique

The proposed graduate school constitutes a response to these concerns. Several existing approaches to research on mathematics teacher education target the visibility issue head on, here referred to as practice-based teacher education. Practice-based teacher education addresses what it takes to learn in and from practice, and how campus-based education can contribute to stronger, research-based teacher education (see Ball & Cohen 1999; Grossman 2018). With current trends towards more school-based teacher education (Reid 2011), it is increasingly important to understand how campus-based and school-based education can interact. This may, for instance, imply working with particular representations of practice to draw attention to aspects which are implicit in the day-to-day work in the classroom or engage in principles of mathematics instruction derived from consolidated practice and research.
That said, focusing on core practices of teaching have been criticised for risking a shift of equity and justice issues to the periphery (Philip et al. 2019), and there is a need for specific focus on teaching in diverse classrooms (Turner et al. 2012).
Current approaches to researching the extent to which teacher education is practice-based or documenting interventions of this nature are emerging, but undertheorised. For instance, in the Anthropological Theory of the Didactic (ATD), techniques used in the didactical organisation of teacher education are studied, such as ways of making the technology of the mathematical and didactical organisations of school mathematics explicit (e.g., Asami-Johansson et al. 2020). Teacher education pedagogies may also be engaged in terms of whether and how they (a) represent teachers’ practice to students, (b) decompose practice for analysis, and (c) engage students in approximations of practice (Grossman et al. 2009).
It is on this basis that the proposed graduate school has as its unifying focus the study of both current and alternative implementations of practice-based mathematics teacher education to understand what it takes for student teachers to learn the mathematical work of teaching needed to engage in deliberate and equitable practice.
As a direct result, REMATH graduates will be well positioned to both provide a substantial lift to mathematics teacher education research in Scandinavia, and contribute towards more coherent and research-informed organisation and pedagogies of mathematics teacher education.

Research foci

While space must be allowed for additional directions to evolve over time, the current vision is for the graduate school to have the following foci:

1. Study current implementations of elements of practice-based mathematics teacher education across teacher education environments in Sweden and abroad.
The desired teacher in Sweden engages in deliberate practice and professional judgement (Christiansen et al. 2019). This includes notions of the desired teacher as a ‘reflective practitioner’—autonomous, with critical agency, part of an intellectual profession involving collective intellectual labour, and able to make deliberate, informed, and balanced judgements about what is educationally desirable, including for learners from diverse backgrounds. Yet the practices currently used to prepare mathematics teachers to implement this vision are under-researched. To understand what works, learn from each other, and contribute to the knowledge base around mathematics teacher education, studies of current practices across Swedish institutions and comparisons to practices in other contexts are needed.


2. Research alternative implementations of practice-based mathematics teacher education in Swedish and international contexts.
It is well known that education is a culturally situated practice, and that ‘what works’ in one context cannot be transferred to another without undergoing transformations. It is therefore crucial to conceptualise, implement, and evaluate interventions. However, as argued above, such interventions should be viewed in thoughtful relation to a programme as a whole, not as isolated fragments. After all, as previous research suggests, strong teacher education programmes are tightly coherent with integration among courses; integrate course work and practicum; and the practicum provides a space for linking theory to practice (Canrinus 2017; Darling-Hammond 2006).


3.  Researching teaching for equity and social justice in mathematics teacher education.
There is limited research on mathematics teachers’ reasoning about their pedagogical responsibilities, Chen et al. (2020) argue. As with other, relatively invisible, work of teachers, this needs to be understood in order to be made explicit and thereby accessible to student teachers. This is particularly pertinent to provide epistemic access to students from non-academic backgrounds, etc. (e.g., Ramdhany et al. 2018). Research on teaching for equity and social justice in mathematics teacher education is dispersed and lacking in scope and transferability, and furthermore tends to leave student teachers voiceless. Further, this research needs to be more strongly connected to the mathematically informed decisions teachers make.

The doctoral projects in the graduate school are intended to address these questions as well as generate new questions under the theme of REMATH. As part of the work, it is expected that the projects will collectively contribute to furthering the understanding and characterisation of the mathematical work of teaching, how teacher knowledge informs this work, and the effect mathematical work of teaching has on learners’ learning. This will contribute to the above-mentioned foci both through elaborating key concepts theoretically and through critically engaging desired mathematics education practices (e.g., Nachlieli & Tabach 2019).

References

Adler, J., Ball, D., Krainer, K., Lin, F.-L., & Novotna, J. (2005). Reflections on an emerging field: Researching mathematics teacher education. Educ. Stud. Math., 60(3), 359–381.
Amador, J.M., & Carter, I.S. (2016). Audible conversational affordances and constraints of verbalizing professional noticing during prospective teacher lesson study. J. Math. Teach. Educ., https://doi.org/10.1007/s10857-016-9347-x
Amador, J.M., Carter, I., & Hudson, R.A. (2016). Analyzing preservice mathematics teachers’ professional noticing. Action Teach. Educ., 38(4), 371-383.
Asami-Johansson, Y., Attorps, I., & Winsløw, C. (2020). Comparing mathematics education lessons for primary school teachers: Case studies from Japan, Finland and Sweden. Int. J. Math. Educ. Sci. Technol., 51(5), 688-712.
Ball, D. L. (2017). Uncovering the special mathematical work of teaching. In Proceedings of the 13th International Congress on Mathematical Education (pp. 11-34). Springer.
Ball, D., & Cohen, D. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the Learning Profession (pp. 3-32). Jossey-Bass.
Basturk, S. (2016). Investigating the effectiveness of microteaching in mathematics of primary pre-service teachers. J. Educ. Train. Stud., 4(5), 239-249.
Canrinus, E. T., Bergem, O.K., Klette, K., & Hammerness, K. (2017). Coherent teacher education programmes: taking a student perspective, J. Curric. Stud., 49(3), 313-333.
Chen, G. A., Marshall, S. A., & Horn, I. S. (2020). ‘How do I choose?’: mathematics teachers’ sensemaking about pedagogical responsibility. Pedagog. Cult. Soc., 1-18.
Christiansen, I. M., Österling, L., & Skog, K. (2019). Images of the desired teacher in practicum observation protocols. Res. Pap. Educ., 1-22.
Darling-Hammond, L. (2006). Constructing 21st-century teacher education. J. Teach. Educ., 57(3), 300-314.
Grossman, P. (Eds.) (2018). Teaching Core Practices in Teacher Education, Harvard.
Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. (2009). Teaching practice: A cross-professional perspective. Teach. Coll. Rec., 111(9), 2055-2100.
Kazemi, E., & Wæge, K. (2015). Learning to teach within practice-based methods courses. Math. Teach. Educ. Dev., 17(2), 125-145.
Kleickmann, T., Richter, D., Kunter, M., Elsner, J., Besser, M., Krauss, S., & Baumert, J. (2013). Teachers’ content knowledge and pedagogical content knowledge: The role of structural differences in teacher education. J. Teach. Educ., 64(1), 90–106.
Klette, K., Blikstad-Balas, M., & Roe, A. (2017). Linking instruction and student achievement: Research design for a new generation of classroom studies. Acta Didactica Norge, 11(3), Art. 10. DOI: http://dx.doi.org/10.5617/adno.4729
Mosvold, R. (2017). Studier av undervisningskunnskap i matematikk: Internasjonale trender og nordiske bidrag. Nordic Studies in Mathematics Education, 22(2), 51-69.
Nachlieli, T., & Tabach, M. (2019). Ritual-enabling opportunities-to-learn in mathematics classrooms. Educ. Stud. Math., 101(2), 253-271.
Nilssen, V. (2010). Guided planning in first-year student teachers’ teaching. Scand. J. Educ. Res., 54(5), 431–449.
Philip, T. M., Souto-Manning, M., Anderson, L., Horn, I., J. Carter Andrews, D., Stillman, J., & Varghese, M. (2019). Making justice peripheral by constructing practice as “core”: How the increasing prominence of core practices challenges teacher education. J. Teach. Educ., 70(3), 251-264.
Potari, D., & Stouraitis, K. (2019). Teacher decision making: Developments in research and theory. In D. Potari & O. Chapman (Eds.), International Handbook of Mathematics Teacher Education: Volume 1 (pp. 303-325). Brill Sense.
Ramdhany, V., Venkat, H., & Christiansen, I. M. (2018). Dissonance and continuity in the mathematical education and training experiences of pre-service secondary mathematics teachers. Afr. J. Res. Math., Sci. Technol. Educ., 22(2), 186-195.
Ryve, A., Nilsson, P., & Mason, J. (2012). Establishing mathematics for teaching within classroom interactions in teacher education. Educ. Stud. Math., 81(1), 1-14.
Santagata, R., & Yeh, C. (2014). Learning to teach mathematics and to analyze teaching effectiveness: Evidence from a video- and practice-based approach. J. Math. Teach. Educ., 17(6), 491-514.
Skog, K. (2014). Power, positionings and mathematics. Discursive practices in mathematics teacher education. (Doctoral dissertation). Stockholm University.
Stahnke, R., Schueler, S., & Roesken-Winter, B. (2016). Teachers’ perception, interpretation, and decision-making: a systematic review of empirical mathematics education research. ZDM, 48(1), 1-27.
Turner, E. E., Drake, C., McDuffie, A. R., Aguirre, J., Bartell, T. G., & Foote, M. Q. (2012). Promoting equity in mathematics teacher preparation: A framework for advancing teacher learning of children’s multiple mathematics knowledge bases. J. Math. Teach. Educ., 15(1), 67-82.
UKÄ (2020). Lärarförsörjning i lärarutbildning – problem, strategier och lösningar, rapport, https://www.uka.se/kvalitet--examenstillstand/utbildningsutvarderingar/utvardering-av-lararutbildningar/lararforsorjning-i-lararutbildningarna.html
Österling, L. (2021). Desires for mathematics teachers and their knowledge. Doctoral dissertation. Stockholm University.

 

More about this project

Partners and Research Environment

REMATH is a collaboration between the Departments of Mathematics and Science Education at Stockholm University, Mälardalen University, and Kristianstad University, and the School of Education, Health and Social Studies at Dalarna University.

  • Stockholm University
  • Mälardalen University
  • Kristianstad University
  • Dalarna University

Working across a range of Swedish teacher education institutions and collaborating with international research environments will ensure that the doctoral research projects generate insights that are less context-dependant, but at the same time can complement existing research within the USA-dominated field. It will contribute to a shared register for mathematics teacher education, cement a research community in the field, and inform pre-service teacher education nationally. It is therefore particularly pertinent and intentional that REMATH spans four institutions with rather different traditions and histories, and that the international collaborations are chosen from very different contexts (Brazil, Israel, Japan, South Africa, and USA).
Most researchers associated with the graduate school have recently conducted research in mathematics teacher education, and one professor specialises in general teacher education. The broad range of expertise and the diverse research environments ensure a dynamic context for the programme, thereby supporting the doctoral students in achieving the connection between themes and the consolidation we see as necessary for the research area to be well established and linked to practice. Supervisors in the programme are continuously developing through the joint supervision in the programme, the involvement with international eminent researchers in the field, and an annual reflective workshop/seminar on supervision practices.
Each doctoral student is assigned two supervisors, from two different universities.

Doctoral students:

To be announced

Programme

The graduate school REMATH will finance nine doctoral students over a five year period. To ensure a connection to the practice of teacher education, students are enrolled 80% in the graduate school, with 20% reserved for teaching at their respective institutions.

The doctoral students are required to complete 3 compulsory 10-ECTS-point courses and an obligatory seminar series equivalent to 20 ECTS points. These courses provide a core of relevant empirical research results, theoretical perspectives, and methodology, and the obligatory seminar series further consolidates the students’ capacity for scholarly work and ensures a strong inter-institutional environment.

Additional courses, which may come from any of the institutions’ regular doctoral courses or from the graduate schools ASSESS or RelMaS, will be chosen by the doctoral students in partnership with their supervisors, and in accordance with the institutional requirements of the host institution.

Courses

State of the art—Current and consolidated research in maths teacher education (10 ECTS points)
An introduction to and critical engagement with research on (a) the mathematical work of teachers, (b) mathematics teacher knowledge research in relation to teacher education, (c) research on existing mathematics teacher education practices, (d) theorisations within mathematics teacher education. The course examination provides students with the opportunity to demonstrate their ability to engage in independent critical review and synthesis. The course is based at Mälardalen University.


The nature of maths and school maths—historical and modern perspectives (10 ECTS points)
The course engages philosophies of mathematics and their relation to school mathematics, and introduces students to more recent perspectives on mathematics and school mathematics. Explicit connections to mathematics teacher education are established through mathematics education and curriculum studies research and theories and related to questions of in-/exclusion. By engaging the perspectives systematically and connecting the nature of mathematics, school mathematics, and teacher education, participants are encouraged to think about mathematics education as a multidimensional system, which will facilitate their engagement with the goals of the programme. The course is based at Stockholm University.


Researching maths teacher education—introduction to methodology, quality issues and ethics (10 ECTS points)
The course introduces methodologies relevant to mathematics teacher education, specifically the ‘two-layer issue’ of engaging learner and student learning concurrently. It addresses issues of quality of research in relation to ontology, epistemology, and methodology; ethical issues of undertaking research in relation to global issues; and ethical issues of joint research—an often-overlooked aspect of research learning. Course examination provides the students with an opportunity to demonstrate familiarity with the scientific methodology of the field, scientific integrity, and ability to make research-ethical assessments. The course is based at Kristianstad University.


Seminar series—Theory and practice in mathematics teacher education research (20 ECTS points)
The seminar series engages framework development and operationalisation, analysis and interpretation of data, and theorising. General issues and principles are discussed in relation to cases from the doctoral projects. Draft publications are scrutinised to offer rich and deep support for students’ writing process. This model facilitates doctoral students’ entry into research communities and contributes to innovation and development of the surrounding research environment, due to the perspectives offered by ‘fresh eyes’.

Participation in conferences and short stay abroad
Students are expected to participate in national and international conferences to present their work. They are encouraged to organize a minimum of 2 weeks stay in a research environment outside of Sweden, where they can interact with researchers of relevance for their work.

Organisation:

National coordination
The programme is coordinated by Stockholm University under the auspices of Associate Professor I.M. Christiansen, with assistance from Professor P. Lindqvist (Mälardalen University). Institutional coordinators are Professor K. Juter (Kristianstad University), Professor A. Ryve (Mälardalen University), and Dr. E. Erixon (Dalarna University). The coordinators and two doctoral student representatives (t.b.a.) form a programme team which oversees course development, management, the seminar series, and quality assurance processes. The team is assisted by an advisory committee of international researchers.

International advisory committee
The following leading researchers of mathematics teacher education have agreed to serve on the advisory committee:

  • Associate Professor Julie Amador, Department of Curriculum and Instruction, University of Idaho, USA;
  • Professor Marcio da Silva, Federal University of Mato Grosso do Sul, Brazil;
  • Professor Takeshi Miyakawa, School of Education, Waseda University, Japan;
  • Associate Professor Craig Pournara, University of the Witwatersrand, South Africa;
  • Professor Anna Sfard, University of Haifa, Israel.

The advisory committee members have provided input on the overall focus of the programme and will assist in development of the obligatory courses and quality assurance procedures. At strategic times, they will be asked to comment on students’ proposals and drafts. They will act as critical readers, lecture on courses, and participate in the seminar series.
 
International collaborators
The programme collaborates with centres of excellence in mathematics education/ mathematics teacher education, contributing to anchoring the programme in existing international research:

  • The Marang Centre for Mathematics and Science Education at the University of the Witwatersrand, South Africa
  • University of Nebraska-Lincoln’s the project on prospective teachers learning to use mathematics curriculum materials run by Associate Professor Lorraine Males (USA).

 
Associated Research Projects:
The graduate school connects to existing research projects on teacher education: