**Course description**

Mathematics education as a field of research is one of the largest, international sub-branches of educational research. Nowadays, it is a growing field not only in terms of the topics of research and publication, but also in the variety of theories and methods that it deploys. The course examines the formation and development of mathematics education as a field of academic inquiry from a historical and epistemological perspective. Historically, it is studied how mathematics education emerged in the context of the consolidation of educational and social sciences; the problem of the higher qualification (in colleges or universities) of mathematics teachers, both in particular national contexts and internationally; and the problem of the expansion of massive education systems providing mathematics to a wide number of the population. Epistemologically, the course explores how and why there have been different views on what is conceived as “research”, but also education in mathematics. Here attention is paid to the theoretical foundations for the understanding of the objects of research of mathematics education. In the course the epistemological and historical perspectives intertwine to answer questions about the constitution of the production of academic enquiry and its connection to the teaching/learning of mathematics in different educational settings.

The course will make participants acquainted with tools for understanding what it means to address the epistemological and historical dimensions of mathematics education in general. In particular, the students will be invited to clarify their own placing in an epistemological perspective and how it relates to their own research project. They will also be invited into an exercise of historization of the topic of their research as a way of experiencing the meaning of historical configurations in relation to defining and investigating mathematics education practices. The seminar combines individual study and writing, intensive seminars

**Expected results**

After the course, it is expected that the students are able to:

- Construct an account of mathematics education as a field of academic research and of its constitution and development.
- Identify different epistemological positions and their implications in relation to their own research.
- Provide a limited historical contextualization of their own research objects.

**Forms of participation**

The course is designed in the form of 2 intense work seminars and one examination seminar. At the seminars there will be a combination of lectures and discussions, on the ground of readings and tasks of preparation that the participants have to bring to the sessions. There will be interaction between the lecturers and the participants. The course demands serious preparation for the sessions.

**Examination**

The course examination consists of a text that can make part of the students’ thesis. The text of an extension of max 8.000 words, can be a historization of the topic of study or object of study in the thesis, or an epistemological exploration of the theoretical and methodological position adopted in the thesis.

**Course plan**

*Seminar 1. Knowing the narratives of mathematics education as a field of knowledge*

The course starts on the present of mathematics education research with its wide variety of defining research objects and perspectives, as well as aims. In this seminar the core of study is the relationship between a research object and a theoretical perspective, and how different theories offer particular definitions of what counts as mathematics education, what it studies, how it is studied, and for which purposes.

Topics:

- Examining mathematics education as a field of research: What does it mean to talk about epistemology and ontology of a field of study? Why and how to do it from a historical perspective?
- The creation of the objects of study of mathematics education: From issues of mathematics to issues of learning
- A century of theories and methodologies
- Current tensions in the making of mathematics education research as a field

*Seminar 2. *Historicizing the narratives on the history of mathematics education

Building on the first seminar, the second seminar opens the question of how come the epistemologies of mathematics education have been configured in such a way. In other words, by historicizing what counts as mathematics education form different theoretical perspectives, the rooting of such research in the institutions and trends in different periods during the 20^{th} century will be explored.

Topics:

- What does it mean to historicize mathematics education research? A critical comment on the historiography of mathematics education
- Mathematics education, the school curriculum and the making of the citizen
- Mathematics education and the raise of the social and educational sciences: the scientifization of mathematics education
- Mathematics education and social needs
- Beyond an internalistic perspective of mathematics education research

*Examination seminar*

For this seminar, participants will have the first complete draft of their exam text. The seminar has the purpose of presenting and discussing them, and giving feedback for the preparation of the final submission of the paper with is due on January 15^{th} 2017.

This seminar will be round up the topics of the course by connecting with the texts of the participants, and by doing reading and commenting of the texts by other participants. This is a form of not only gaining information on the varieties of topics worked by other participants, but also gaining competence in reviewing and commenting.

## Literature

The course involves the reading of many key texts, in mathematics education research, but also in other social sciences and general education. The purpose is to provide participants with a sense of what it means to think about the epistemology and the historical in general, and in particular related to mathematics education as a filed of study and to the particular topic and problem of research of the students’ projects.

**Seminar 1**

*Compulsory readings*

De Freitas, E., & Sinclair, N. (2013). New materialist ontologies in mathematics education: the body in/of mathematics. Educational Studies in Mathematics, 83(3), 453-470. doi: 10.1007/s10649-012-9465-z

Popkewitz, T. S. (1984). Paradigms in educational science: Different meanings and purpose to theory. *Paradigm and ideology in educational research: the social functions of the intellectual* (pp. 31-58). New York: Falmer Press.

Silver, E. A., & Herbst, P. (2007). Theory in Mathematics Education Scholarship. In F. Lester (Ed.), *Second Handbook of Research on Mathematics Teaching and Learning* (pp. 39–67). New York: IAP.

http://libris.kb.se/bib/9954925?vw=short

Schoenfeld, A. H. (2007). Method. In F. Lester (Ed.), *Second Handbook of Research on Mathematics Teaching and Learning* (pp. 69-107). New York: NCTM – IAP.

http://libris.kb.se/bib/9954925?vw=short

Sriraman, B., & English, L. D. (2005). Theories of Mathematics Education: A global survey of theoretical frameworks/trends in mathematics education research. ZDM, 37(6), 450-456.

http://link.springer.com/article/10.1007/BF02655853 (doi: 10.1007/bf02655853)

Sriraman, B., & Nardi, E. (2013). Theories in Mathematics Education: Some Developments and Ways Forward. In M. A. Clements, A. J. Bishop, C. Keitel, J. Kilpatrick & F. K. S. Leung (Eds.), *Third International Handbook of Mathematics Education* (Vol. 27, pp. 303-325): Springer New York.

http://link.springer.com/chapter/10.1007/978-1-4614-4684-2_10

Valero, P. (2010). Mathematics education as a network of social practices. In V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (Eds.), *Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education* (pp. LIV-LXXX). Lyon: Institut National de Récherche Pédagogique.

*Complementary readings*

De Freitas, E., & Sinclair, N. (2014). *Mathematics and the body: Material entanglements in the classroom*. New York: Cambridge University Press.

Lerman, S. (2006). Theories of mathematics education: Is plurality a problem? *Zentralblatt für Didaktik der Mathematik*, *38*(1), 8-13.

doi: 10.1007/bf02655902

Sierpinska, A., & Kilpatrick, J. (1998). *Mathematics education as a research domain: A search for identity*. Dordrecht: Kluwer.

Restivo, S. P., Bendegem, J. P. v., & Fischer, R. (1993). *Math worlds: Philosophical and social studies of mathematics and mathematics education*. Albany: State University of New York Press.

**Seminar 2**

*Compulsory readings*

Furinghetti, F., Matos, J. M., & Menghini, M. (2013). From Mathematics and Education, to Mathematics Education. In M. A. Clements, J. A. Bishop, C. Keitel, J. Kilpatrick & K. S. F. Leung (Eds.), *Third International Handbook of Mathematics Education* (pp. 273-302). New York, NY: Springer New York.

http://link.springer.com/chapter/10.1007/978-1-4614-4684-2_9

Kilpatrick, J. (1992). A History of Research in Mathematics Education. In D. A. Grouws (Ed.), *Handbook of Research on Mathematics Teaching and Learning* (pp. 3-38). New York: Macmillan.

http://libris.kb.se/bib/4475899

Lundin, S. (2012). Mechanism, understanding and silent practice in the teaching of arithmetic. On the intention, critique and defense of Carl Alfred Nyström’s Digit-Arithmetic 1853-1888. In *Vetenskapsteori, serie 1*. Gothenburg: Department of Philosophy Linguistics and Theory of Science, University of Gothenburg.

http://hdl.handle.net/2077/32918

Meaney, T. (2014). Back to the future? Children living in poverty, early childhood centres and mathematics education. *ZDM*, *46*(7), 1-13.

doi: 10.1007/s11858-014-0578-y

Radford, L. (2004). From truth to efficiency: Comments on some aspects of the development of mathematics education. *Canadian Journal of Science, Mathematics and Technology Education*, *4*(4), 551-556.

Tröhler, D. (2015). The medicalization of current educational research and its effects on education policy and school reforms. *Discourse: Studies in the Cultural Politics of Education, 36*(5), 749-764.

doi: 10.1080/01596306.2014.942957

Valero, P. (2017). Mathematics for all, economic growth, and the making of the citizen-worker. In T. S. Popkewitz, J. Diaz & C. Kirchgasler (Eds.), *A political sociology of educational knowledge: Studies of exclusions and difference*. New York: Routledge.

*Complementary readings*

Coray, D., Furinghetti, F., Gispert, H., & Schubring, G. (Eds.). (2003). *One hundred years of L'Enseignement Mathématique: Moments of mathematics education in the twentieth century*. Geneve: L' Enseignement Mathématique.

Gutiérrez, A., Leder, G. C., & Boero, P. (Eds.). (2016). *The Second Handbook of Research on the Psychology of Mathematics Education. The Journey Continues*. Rotterdam: Sense Publishers.

Karp, A., & Schubring, G. (Eds.). (2014). *Handbook on the history of mathematics education*. New York: Springer.

Menghini, M., Furinghetti, F., Giacardi, L., & Arzarello, F. (Eds.). (2008). *The first century of the International Commission of Mathematical Instruction (1908-2008). Reflecting and shaping the world of mathematics education*. Roma: Istituto della Enciclopedia Italiana fondata da Giovanni Treccani.