Draft:Ole Skovsmose
ARTICLE: OLE SKOVSMOSE
Ole Skovsmose is a mathematics educator, philosopher, and artist. He was born in 1944 in Hjørring, a small town in northern Denmark. He is acknowledged for his studies in critical mathematics education and, within this field, his research especially addresses the following themes: landscapes of investigation, dialogue, students’ foreground, inclusive mathematics education, pedagogical imagination, mathematics in action, philosophy of mathematics education, and philosophy of mathematics. He is an emeritus professor at the Department of Culture and Learning at Aalborg University, Denmark, and a volunteer professor at the Graduate Program in Mathematics Education at the Sao Paulo State University (Unesp), Rio Claro campus. As an artist, he has exhibited his works in galleries and museums around the world, and he is a member of the Association Internationale des Arts Plastiques and the Danish Association of Visual Artists (Billedkunstnernes Forbund). [1]
Biography
From a very young age, Ole Skovsmose was fond of drawing. At first, he did it using pencil and watercolor, and from the age of 14, he started to use oil paint as well. From that age on he wanted to become a teacher. This inspiration did not come from his family, as his father worked as a low-paid tailor as an employee in a workshop; and his mother was dedicated to domestic activities. In any case, Skovsmose always enjoyed working with children, and before dedicating himself to teaching, he was also a handball coach and an employee at a surveying company. Ole Skovsmose lived in the town of Hjørring until he was 24 years old. There he attended Folkeskole (equivalent to Elementary School). Then, he studied at Hjørring Teacher Training College, with an emphasis on studies in mathematics. There he graduated as a teacher in 1967. In 1968, Skovsmose started studying at Copenhagen University and throughout the whole university period, he taught mathematics. From 1972 he taught mathematics at a teacher training college in Copenhagen. In 1975, he completed a Master's Degree in philosophy and mathematics at the University of Copenhagen. The same year, he was introduced to a translation of the book Pedagogy of the Oppressed, by Paulo Freire. Both this reading and the German discussion of kritische mathematik-unterriecht (critical mathematics education) that were circulating at the time, inspired him. In 1982 he accomplished a Doctorate in mathematics education at the Royal Danish School of Educational Studies, defending the thesis “Kritik, matematik og undervisning” (“Criticism, mathematics, and education”), under the supervision of Bent Christiansen [2]. In this way, Ole Skovsmose became the first doctor in mathematics education in Denmark.
In 1995 Skovsmose accomplished a Dr. Science at Aalborg University, defending the thesis Towards Philosophy of Critical Mathematics Education. It is from that work that he grounded what would be his main field of study, critical mathematics education. At Aalborg University he worked for 25 years first as an associate professor and later as a full professor. He currently holds the position there as professor emeritus. Ole Skovsmose's ideas are present in more than 50 books, including authored books, book chapters, and edited books. They are as well elaborated in more than 150 scientific articles, as an author or in co-authorship. Currently, he lives in São Paulo, Brazil, working as a volunteer professor at the Graduate Program in Mathematics Education at the São Paulo State University (Unesp), Rio Claro campus, acting especially in supervising doctoral students. He is the father of two children and married to mathematics educator Miriam Godoy Penteado.
Artistic work
Parallel to his work as an educator and academic, Ole Skovsmose stood out as an artist. He has held exhibitions in galleries and museums in England, USA, Germany, Finland, Sweden, Spain, Portugal, Holland, Norway, Bulgaria, Brazil, and Denmark, as, for instance, Lessedra Art Gallery (Bulgaria), Carrousel du Louvre (France), and the Museu Histórico Nacional (Brazil). In 2015 Skovsmose also presented works during the European and Latin American Biennial of Contemporary Art, and at the time was interviewed by TV Brasil [1]. He has participated in several collaborative artistic projects, combining music and painting. He is a member of the Association Internationale des Arts Plastiques.[1] In the book SAUDADE [1], one can read about the history of some of his paintings, including those that are part of the projects: Faces as Landscapes, Touching the Horizon and The Four Graces.
Theoretical Contributions
Since his first academic works, Ole Skovsmose has been concerned with the socio-political aspects of mathematics education and of mathematics in general. These concerns resulted in the development of several notions and concepts.
Critical mathematics education. Skovsmose’s first contributions to the formulation of a critical mathematics education is found in Skovsmose (1980, 1981a, 1981b, 1984). In Towards a Philosophy of Critical Mathematics Education (Skovsmose, 1994), Skovsmose provided a comprehensive presentation of the basic ideas of critical mathematics education. The presentation was based on his experiences in a Danish and Scandinavian context. In Traveling Through Education (Skovsmose, 2005) he established a broader perspective by also considering his experiences from a project in South Africa, where he was supervising students, belonging to the first generation of PhD students in mathematics education in post-apartheid South Africa. His recent contribution to the development of critical mathematics education can be found in Critical Mathematics Education (Skovsmose, 2023). Here he addresses the notions of hope and concern, and phenomena such as the erosion of democracy, racism, and symbolic violence. He shows how such phenomena can be related to mathematics, and how they can be critically approached in mathematics education. He formulates a dialogic theory of mathematics learning, showing the intimate relationship between dialogue and critique. This formulation is based on the study of dialogue presented in Alrø and Skovsmose (2002).
Landscapes of investigation. This notion was presented by Skovsmose in 1996, and it has been developed ever since. A landscape of investigation invites students and teachers to work together in explorative processes. Such a landscape forms a learning-teaching environment, different from the one dominating the school mathematics tradition. Landscapes of investigation invite for dialogic interactions, crucial for establishing critical activities. Many studies, both Master’s thesis and Ph.D. dissertations, have presented and investigated examples of landscapes of investigation in different areas of mathematics and in different geographical contexts. The book Landscapes of Investigation: Contributions to Critical Mathematics Education (Penteado and Skovsmose, 2022) documents the most recent development of the notion.
Students’ foregrounds. This notion was first presented in the book Towards a Philosophy of Critical Mathematics Education (Skovsmose, 1994), and since then the notion has been developed considerably. With reference to the South African context Skovsmose recognised a new significance of the notion of students’ foregrounds. During the apartheid regime, some research in mathematics education claimed to have documented that black students’ performances in mathematics would be much lower than white students’ performances. However, due to the very apartheid regime, back students’ foregrounds have been devastating amputated. This annihilated possible motives for learning mathematics. Black students’ performances tell first of all about the social, political, and economic oppressions that they are subjected to. In Foregrounds: Opaque Stories about Learning, Skovsmose (2014a) investigates more carefully the notion of foreground as it, for instance, can be related to the notion of life-world. In Critical Mathematics Education (Skovsmose, 2023), he relates the notions of foreground and motive for learning.
Inclusive mathematics education. A principal presentation of inclusive mathematics education is found in Inclusive Mathematics Education: State-of-the-Art Research from Brazil and Germany (Kollosche, Marcone, Knigge, Penteado and Skovsmose, 2019). Here Skovsmose contributes to the formation of inclusive mathematics education by elaborating on the notion of “inclusive landscape for investigation”. He has also contributed to the general interpretation of inclusive mathematics education by interpreting it in terms of “meetings across differences”. This notion gets further elaborated into the conception of “inclusive citizenship” (see Skovsmose, Moura, and Carrijo (2022) [3]).
Pedagogical imagination. Critical mathematics education recognises the importance of providing descriptions based on both quantitative and qualitative studies. However, it is also important to move beyond the descriptive research paradigm. It is not only vital to research “what is”, but also to research “what could be”. This means to research alternative educational possibilities, otherwise research might be confined by the limitations imposed by the political status quo. This brings the notion of pedagogical imagination into the centre of research methodology. A pedagogical imagination can be based on loose speculations, but it can also be based on systematic studies. Pedagogical imagination as integral part of research methodology is discussed in Skovsmose and Borba (2004) [4], Skovsmose (2009), and Skovsmose, Lima and Penteado (in print).
Mathematics in action. In order to address the intimate relationship between mathematical knowledge and power, Skovsmose has coined the notion of the formatting power of mathematics. He argues that mathematics is performative. By means of mathematics one can create new technological possibilities. It might be possibilities associated to dramatic social risks, but mathematics can also be brought into action for identifying cases of social injustice. Mathematics as such is not neutral, but can come to serve any kind of interest. Skovsmose has tried to condense this observation by relating both the application of mathematics and social critique to uncertainty. This idea is, for instance, expressed in the book Critique as Uncertainty (Skovsmose, 2014).
Philosophy of mathematics. In Connecting Humans to Equations: A Reinterpretation of the Philosophy of Mathematics, Ravn and Skovsmose (2019) present a four-dimensional philosophy of mathematics. While classic approaches - like logicism, formalism, and intuitionism - are two-dimensional by focusing on ontological and epistemic issues, a four-dimensional philosophy also addresses sociological and ethical issues. A four-dimensional philosophy of mathematics resonates with the outlook of critical mathematics education. Skovsmose develops these ideas further as an integral part of a philosophy of critical mathematics education. Steps in such direction are presented in the articles Banality of Mathematical Expertise (Skovsmose, 2020) [5], Mathematics and Ethics (Skovsmose, 2020) [6], and Mathematics and Crises (Skovsmose, 2021) [7]. In 2023 and 2024, he will concentrate on writing a book with the working title Philosophy of Mathematics: A Critical and Educational Endeavour.
Books
As author or coauthor:
Skovsmose, O. (2023). Critical mathematics education. Cham: Springer.
Ravn, O.; Skovsmose, O. (2019). Connecting humans to equations: A reinterpretation of the philosophy of mathematics. Cham: Springer.
Skovsmose, O. (2014). Um convite à educação matemática crítica. Campinas: Papirus.
Skovsmose, O. (2014a). Foregrounds: Opaque stories about learning. Rotterdam: Sense Publishers.
Skovsmose, O. (2014). Critique as uncertainty. Charlotte: Information Age Publishing.
Skovsmose, O.; Ravn, O. (2011). Matematikfilosofi. Aarhus: Systime.
Skovsmose, O. (2009). In Doubt: About language, mathematics, knowledge and life-worlds. Rotterdam: Sense Publishers.
Skovsmose, O. (2008). Desafios da reflexão: Em educação matemática crítica. 1 Campinas: Papirus.
Skovsmose, O. (2007). Educação crítica: Incerteza, Matemática, Responsabilidade. São Paulo: Cortez Editora. Alrø, H.; Skovsmose. (2006). Diálogo e aprendizagem em educação matemática. Belo Horizonte: Autêntica.
Skovsmose, O. (2005). Travelling through education: Uncertainty, mathematics, responsibility. Rotterdam: Sense Publishers.
Alrø, H.; Skovsmose (2002). Dialogue and learning in mathematics education: Intention, reflection, critique. Dordrecht: Kluwer.
Skovsmose, O. (2001). Educação matemática crítica: A questão da democracia. Campinas: Papirus.
Nielsen, L.; Patronis, T.; Skovsmose, O. (1999). Connecting corners: A Greek-Danish project in mathematics education. Aarhus: Systime.
Skovsmose, O. (1999). Hacia una Filosofía de la Educación Matemática Crítica. Bogotá: Una Empresa Docente.
Skovsmose, O. (1994). Towards a philosophy of critical mathematics education. Dordrecht: Kluwer Academic Publishers.
Skovsmose, O. (1990). Ud over matematikken. Aarhus: Systime.
Siggaard, H.; Skovsmose, O. (1986). Teknologikritik. Herning: Systime.
Skovsmose, O. (1984). Kritik, undervisning og matematik. Copenhagen: Lærerforeningernes Materialeudvalg.
Skovsmose, O. (1981b). Alternativer i matematikundervisningen. Copenhagen: Gyldendal.
Skovsmose, O. (1981a). Matematikundervisning og kritisk pædagogik. Copenhagen: Gyldendal.
Skovsmose, O. (1980). Forandringer i matematikundervisningen. Copenhagen: Gyldendal.
As coeditor:
Valero, P.; Skovsmose, Ole (Eds.). (2012). Educación matemática crítica: Una visión sociopolítica del apendizaje y la enseñanza de las matemáticas. Bogotá: Universidad de Los Andes.
Skovsmose, O.; Valero, P.; Christensen, O. R. (Eds.). (2009). University science and mathematics education in transition. New York: Springer.
Skovsmose, O.; Blomhøj M. (Eds). (2006). Kunne det tænkes? Om matematiklæring. Copenhagen: Akademisk Forlag.
Kilpatrick, J.; Hoyles, C.; Skovsmose, O. in collaboration with Valero (Eds.). (2005). Meaning in mathematics education. New York: Springer.
Skovsmose, O.; Blomhøj. M. (Eds.). (2003). Kan det virkelig passe? Copenhagen: Akademisk Forlag.
References
[1] Art Forum Artavita: https://www.artavita.com/artists/7085-ole-skovsmose
[2] Bent Christiansen Quick Info: https://mathshistory.st-andrews.ac.uk/Biographies/Christiansen/
[3] Skovsmose, O., Maura, A., & Carrijo, M. (2023). Inclusive citizenship through mathematics education. ZDM.
[4] Skovsmose, O., & Borba, M. (2004). Research methodology and critical mathematics education. In Researching the socio-political dimensions of mathematics education: Issues of power in theory and methodology (pp. 207-226). Boston, MA: Springer US.
[5] Skovsmose, O. (2020). Banality of mathematical expertise. ZDM, 52(6), 1187-1197.
[6] Skovsmose, O. (2020). Mathematics and ethics. Qualitative Research Journal, 8(18), 479-503. Special Edition: Philosophy of Mathematics. Reprinted in Philosophy of Mathematics Education Journal, (36).
[7] Skovsmose (2021). Mathematics and crises. Educational Studies in Mathematics, 108(1-2), 369-383.