# Critical Mathematics Education

**DOI:**https://doi.org/10.1007/978-3-319-77487-9_34-3

## Keywords

Mathematics education for social justice Critical mathematics education Ethnomathematics Mathematics in action Students’ foregrounds Mathemacy Landscapes of investigation Mathematization Dialogic teaching and learning## Definition

Critical mathematics education can be characterized in terms of concerns: to address social exclusion and suppression, to work for social justice, to open new possibilities for students, and to address critically mathematics in all its forms and application.

## Characteristics

### Critical Education

Inspired by the students’ movement, a New Left, peace movements, feminism, and antiracism, critical education proliferated. A huge amount of literature became published, not least in Germany, and certainly the work of Paulo Freire was recognized as crucial for formulating radical educational approaches.

However, critical education was far from expressing any interest in mathematics. In fact, with reference to the Frankfurt School, mathematics was considered almost an obstruction to critical education. Thus, Habermas, Marcuse, and many others associated instrumental reason with, on the one hand, domination and, on the other hand, the rationality cultivated by natural science and mathematics. Mathematics appeared as the grammar of instrumental reason. How could one imagine any form of emancipatory interests being associated to this subject?

### Steps into Critical Mathematics Education

Although there were no well-defined theoretical frameworks to draw on, there were from the beginning of the 1970s many attempts in formulating a critical mathematics education. Let me mention some publications.

The book *Elementarmathematik: Lernen für die Praxis* (*Elementary mathematics: Learning for the praxis*) by Peter Damerow, Ulla Elwitz, Christine Keitel, and Jürgen Zimmer from 1974 was crucial for the development of critical mathematics education in a German context. In the article “Plädoyer für einen problemorientierten Mathematikunterrich in emanzipatorisher Absicht” (“Plea for a problem-oriented mathematics education with an emancipatory aim”) from 1975, Dieter Volk emphasized that it is possible to establish mathematics education as a critical education. The book *Indlæring som social proces* (*Learning as a social process*) by Stieg Mellin-Olsen was published in 1977. It provided an opening of the political dimension of mathematics education, a dimension that was further explored in Mellin-Olsen (1987). *Indlæring som social proces* was crucial for the development of critical mathematics education in the Scandinavian context. An important overview of Mellin-Olsen’s work is found in Kirfel and Lindén (2010). Dieter Volk’s *Kritische Stichwörter zum Mathematikunterricht* (*Critical notions for mathematics education*) from 1979 provided a broad overview of what could be called the first wave in critical mathematics education, soon after followed, in Danish, Skovsmose (1980, 1981a, b).

Marilyn Frankenstein (1983) provided an important connection between critical approaches in mathematics education and the outlook of Freire, and in doing so, she was the first in English to formulate a critical mathematics education (see also Frankenstein 1989). Around 1990, together with Arthur Powell and several others, she formed the critical mathematics education group, emphasizing the importance of establishing a united concept of critique and mathematics (see Frankenstein 2012; Powell 2012). Skovsmose (1994) provided an interpretation of critical mathematics education and Skovsmose (2012) a historical perspective.

Critical mathematics education developed rapidly in different directions. As a consequence, the very notion of critical mathematics education came to refer to a broad range of approaches, such as mathematics education for social justice (see, e.g., Sriraman 2008; Penteado and Skovsmose 2009; Gutstein 2012), pedagogy of dialogue and conflict (Vithal 2003), responsive mathematics education (Greer et al. 2009), and, naturally, critical mathematics education (Skovsmose 2011). Many ethnomathematical studies also link closely with critical mathematics education (see, e.g., D’Ambrosio 2006; Knijnik 1996; Powell and Frankenstein 1997).

### Some Issues in Critical Mathematics Education

can be brought in action in technology, production, automatization, decision-making, management, economic transaction, daily routines, information procession, communication, security procedures, etc. In fact, mathematics in action plays a part in all spheres of life. It is a concern of a critical mathematics education to address mathematics in its very many different forms of applications and practices. There are no qualities, like objectivity and neutrality, that automatically can be associated to mathematics. Mathematics-based actions can have all kind of qualities, being risky, reliable, dangerous, suspicious, misleading, expensive, brutal, profit generating, etc. Mathematics-based action can serve any kind of interest. As with any form of action, also mathematics in action is in need of being carefully criticized. This applies to any form of mathematics: everyday mathematics, engineering mathematics, academic mathematics, and ethnomathematics.**Mathematics**. To a critical mathematics education, it is important to consider students’ interests, expectations, hopes, aspirations, and motives. Thus, Frankenstein (2012) emphasizes the importance of respecting student knowledge. The notion of students’ foregrounds has been suggested in order to conceptualize students’ perspectives and interests (see Skovsmose 2014a). A foreground is defined through very many parameters having to do with economic conditions, social-economic processes of inclusion and exclusion, cultural values and traditions, public discourses, and racism. However, a foreground is, as well, defined through the person’s experiences of possibilities and obstructions. It is a preoccupation of critical mathematics education to acknowledge the variety of students’ foregrounds and to develop a mathematics education that might provide new possibilities for the students. The importance of recognizing students’ interest has always been a concern of critical mathematics education.**Students**. As it is important to consider the students’ interests, it is important to consider the teachers’ interests and working conditions as well. Taken more generally, educational systems are structured by the most complex sets of regulations, traditions, and restrictions, which one can refer to as the “logic of schooling.” This “logic” reflects (if not represents) the economic order of today, and to a certain degree, it determines what can take place in the classroom. It forms the teachers’ working conditions. It becomes important to consider the space of possibilities that might be left open by this logic. These considerations have to do with the micro–macro (classroom-society) analyses as in particular addressed by Paola Valero (see, e.g., Valero 2009). Naturally, these comments apply not only to the teachers’ working conditions but also to the students’ conditions for learning. While the concern about the students’ interests has been part of critical mathematics education right from the beginning, a direct influence from the students’ movements, the explicit concern about teaching conditions is a more recent development of critical mathematics education.**Teachers**can be changed. This is the most general claim made in politics. It is the explicit claim of any activism. And it is as well a concern of critical mathematics education. Following Freire’s formulations, Gutstein (2006) emphasizes that one can develop a mathematics education which makes it possible for students to come to read and write the world: “read it,” in the sense that it becomes possible to interpret the world filled with numbers, diagrams, figures, and mathematics, and “write it,” in the sense that it becomes possible to make changes. However, a warning has been formulated: one cannot talk about making sociopolitical changes without acknowledging the conditions for making changes (see, e.g., Pais 2012). Thus, the logic of schooling could obstruct many aspirations of critical mathematics education. Anyway, I find that it makes good sense to articulate a mathematics education for social justice, not least in a most unjust society.**Society**

### Some Notions in Critical Mathematics Education

. Critical mathematics education includes a concern for addressing any form of suppression and exploitation. As already indicated, there is no guarantee that an educational approach might in fact be successful in bringing about any justice. Still, working for social justice is a principal concern of critical mathematics education. Naturally, it needs to be recognized that “social justice” is an open concept, the meaning of which can be explored in many different directions. Addressing**Social justice***equity*also represents concerns of critical mathematics education, and the discussion of social justice and equity brings us to address processes of*inclusion*and*exclusion*. Social exclusion can take the most brutal forms being based on violent discourses integrating racism, sexism, and hostility toward “foreigners” or “immigrants.” Such discourses might label groups of people as being “disposable,” “a burden,” or “nonproductive,” given the economic order of today. It is a concern of critical mathematics education to address any form of social exclusion. As an example, I can refer to Martin (2009). However, social inclusion might also represent a questionable process: it could mean an inclusion into the capitalist mode of production and consumption. So critical mathematics education needs to address inclusion–exclusion as contested processes. However, many forms of inclusion–exclusion have until now not been discussed profoundly in mathematics education: the conditions of blind students, deaf students, and students with different handicaps – in other words, students with particular rights. However, such issues are now being addressed in the research environment created by the Lulu Healy and Miriam Goody Penteado in Brazil. Such initiatives bring new dimensions to critical mathematics education.is closely related to literacy, as formulated by Freire, being a competence in reading and writing the world. Thus, D’Ambrosio (1998) has presented a “New Trivium for the Era of Technology” in terms of literacy, matheracy, and technoracy. Anna Chronaki (2010) provided a multifaceted interpretation of mathemacy, and in this way, it is emphasized that this concept needs to be reworked, reinterpreted, and redeveloped in a never-ending process. Different other notions have, however, been used as well for these complex competences, including**Mathemacy***mathematical literacy*and*mathematical agency*. Eva Jablonka (2003) provides a clarifying presentation of mathematical literacy, showing how this very notion plays a part in different discourses, including some which hardly represent critical mathematics education. The notion of mathematical agency helps to emphasize the importance of developing a capacity not only with respect to understanding and reflection but also with respect to acting.. Not least due to the inspiration from Freire, the notion of dialogue has played an important role in the formulation of critical mathematics education. Dialogic teaching and learning has been presented as one way of developing broader critical competences related to mathematics. Dialogic teaching and learning concerns forms of interaction in the classroom. It can be seen as an attempt to break at least some features of the logic of schooling. Dialogic teaching and learning can be seen as a way of establishing conditions for establishing mathemacy (or mathematical literacy, or mathematical agency).**Dialogue***Problem-based learning*and*project work*can also be seen as way of framing a dialogic teaching and learning.. Critique cannot be any dogmatic exercise, in the sense that it can be based on any well-defined foundation. One cannot take as given any particular theoretical basis for critical mathematics education; it is always in need of critique (see, e.g., Ernest 2010, and Skovsmose 2014b). In particular one cannot assume any specific interpretation of social justice, mathemacy, inclusion–exclusion, dialogue, critique, etc. They are all contested concepts. We have to do with concepts under construction.**Uncertainty**

### Critical Mathematics Education for the Future

The open nature of critical mathematics education is further emphasized by the fact that forms of exploitations, suppressions, environmental problems, and critical situations in general are continuously changing. Critique cannot develop according to any preset program.

For recent developments of critical mathematics education, see, for instance, Alrø, Ravn, and Valero (Eds.) (2010), Wager, A. A. and Stinson, D. W. (Eds.) (2012), Skovsmose and Greer (Eds.) (2012), and Ernest, Sriraman, and Ernest (Eds.) (2015). In Portuguese, one also finds important new contributions to critical mathematics education. Denival Biotto Filho (2015) addresses students in precarious situations and in particular their foregrounds. Raquel Milani (2015) and Ana Carolina Faustino (in progress) explore further the notion of dialogue, while Renato Marcone (2015) addresses the notion of inclusion–exclusion, emphasizing that we do not have to do with a straightforward good-bad duality. Inclusion could also mean an inclusion into the most questionable social practices.

Critical mathematics education is an ongoing endeavor. And naturally we have to remember that as well the very notion of critical mathematics education is contested. There are very many different educational endeavors that address critical issues in mathematics education that do not explicitly refer to critical mathematics education. And this is exactly as it should be as the concerns of critical mathematics cannot be limited by choice of terminology.

## Cross-References

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