Critical Mathematics

Defining Terms

The modifier mathematics at once assumes a need for a special set of questions and issues peculiar to a [Page 194]subject area while also raising the specter of challenges to a disciplinary orientation to educational programs. Is there something special about mathematics that warrants a separate entry in this volume, distinct from, say, language arts, social studies, science, vocational education, and so on?

One might define mathematics as a subset of literacy, involving reading, writing, listening, speaking, and otherwise representing ideas that focus on patterns, numbers, shapes, space, probabilities, and informatics. If so, do we need unique approaches to teaching, learning, and assessment, or are the methods of instruction and theorizing pretty much the same as for any other subject area of a school curriculum? Such questions are of interest because of the specific history of (Western) mathematics, which has so often been used as a model of rational thought and knowledge in general. Because this history is so intertwined with the history of Amero-European thought, mathematics is in its own way a symbol of the intellectual history of colonialism and imperialism, as demonstrated in the fields of ethno-mathematics and in ideological analyses of mathematics as constructed in ways that mask its relationships with power and social inequalities.

The modifier critical is added by theorists who are concerned with the constraining and enabling functions of mathematics education within a democratic society: As with any form of education, mathematical experiences may empower and disempower at the same time. Many mathematical innovations have been created in order to serve those who control, for example, within the development of military weapons and strategies, governmental accounting systems, and business practices. Issues of access internationally and in local contexts set up systems of social reproduction of inequality, where students of mathematics at various levels of education experience different forms of mathematics curriculum, with further implications for equity and diversity.

On the other hand, movements to introduce critical mathematics education and mathematics education for social justice enable students to use mathematics as a tool for social critique and personal empowerment. And knowledge of mathematics, as with any specific knowledge area, can be used as a cultural resource for reading the world and in the process transforming one's place within that world. Malcolm X's use of the concept of a variable for his name both represented the legacy of slavery and defined a political, cultural, and historic moment in the history of the United States. Students who invent their own algorithms for distributing governmental funds are confronted with the limitations of “mathematizing” social decisions.

Implementation

Critical mathematics education demands a critical perspective on both mathematics and the teaching and learning of mathematics. As Ole Skovsmose describes a critical mathematics classroom, the students (and teachers) are attributed a “critical competence.” A century ago, mathematics educators moved from teaching critical thinking skills to using the skills that students bring with them. It was accepted that students, as human beings, are critical thinkers and would display these skills if the classroom allowed such behavior. It seemed that critical thinking was not occurring simply because the teaching methods were preventing it from happening; through years of school, students were unwittingly “trained” not to think critically in order to succeed in school mathematics. Later, ways were found to lessen this “dumbing down of thinking through school experiences.”

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