Bibliographic Information
Title: Critical Mathematics Education: An Application of Paulo Freire’s Epistemology
Author: Marilyn Frankenstein
Year: 1987
Citation
Frankenstein, M. (1987). Critical Mathematics Education: An Application of Paulo Freire’s Epistemology. In Shor, I. (Ed.). (1987). Freire for the classroom: A sourcebook for liberatory teaching (1st. ed, pp. 180-210). Boynton/Cook.
Realms of Application
Summary
Frankenstein reconstructs Freire’s epistemology and uses it as a launching point to explore how to teach Mathematics in a critical fashion. In an appendix, she includes many examples of specific exercises and lessons she employs in her practice.
Frankenstein frames her contribution through a grounding in tools of Theory. Leaving aside the revolutionary current in Freire’s writing, she reconstructs his epistemological stance, starting from the question of knowledge: “For Freire, the purpose of knowledge is for people to humanize themselves by overcoming dehumanization through the resolution of the fundamental contradiction of our epoch: that between domination and liberation” (p. 183). She identifies this knowledge as socially constructed, and highlights dialectics as a mode of analysis to clarify critical knowledge and connect it to emancipatory social change. Then, she questions education from the perspective of this epistemology, concluding that it should serve to develop critical consciousness in general, and, in particular, “Critical education in the United States, therefore, must (…) show people that they can understand how technology works, and in whose interest. Also, critical education must challenge and expose the contradictions in this society’s definition of ‘progress’ and ‘the good life’” (p. 185).
From this basis in Theory, Frankenstein turns to questions of Methodology. She continues to reconstruct Freire, now with an eye to application. She highlights how both content and methods must be considered in the development of a critical pedagogy, as well as the centrality of literacy in any liberatory curriculum. She also contrasts a Freirean approach with a more traditional problem-solving one: whereas the latter focuses on practice as a form of developing technical capability, the former reveals the complexity of solving problems in the real world, and aims to recognize and understand them better rather than solve them outright.
Frankenstein then uses her own practice as a Mathematics teacher as a case study for implementing a critical methodology. She constructs tools of Context to understand her subject, highlighting the effects of the dominant culture surrounding Mathematics and her students’ relationships with it. She reflects on the discursive and political nature of using statistics, and how even the act of adding the bill for groceries normalizes the idea that food should be monetized. Furthermore, she hones in on “Math anxiety” as a central concept for her program:
Quote
One of the obstacles that critical mathematics education must overcome in the United States is people’s math ‘anxiety’. Since, as Freire stresses, people who are not aware of the raison d’etre of their situation fatalistically ‘accept’ their explotation, teachers and students must consider the causes behind math ‘anxiety’ as part of developing critical mathematics education. The immediate pedagogical causes of the situation –such as meaningless rote drill, taught so that it requires extensive memorization, and unmotivated applications that are unrelated to the math one actually uses in everyday life– create a situation where people ‘naturally’ avoid mathematics.
- pp. 193-194
Based on her analysis of the Context, her approach is two-pronged: Firstly, she focuses on developing students’ technical and dialectical understanding of the basic tools and concept of Mathematics by deploying them to analyze societal discourse. She argues that “most basic math and statistics skills and concepts, as well as the critical nature of statistical knowledge, can be learned in the context of working on applications that challenge the contradictions involved in supporting hegemonic ideologies” (p. 196). She uses concrete examples of mathematics in discourse, drawn from her students’ everyday lives, to explain and illustrate mathematical tools and concepts, thus revealing the underlying structure of the discourse: “As these math examples challenge students to reconsider their previously ‘taken-for-granted’ beliefs, they also deepen and increase the range of questions they ask about the world” (p. 197). She embarks in longer research projects together with her students, using the excuse of math learning as an opportunity to further explore the world.
Secondly, she addresses math anxiety by involving her students in the class emotionally as well as technically. She includes them in evaluation processes, and encourages them to “pinpoint their own misunderstandings and determine how well they understood each problem” (p. 199). She encourages them to keep math journals, where they reflect on their progress and difficulty learning the content, and she comments on the margins with further reflection from her perspective as well as encouragement to continue studying.
Notably, Frankenstein includes in her article an appendix with specific examples of her Lesson tools. She includes exercises to practice diverse mathematical concepts, prompts for the aforementioned math journals, her policy on quizzes, and considerations for group work and evaluation of in-class and homework activities. Thus, she ties her Methodology considerations down with specific examples to illustrate how her Theory considerations translate into practice.