Reflective Inquiries in the Classroom

Kennedy N.S.

This chapter argues that critical mathematics education requires reflective knowledge, which often lies outside of mathematical and technological knowledge and which can be generated through philosophical inquiry in the classroom. I first examine the concept of reflective knowing more closely and suggest that philosophical inquiry in collaborative group settings may be an appropriate vehicle to facilitate critical reflection in the classroom focused on the understanding of mathematics as a tool, its role in society, and the implications of using mathematical and technological knowledge in addressing social problems. I then offer a brief description of the practice of communal philosophical inquiry, the context in which it is conducted, and a framework for practicing it in the mathematics classroom by engaging school students in collective encounters with contestable questions related to mathematics and its role in society. I claim that philosophical inquiry can offer a space for critique and reflection on mathematics and for the development of an epistemological approach that encourages an enriched, overarching view of mathematics and its connections to the other school disciplines, society, and self. It also offers space for the deconstruction and reconstruction of beliefs about mathematics as a form of knowledge, about the social value of mathematical practice, and beliefs about oneself as a mathematics learner/thinker.

Martin D.B.

Despite decades of equity- and inclusion-oriented discourse and reform in mathematics education, Black learners in the U.S. continue to experience dehumanizing and violent forms of mathematics educ...

Martin D.B.

Critical scholars have argued that mathematics education is in danger of becoming increasingly influenced by and aligned with neoliberal and neoconservative market-focused projects. Although this larger argument is powerful, there are often 2 peculiar responses to issues of race and racism within these analyses. These responses are characterized by what the author sees as an unfortunate backgrounding of these issues in some analyses or a conceptually flawed foregrounding in others. These responses obscure the evidence that, beyond being aligned with the market-oriented goals of these projects, mathematics education has also been aligned with their prevailing racial agendas.

Kennedy N.S.

The paper discusses Matthew Lipman’s approach to inquiry as shaped and fashioned by John Dewey’s model of scientific inquiry. Although Lipman’s program adopted the major aspects of Dewey’s pedagogy, at least two characteristics of that program stand out as radically differ ent—his use of relatively free-form philosophical discussions to teach complex thinking, and his formulation and development of what he called a “community of inquiry” as a pedagogical setting for holding and sustaining such discussions. Here Lipman’s Philosophy for Children program is seen as a framework for the design and performance of philosophical inquiry in the disciplines—something that he himself contemplated but never realized. In this paper I outline a few possible directions for opening spaces in school-based mathematical practices for philosophical deliberation in a community of inquiry, Lipman style. I argue that such an opening represents a potential expansion of students’ mathematical experiences—a way of nurturing and integrating a sense of the philosophical perspectives of the discipline into the regular math class that is larger and more encompassing, and that promises to provide bridges for establishing richer and more meaningful connections and interactions with students’ personal experience, with other disciplines, and with the broader culture; and thus a prime example of what Dewey called “educative experience.”

Ball D.L.

Ideas like understanding, authenticity, and community are central in current debates about curriculum, instruction, and assessment. Many believe that teaching and learning would be improved if classrooms were organized to engage students in authentic tasks, guided by teachers with deep disciplinary understandings. Students would conjecture, experiment, and make arguments; they would frame and solve problems; and they would read, write, and create things that mattered to them. This article examines the challenge of creating classroom practices in the spirit of these ideals. With a window on her own teaching of elementary school mathematics, the author presents three dilemmas-of content, discourse, and community-that arise in trying to teach in ways that are, in Bruner's terms, intellectually honest. These dilemmas arise reasonably from competing and worth-while aims and from the uncertainties inherent in striving to attain them. The article traces and explores the author's framing of and response t...

Skovsmose O.

Neither absolutism nor aposteriorism have questioned the progressive elements associated with the applications and the social functions of mathematical knowledge. Aporism raises this question by discussing the thesis of the formatting power of mathematics. This thesis unites linguistic relativism applied to mathematics and the idea that technology is a structuring principle in society. We are no longer surrounded by “nature”, instead we live in a techno-nature. Mathematical abstractions can be projected outside the sphere of mathematics, and in this way they modulate and eventually constitute fundamental categories of techno-nature. The Vico paradox expresses the difficulties of specifying the nature and function of technological actions. We are not even able to grasp and to understand what we have ourselves constructed. A critique cannot be guaranteed by scientific (or mathematical) thinking itself. Critique becomes a much more complex activity including reflections on technological actions. A crifique includes ethical considerations, and therefore a critique of mathematics is also ethical.