On semiotics and subjectivity: a response to Tony Brown’s “signifying ‘students’, ‘teachers’, and ‘mathematics’: a reading of a special issue”

In this response we address some of the significant issues that Tony Brown raised in his analysis and critique of the Special Issue of Educational Studies in Mathematics on “Semiotic perspectives in mathematics education” (Sáenz-Ludlow & Presmeg, Educational Studies in Mathematics 61(1–2), 2006). Among these issues are conceptualizations of subjectivity and the notion that particular readings of Peircean and Vygotskian semiotics may limit the ways that authors define key actors or elements in mathematics education, namely students, teachers and the nature of mathematics. To deepen the conversation, we comment on Brown’s approach and explore the theoretical apparatus of Jacques Lacan that informs Brown’s discourse. We show some of the intrinsic limitations of the Lacanian idea of subjectivity that permeates Brown’s insightful analysis and conclude with a suggestion about some possible lines of research in mathematics education.

The Anthropology of Meaning

Meaning is one of the recent terms which have gained great currency in mathematics education. It is generally used as a correlate of individuals' intentions and considered a central element in contemporary accounts of knowledge formation. One important question that arises in this context is the following: if, in one way or another, knowledge rests on the intrinsically subjective intentions and deeds of the individual, how can the objectivity of conceptual mathematical entities be guaranteed? In the first part of this paper, both Peirce's and Husserl's theories of meaning are discussed in light of the aforementioned question. I examine their attempts to reconcile the subjective dimension of knowing with the alleged transcendental nature of mathematical objects. I argue that transcendentalism, either in Peirce's or Husserl's theory of meaning, leads to an irresolvable tension between subject and object. In the final part of the article, I sketch a notion of meaning and conceptual objects based on a semiotic-cultural approach to cognition and knowledge which gives up transcendentalism and instead conveys the notion of contextual objectivity.     

Lucid education: resisting resistance to inquiry

Within the community of inquiry literature, the absence of the notion of genuine doubt is notable in spite of its pragmatic roots in the philosophy of Charles Saunders Peirce, for whom the notion was pivotal. We argue for the need to correct this oversight due to the educational significance of genuine doubt—a theoretical and experiential understanding of which can offer insight into the interrelated concepts of wonder, fallibilism, inquiry and prejudice. In order to detail these connections, we reinvigorate the ideas of Peirce by borrowing the language and concepts of Albert Camus, at the same time demonstrating their unlikely congruence. In particular, we argue for the necessity of genuine doubt along with the need for the presence of a diversity of prejudices as a starting point for genuine inquiry.     

Signifying “students”, “teachers” and “mathematics”: a reading of a special issue

This paper examines a Special Issue of Educational Studies in Mathematics comprising research reports centred on Peircian semiotics in mathematics education, written by some of the major authors in the area. The paper is targeted at inspecting how subjectivity is understood, or implied, in those reports. It seeks to delineate how the conceptions of subjectivity suggested are defined as a result of their being a function of the domain within which the authors reflexively situate themselves. The paper first considers how such understandings shape concepts of mathematics, students and teachers. It then explores how the research domain is understood by the authors as suggested through their implied positioning in relation to teachers, teacher educators, researchers and other potential readers.

The Restructuring of China's Higher Education: an experience for market economy and knowledge economy

Although we all learn differently, we all need to be able to engage certain fundamental reasoning skills if we are to manoeuvre successfully through life—however we define success. Peirce's philosophy provides us with a framework for helping students (and ourselves) develop and hone the ability for making deliberate and well‐considered choices. For, embedded within Peirce's complete body of work is a design for thinking that provides a sturdy foundation for the development of three important learning capabilities. These capabilities are 1) the ability to identify, compare, and contrast qualities, 2) the ability to perform analyses, and 3) the ability to interpret the meaning of signs. Although these capabilities may seem like the sort of skills that only older and academically inclined students can master, even young children and the intellectually challenged can learn to use them as well. Once teachers learn to develop their own intellectual potential by expanding these capabilities within themselves, they will be able to begin bringing about the development of these capabilities in their students. Once identified, developed, and applied to the mastery of educational skills and subject matter, these three fundamental learning capabilities (qualification, analysis, and interpretation), can form the foundation of a common‐sense approach to educational reform. Peirce asserts that good reasoning must be informed by ethical considerations, which in turn has been informed by the highest of aesthetic impulses. From this, we can extrapolate the importance that an educational model based upon Peirce's philosophy must place upon aesthetic and ethical considerations, as well as logical ones. Once fully understood, the philosophy of education embedded within Peirce's epistemology can revolutionize educational practices at all levels of learning.     

From Environmental Education to Ecopolitics. Affirming Changing Agendas for Teachers1

In this paper I examine Peirce's epistemological and ontological theories and indicate their relevance to educational practice. I argue that Peirces conception of Firsts, Seconds and Thirds entails a fundamental ontological realism. I further argue that Peirce does have a theory of truth, that it is a particular non‐traditional ‘correspondence’ theory, consistent with, and implicit in, an over‐arching position of pragmatic realism. Peirce's epistemological position is subject to misinterpretation when the ontological realism on which it rests is overlooked. Finally I suggest that such a re‐consideration of Peirce's pragmatic ontology and epistemology in an educational context is needed.     

Belief,Doubt and Reason: C. S. Peirce on education

In this paper, we explore Peirce's work for insights into a theory of learning and cognition for education. Our focus for this exploration is Peirce's paper The Fixation of Belief (FOB), originally published in 1877 in Popular Science Monthly. We begin by examining Peirce's assertion that the study of logic is essential for understanding thought and reasoning. We explicate Peirce's view of the nature of reasoning itself—the characteristic guiding principles or ‘habits of mind’ that underlie acts of inference, the dimensions of and interaction between doubt and belief, and his four methods of resolving or ‘fixing’ belief (i.e., tenacity, authority, a priori, and experimentation). The four methods are then juxtaposed against current models of teaching and learning such as constructivism, schema theory, situated cognition, and inquiry learning. Finally, we discuss Peirce's modes of inference as they relate educationally to the resolution of doubt and beliefs and offer an example of belief resolution from an experienced teacher in a professional development environment.     

皮尔士与詹姆斯实用主义之比较

"实用主义"是遭受最多误解和责难的哲学术语之一。在中国,它已经完全成为一个贬义词。通过比较其创始人皮尔士和早期代表人物詹姆斯对实用主义的阐释,也许可以澄清实用主义的最初含义从而使这一哲学思想能够得到应有的正视和理解。