Inferentialism as an alternative to socioconstructivism in mathematics education

Noorloos, Ruben; Taylor, Samuel D.; Bakker, Arthur; Derry, Jan

doi:10.1007/s13394-017-0189-3

Cited by 25 publications

(23 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Yet when teachers attend to the complexity of the individual meaning-making of learners, the nature of the particular knowledge domain in which that meaning-making occurs, and the inferential roles that constitute concept meaning, is often not the focus of attention. The idea that human beings construct meaning out of raw data (the Given referred to earlier) still forms the background to much educational thought and insufficient attention is paid to the interrelation of knowledge and learning (Noorloos et al, 2017). As a result, the lesson that we learn from Brandom is absent, namely, that the inferential should be privileged over the representational when we are considering the process by which learners acquire both meaning and knowledge (Bakker & Derry, 2011;Derry, 2013).…”

Section: Education and The Significance Of Privileging The Inferentialmentioning

confidence: 99%

An introduction to inferentialism in mathematics education

Derry

2017

Math Ed Res J

Self Cite

View full text Add to dashboard Cite

This paper introduces the philosophical work of Robert Brandom, termed inferentialism, which underpins this collection and argues that it offers rich theoretical resources for reconsidering many of the challenges and issues that have arisen in mathematics education. Key to inferentialism is the privileging of the inferential over the representational in an account of meaning; and of direct concern here is the theoretical relevance of this to the process by which learners gain knowledge. Inferentialism requires that the correct application of a concept is to be understood in terms of inferential articulation, simply put, understanding it as having meaning only as part of a set of related concepts. The paper explains how Brandom's account of the meaning is inextricably tied to freedom and it is our responsiveness to reasons involving norms which makes humans a distinctive life form. In an educational context norms, function to delimit the domain in which knowledge is acquired and it is here that the neglect of our responsiveness to reasons is significant, not only for Brandom but also for Vygotsky, with implications for how knowledge is understood in mathematics classrooms. The paper explains the technical terms in Brandom's account of meaning, such as deontic scorekeeping, illustrating these through examples to show how the inferential articulation of a concept, and thus its correct application, is made visible. Inferentialism fosters the possibility of overcoming some of the thorny old problems that have seen those on the side of facts and disciplines opposed to those whose primary concern is the meaning making of learners.Keywords Inferentialism . Epistemology . Pedagogy . Vygotsky . Brandom . Philosophy of mind It is rare that a theory arrives on the scene sufficiently powerful to stimulate inquiry in a wide range of areas. Inferentialism though is such a theory. For the purposes of this Math Ed Res J (2017) 29:403-418

show abstract

Section: Education and The Significance Of Privileging The Inferentialmentioning

confidence: 99%

An introduction to inferentialism in mathematics education

Derry

2017

Math Ed Res J

Self Cite

View full text Add to dashboard Cite

show abstract

“…We see that inferentialism has other strengths and emphases than commonly used background theories such as constructivism and, thus, may offer different viewpoints and insights when applied in mathematics education and empirical studies. Noorloos et al (2017) argued that inferentialism can overcome several philosophical problems that have continued to plague socioconstructivism such as the relation between the social and individual, relativism, and the question of what is constructed according to constructivism. At the same time, inferentialism seems consistent with several pedagogical implications of constructivism that could be judged separately from their problematic philosophical underpinning (cf.…”

Section: Theoretical Framework: Reasoning From An Inferential Perspecmentioning

confidence: 99%

“…As inferentialism is a semantic theory (cf., Noorloos et al 2017), it aims to explain the use and content of concepts (cf. Brandom 2000).…”

Section: Philosophical Background On Inferentialismmentioning

confidence: 99%

“…This is to say that judgments are expressed and take the role as reasons in the language practice and that the view on the reasoning itself is prioritized over the view on students' representations (cf. Noorloos et al 2017). Brandom (1994Brandom ( , 2000 introduces the metaphor of the game of giving and asking for reasons (GoGAR) for describing the social and pragmatic language practice in which the content is inferentially constituted.…”

Section: Philosophical Background On Inferentialismmentioning

confidence: 99%

See 1 more Smart Citation

Sixth-grade students’ reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis

2017

Self Cite

View full text Add to dashboard Cite

Negative numbers are among the first formalizations students encounter in their mathematics learning that clearly differ from out-of-school experiences. What has not sufficiently been addressed in previous research is the question of how students draw on their prior experiences when reasoning on negative numbers and how they infer from these experiences. This article presents results from an empirical study investigating sixth-grade students' reasoning and inferring from school-based and out-of-school experiences. In particular, it addresses the order relation, which deals with students' very first encounters with negative numbers. Here, students can reason in different ways, depending on the experiences they draw on. We study how students reason before a lesson series and how their reasoning is influenced through this lesson series where the number line and the context debts-and-assets are predominant. For grasping the reasoning's inferential and social nature and conducting in-depth analyses of two students' reasoning, we use an epistemological framework that is based on the philosophical theory of inferentialism. The results illustrate how the students infer their reasoning from out-of-school and from school-based experiences both before and after the lesson series. They reveal interesting phenomena not previously analyzed in the research on the order relation for integers.

show abstract

“…The discussion has helped authors of articles for a special issue to appear in Mathematics Education Research Journal (e.g., Bakker, Ben-Zvi, & Makar, 2017;Derry, 2017;Mackrell & Pratt, 2017;Noorloos, Taylor, Bakker, & Derry, 2017; Schindler, Hußmann, Nilsson, & Bakker, submitted).…”

mentioning

confidence: 99%

Applying Contemporary Philosophy in Mathematics and Statistics Education: The Perspective of Inferentialism

Mackrell¹,

Pratt²,

Bakker³

2017

Proceedings of the 13th International Congress on Mathematical Education

Self Cite

View full text Add to dashboard Cite

The aim of this discussion group was to put contemporary philosophy to work (cf. Cobb, 2007). Inferentialism is an example of contemporary philosophy (Brandom, 2000) that increasingly receives interest in mathematics and statistics education. It can be considered an orienting framework that provides epistemological foundations for conceptualizing and analyzing knowledge, learning, communication, and reasoning in the fields of mathematics and statistics. Inferentialism avoids a representationalist perspective on knowledge and learning by focusing on reasoning and inferences (Bakker & Derry, 2011). The Discussion Group (DG) brought together researchers who are interested in the role and use of inferentialism or other contemporary philosophies in mathematics and statistics education. It gave the attendants the opportunity to share perspectives, to question, to discuss, and to make joint efforts in answering the posed key issues. The DG format at ICME provided the opportunity to discuss the significance and the restrictions of the perspective of inferentialism and other contemporary philosophies on the learning and teaching of mathematics and statistics. The discussion was initiated by several talks: Arthur Bakker (Utrecht) introduced inferentialism as a semantic theory and Maike Schindler (Örebro) gave an overview on researchers presently working with inferentialism in mathematics and statistics education. Paul Ernest (Exeter) talked about meaning in mathematics and mathematics education and anti-representationalism, and Dave Pratt (London) gave a talk on constructionism. Alexandra Thiel-Schneider (Dortmund) presented an empirical study using inferentialism and Luis Radford (Ontario) summarized the discussion elaborating on how inferentialism relates to existing theories in our domain. The participants experienced the discussion group as a fruitful gathering of researchers interested in philosophy in mathematics education; and of various perspectives on inferentialism and its possible use. The talks were welcomed as an input and promoter of discussion among all participants.

show abstract

Inferentialism as an alternative to socioconstructivism in mathematics education

Cited by 25 publications

References 46 publications

An introduction to inferentialism in mathematics education

An introduction to inferentialism in mathematics education

Sixth-grade students’ reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis

Applying Contemporary Philosophy in Mathematics and Statistics Education: The Perspective of Inferentialism

Contact Info

Product

Resources

About