Intersubjectivity in Mathematics Learning: A Challenge to the Radical Constructivist Paradigm?

Lerman, Stephen

doi:10.2307/749597

Cited by 142 publications

(60 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Upon engaging in a new experience, learners reorganise their conceptual framework to assimilate or accommodate this experience (von Glasersfeld, 1984). This is when learning takes place (Lerman, 1996), a process also captured by Piaget's notion of cognitive disequilibrium, where previous knowledge is challenged by unfamiliar or misunderstood experiences and moves towards cognitive equilibrium, as these experiences are reconceptualised and the knowledge has been constructed and accommodated (Simon, 1995).…”

Section: Constructivismmentioning

confidence: 99%

Students’ conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma

Bragg¹

2007

Math Ed Res J

View full text Add to dashboard Cite

Mathematics games are widely employed in school classrooms for such reasons as a reward for early finishers or to enhance students' attitude towards mathematics. During a four week period, a total of 222 Grade 5 and 6 (9 to 12 years old) children from Melbourne, Australia, were taught multiplication and division of decimal numbers using calculator games or rich mathematical activities. Likert scale surveys of the children's attitudes towards games as a vehicle for learning mathematics revealed unexpectedly high proportions of negative attitudes at the conclusion of the research. In contrast, student interview data revealed positive associations between games and mathematical learning. This paper reports on the methodological dilemma of resultant conflicting attitudinal data related to game-playing. Concerns arising from the divergence in the results are raised in this paper. Implications based on the experience of this study may inform educational researchers about future methodological choices involving attitudinal research.Mathematical games are popular with teachers as alternatives to more traditional forms of repetitive practice, for many parts of the mathematics curriculum, and especially for arithmetical computation. The research literature, as well as popular commercial publishing, supports the idea that games can fire children's interest and motivation because students enjoy competition, challenge, and fun (Bragg, 2003;Bright, Harvey, & Wheeler, 1985;Ernest, 1986;Gough, 1999;Owens, 2005).This research began by assuming that a novel pedagogical approach, such as game-playing, might have a positive effect on students' classroom engagement and attitudes towards mathematics. What is reported here is based on a larger study which explored games as a pedagogical approach to enhance mathematical learning (see . Games were examined in that larger study for their potential to promote mathematical learning, but that aspect is not reported in this paper. Surprisingly, triangulation of the data revealed conflicting attitudinal responses from the students about games. These attitudinal data were collected via Likert scales and student interviews. This paper focuses on the methodological difficulty of interpreting conflicting results and raises some possible explanations as to the contradictory nature of these data. Background and Theoretical FrameworkAttitudes

show abstract

Section: Constructivismmentioning

confidence: 99%

Students’ conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma

Bragg¹

2007

Math Ed Res J

View full text Add to dashboard Cite

show abstract

“…There seems to be a mutually reflexive process of knowledge growth between individuals and the community. This raises epistemological questions of the nature and status of knowledge in individual versus social domains, and indeed of societal knowledge (Lerman, 1996;Steffe & Thompson, 2000;Kieran, Forman & Sfard, 2001). Lerman's (2001) metaphor of the zoom of a lens encourages an eclectic position with respect to the growth of knowledge: where the focus is on individual teachers' learning, for example, a constructivist perspective can explain coming to know; zooming out to community or societal influences suggests the need for sociocultural perspectives.…”

Section: Intersubjectivity and Community Knowledgementioning

confidence: 99%

Research Practice into/influencing Mathematics Teaching and Learning Development: Towards a Theoretical framework based on co-learning partnerships

Jaworski

2003

Educational Studies in Mathematics

108

View full text Add to dashboard Cite

“…These two orientations, which we will now begin to explain, are sufficient to lay socioconstructivism open to the problems that we describe in the next three sections. Socioconstructivism was originally developed as a response to a perceived tension between the way the social and individual aspects of learning were theorized (Ernest 1991;Lerman 1996;Steffe and Gale 1995). Socioconstructivism was intended to overcome a dichotomy that many scholars saw between the theoretical perspectives of cognitive constructivism on one hand and sociocultural theories on the other.…”

Section: What Is Socioconstructivism?mentioning

confidence: 99%

Inferentialism as an alternative to socioconstructivism in mathematics education

et al. 2017

View full text Add to dashboard Cite

The purpose of this article is to draw the attention of mathematics education researchers to a relatively new semantic theory called inferentialism, as developed by the philosopher Robert Brandom. Inferentialism is a semantic theory which explains concept formation in terms of the inferences individuals make in the context of an intersubjective practice of acknowledging, attributing, and challenging one another's commitments. The article argues that inferentialism can help to overcome certain problems that have plagued the various forms of constructivism, and socioconstructivism in particular. Despite the range of socioconstructivist positions on offer, there is reason to think that versions of these problems will continue to haunt socioconstructivism. The problems are that socioconstructivists (i) have not come to a satisfactory resolution of the social-individual dichotomy, (ii) are still threatened by relativism, and (iii) have been vague in their characterization of what construction is. We first present these problems; then we introduce inferentialism, and finally we show how inferentialism can help to overcome the problems. We argue that inferentialism (i) contains a powerful conception of norms that can overcome the social-individual dichotomy, (ii) draws attention to the reality that constrains our inferences, and (iii) develops a clearer conception of learning in terms of the mastering of webs of reasons. Inferentialism therefore represents a powerful alternative theoretical framework to socioconstructivism.

show abstract

Intersubjectivity in Mathematics Learning: A Challenge to the Radical Constructivist Paradigm?

Cited by 142 publications

References 0 publications

Students’ conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma

Students’ conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma

Research Practice into/influencing Mathematics Teaching and Learning Development: Towards a Theoretical framework based on co-learning partnerships

Inferentialism as an alternative to socioconstructivism in mathematics education

Contact Info

Product

Resources

About