Diagrammatic reasoning and hypostatic abstraction in statistics education
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Arthur Bakker
Arthur Bakker (b. 1970). His research interests include statistics education, workplace learning, technology, history of statistics and semiotics. His recent publications include ‘Reasoning about shape as a pattern in variability’ (2004); ‘Diagrammatic reasoning as the basis for developing concepts: A semiotic analysis of students' learning about statistical distribution’ (with M. H. G. Hoffmann, 2005); and ‘A historical phenomenology of mean and median’ (with K. P. E. Gravemeijer, 2006).
Abstract
Peirce's notions of diagrammatic reasoning and hypostatic abstraction are relevant to educational research in areas where diagrams and abstraction play an important role. In this paper, I analyze an example from statistics education in which diagrammatic reasoning created opportunities for hypostatic abstraction. For instance, where students initially characterized data points as being ‘spread out,’ they later said, ‘the spread is large.’ This is a prototypical example of hypostatic abstraction — taking a predicate as a new object that can have predicates itself. More generally, the notion of diagrammatic reasoning proved helpful to identify the key learning processes involved in learning to reason about statistical concepts.
About the author
Arthur Bakker (b. 1970). His research interests include statistics education, workplace learning, technology, history of statistics and semiotics. His recent publications include ‘Reasoning about shape as a pattern in variability’ (2004); ‘Diagrammatic reasoning as the basis for developing concepts: A semiotic analysis of students' learning about statistical distribution’ (with M. H. G. Hoffmann, 2005); and ‘A historical phenomenology of mean and median’ (with K. P. E. Gravemeijer, 2006).
© Walter de Gruyter
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- Educating the semiotic mind: Introduction to special issue on ‘Semiotics and education’
- Diagrammatic reasoning and hypostatic abstraction in statistics education
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- Semiosis as an educational instrument: The irrelevance of mediation and the relevance of social capital
- The complementarity of a representational and an epistemological function of signs in scientific activity
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- A preliminary examination of a theoretical model for researching educator beliefs
- Learners' idiosyncratic links as affordances for meaning making in the semiotic process
- Towards a semiotic theory of learning: Deleuze's philosophy and educational experience
- Regina Rex or, a semiotic fable from the end of education
- Reflections on semiotics, visual culture, and pedagogy
- Education à la Silhouette: The need for semiotically-informed curriculum consciousness
Articles in the same Issue
- Educating the semiotic mind: Introduction to special issue on ‘Semiotics and education’
- Diagrammatic reasoning and hypostatic abstraction in statistics education
- The give and take between semiotics and second-order cybernetics
- Conversational structures of ‘reports’ in writing class group work
- Semiosis as an educational instrument: The irrelevance of mediation and the relevance of social capital
- The complementarity of a representational and an epistemological function of signs in scientific activity
- Semiotics and classroom interaction: Mediated discourse, distributed cognition, and the multimodal semiotics of Maguru Panggul pedagogy in two Balinese Gamelan classrooms in the United States
- A preliminary examination of a theoretical model for researching educator beliefs
- Learners' idiosyncratic links as affordances for meaning making in the semiotic process
- Towards a semiotic theory of learning: Deleuze's philosophy and educational experience
- Regina Rex or, a semiotic fable from the end of education
- Reflections on semiotics, visual culture, and pedagogy
- Education à la Silhouette: The need for semiotically-informed curriculum consciousness
