Sowing the seeds of algebraic generalization: designing epistemic affordances for an intelligent microworld

This paper describes the design of a mathematical microworld to tackle the persistent difficulties that secondary school students have with the idea of algebraic generalization, which is a key stumbling block in secondary‐school mathematics classrooms. Our focus is to characterize algebraic ways of...

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Published in:Journal of computer assisted learning 2013-02, Vol.29 (1), p.68-84
Main Authors: Mavrikis, M., Noss, R., Hoyles, C., Geraniou, E.
Format: Article
Language:English
Subjects:
Algebra
Blocking
CAI
Computer Assisted Instruction
design
Design engineering
epistemic affordances
Epistemology
Generalization
intelligent support
Intelligent Tutoring Systems
Learning
Mathematical models
Mathematics education
Mathematics Instruction
microworlds
Secondary School Students
Students
Symbols (Mathematics)
Tasks
Teaching Methods
Thinking Skills
Vignettes
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container_title Journal of computer assisted learning
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creator Mavrikis, M.
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Geraniou, E.
description This paper describes the design of a mathematical microworld to tackle the persistent difficulties that secondary school students have with the idea of algebraic generalization, which is a key stumbling block in secondary‐school mathematics classrooms. Our focus is to characterize algebraic ways of thinking and to design both affordances of the system as well as suitable tasks and pedagogies that provide a substrate of activity and experience for the teaching and learning of algebraic generalizations. Using as reference illustrative cases of 12 to 13‐year‐old students' interaction with the microworld, we demonstrate the strong interplay between epistemology and the design of the microworld and draw conclusions regarding its potential to support the development of algebraic ways of thinking.
doi_str_mv 10.1111/j.1365-2729.2011.00469.x
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source Wiley-Blackwell Read & Publish Collection; ERIC
subjects Algebra
Blocking
CAI
Computer Assisted Instruction
design
Design engineering
epistemic affordances
Epistemology
Generalization
intelligent support
Intelligent Tutoring Systems
Learning
Mathematical models
Mathematics education
Mathematics Instruction
microworlds
Secondary School Students
Students
Symbols (Mathematics)
Tasks
Teaching Methods
Thinking Skills
Vignettes
title Sowing the seeds of algebraic generalization: designing epistemic affordances for an intelligent microworld
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