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• ISBN 10:0415556740 

• ISBN 13:9780415556743

• Author:Lieven Verschaffel, Erik de Corte, Ton de Jong, Jan Elen 

Use of Representations in Reasoning and Problem Solving
Analysis and Improvement
Within an increasingly multimedia focused society, the use of external representations in learning, teaching and communication has increased dramatically. Whether in the classroom, university or workplace, there is a growing requirement to use and interpret a large variety of external representational forms and tools for knowledge acquisition, problem solving, and to communicate with others. Use of Representations in Reasoning and Problem Solving brings together contributions from some of the world’s leading researchers in educational and instructional psychology, instructional design, and mathematics and science education to document the role which external representations play in our understanding, learning and communication. Traditional research has focused on the distinction between verbal and non-verbal representations, and the way they are processed, encoded and stored by different cognitive systems. The contributions here challenge these research findings and address the ambiguity about how these two cognitive systems interact, arguing that the classical distinction between textual and pictorial representations has become less prominent. The contributions in this book explore: how we can theorise the relationship between processing internal and external representations what perceptual and cognitive restraints can affect the use of external representations how individual differences affect the use of external representations how we can combine external representations to maximise their impact how we can adapt representational tools for individual differences. Using empirical research findings to take a fresh look at the processes which take place when learning via external representations, this book is essential reading for all those undertaking postgraduate study and research in the fields of educational and instructional psychology, instructional design and mathematics and science education.
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Use of Representations in Reasoning and Problem Solving Analysis and Improvement New Perspectives on Learning and Instruction 1st Table of contents:

Part I Theoretical and empirical analyses of psychological processes in thinking and learning with representations
Chapter 1 Creative thinking and problem solving with depictive and descriptive representations
Introduction
Different views on thinking and problem solving
Gestalt psychology: finding the right representation
Psychology of information processing: finding the right path
Synthesis: combining structure and process
The semiotics of representations
The representational and inferential power of descriptions and depictions
External and internal representations in comprehension, thinking and problem solving
Descriptive and depictive representations in science education and in mathematics
Science education in physics
Mathematics education
Conclusion: teaching for flexibility in thinking and problem solving
Note
References
Chapter 2 Instructional considerations in the use of external representations
Existing research on the comprehension of text and pictures
Two kinds of external representations: perceptually based depictions and conceptual models
Conceptual models are difficult to understand
Why are conceptual models difficult for students to understand?
Instruction to help students understand conceptual models
Concluding remarks
Acknowledgement
Note
References
Chapter 3 Critical thinking about biology during web page reading
Introduction
Epistemic evaluation of web sources
Epistemic beliefs and web navigation
Eye tracking and web page reading
The present study
Research questions and hypotheses
Method
Participants
Material
Measures
Procedure
Results
Attention allocation and source authoritativeness
Attention allocation within each source
Attention allocation across sources
Attention allocation and individual differences
PRIOR KNOWLEDGE
EPISTEMIC BELIEFS
ARGUMENTATIVE REASONING SKILL
Discussion and conclusion
Note
References
Chapter 4 Representational flexibility in linear-function problems
Theoretical background
Representational fluency and flexibility in mathematical problem solving
Representational choices in mathematical problem solving
Design of the study
Participants
Task
Method
Procedure
Analysis
Task-based flexibility
Task×student-based flexibility
Results
Representational efficiency
Accuracy data
Speed data
Representational flexibility
Frequency of representational choice
Task-based flexibility
Task×student-based flexibility
Discussion
Representational efficiency
Representational flexibility
Implications for research
Implications for instruction
Notes
References
Chapter 5 Representations and proof
Introduction
Variety of approaches to a proof for the Isis problem
Empirical
Algebraic
Completing the rectangle (by analogy with completing the square)
Writing one variable as a function of the other
Unit fractions
Harmonic mean
A ‘silly’ equation
Considerations of equality/inequality
Geometrical
An experimental study: student teachers’ initial attempts to solve the problem and their ideas about proof
Generation of proofs
Evaluation of proofs
Links with theories of problem solving and proof
Theoretical and pedagogical implications
Theoretical implications
Pedagogical implications
Acknowledgement
References
Chapter 6 Secondary school students’ availability and activation of diagrammatic strategies for learning from texts
Introduction
Availability of diagrammatic strategies
Activation of diagrammatic strategies
Experiment 1: spontaneous and evoked diagram use
Method
Participants
Procedure
Material
Experimental manipulation
Coding
Results
Discussion
Experiment 2: the activation of diagrammatic strategies
Method
Participants
Materials
Procedure and design
Results and discussion
General discussion
Acknowledgements
Appendix: texts and test questions presented in the two experiments
Problem 1
Text
Most appropriate diagram: clusters
Questions
Problem 2
Text
Most appropriate diagram: no diagram
Questions
Problem 3
Text
Most appropriate diagram: hierarchical tree
Questions
Problem 4
Text
Most appropriate diagram: linear ordering
Questions
Problem 5
Text
Most appropriate diagram: linear ordering
Questions
Problem 6
Text
Most appropriate diagram: map
Questions
Problem 7
Text
Most appropriate diagram: two-dimensional representation
Questions
Problem 8
Text
Most appropriate diagram: Cartesian product in a two-dimensional representation
Questions
Problem 9
Text
Most appropriate diagram: two-dimensional representation
Questions
Problem 10
Text
Most appropriate diagram: Cartesian product in a two-dimensional representation
Questions
References
Part II Development of representational tools and evaluation of their effects on student learning
Chapter 7 Conceptual change in learning electricity
Introduction
Method
Design
Participants
Materials
Simulation
Real circuits
Worksheets
Procedure
Pre-test and post-test
Intervention
Data collection and analysis
Results
Cognitive conflicts and self-explanations in different learning conditions
Excerpt 1
SEQUENCE 1
SEQUENCE 2
Analogical encoding in the hybrid environment
Excerpt 2
Excerpt 3
Excerpt 4
SEQUENCE 1
SEQUENCE 2
Discussion
Acknowledgement
Notes
References
Chapter 8 Using static and dynamic visualisations to support the comprehension of complex dynamic phenomena in the natural sciences
Introduction
Drawbacks and advantages of static and dynamic visualisations
Transience
Visual complexity
Mental animation
Direct depiction of dynamic features
Empirical findings
Overview of experiments
Study 1: Conceptual understanding of the physics of fish locomotion
Study 2: Perceptual classification of fish locomotion
Study 3: Sequential versus simultaneous presentation of static visualisations
Study 4: Combining mobile learning with real-life experiences
Discussion
References
Chapter 9 The role of external representations in learning combinatorics and probability theory
Introduction
Representations in combinatorics and probability instruction
Types of knowledge
Study I: which format is most effective in a computer simulation?
Method
Participants
Design
Measures
KNOWLEDGE MEASURES
COGNITIVE LOAD
Instruction
Procedure
Results
Test results
Cognitive load
Conclusion
Study II: do representational tools support understanding in individual and collaborative learning?
Method
Participants
Design
Learning environment
Representational tools
Knowledge measures
Procedure
Data preparation
Results
Use of representational tools
Knowledge measures
Conclusion
Theoretical implications and general conclusions
Acknowledgement
References
Chapter 10 Symbolising and the development of meaning in computer-supported algebra education
Introduction
Visual representations
Emergent modelling
Emergent modelling applied to functions
Computer applet
Conclusion
Acknowledgements
Notes
References
Chapter 11 The ‘numbers are points on the line’ analogy
Problems of conceptual change in the development of the rational number concept
Cross-domain mapping: a mechanism to foster conceptual restructuring
Number and the line: a case of long-term cross-domain mapping
The school number line: affordances and limitations
Investigating the effect of the number line on students’ judgements about the number of numbers in an interval
Bridging the gap between discreteness and density with the ‘rubber line’
Concluding remarks
Acknowledgement
Note
References
Chapter 12 Use of external representations in science
Introduction
Prior knowledge activation
The use of external representations in prior knowledge activation
Dimensions of external representations
Verbal and pictorial external representations
Provided and self-constructed external representations
Prompting prior knowledge activation
Reinforcing prior knowledge activation
External representations, prior knowledge activation, and level of prior knowledge
General discussion
References
Chapter 13 Visualisation of argumentation as shared activity
Introduction
Representational guidance of two argumentative maps
The COSAR project
Method
Design
Participants
Task
Analyses
Results
Quality of essays
Online collaboration
Conclusions for COSAR project
The CRoCiCL project
Method
Design
Participants
CSCL environment: VCRI
Task
Analyses
Results
Quality of constructed argumentative diagrams
Quality of essays
Post-test performance
Online collaboration
Conclusions for the CRoCiCL project
Conclusions and discussion
References
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Use of Representations,Reasoning and Problem, Lieven Verschaffel, Erik de Corte, Ton de Jong, Jan Elen