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Using Anticipatory Diagrammatic Self-explanation to Support Learning and Performance in Early Algebra
Tomohiro Nagashima1, Anna N. Bartel2, Gautam Yadav1, Stephanie Tseng1,
Nicholas A. Vest2, Elena M. Silla2, Martha W. Alibali2, & Vincent Aleven1
1Carnegie Mellon University , 2University of Wisconsin - Madison
tomonagashima
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Background
Self-explanation is an established effective learning strategy
(Bisra et al., 2018; Chi et al., 1989; Rittle-Johnson et al., 2017)
From Understanding How We Learn; A Visual Guide By Yana Weinstein and Megan Sumeracki, with Illustrations by Oliver Caviglioli, taken from https://www.learningscientists.org/blog/2020/2/20-1
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Background
Self-explanation is an established effective learning strategy
(Bisra et al., 2018; Chi et al., 1989; Rittle-Johnson et al., 2017)
From Understanding How We Learn; A Visual Guide By Yana Weinstein and Megan Sumeracki, with Illustrations by Oliver Caviglioli, taken from https://www.learningscientists.org/blog/2020/2/20-1
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Background
Self-explanation is an established effective learning strategy
(Bisra et al., 2018; Chi et al., 1989; Rittle-Johnson et al., 2017)
From Understanding How We Learn; A Visual Guide By Yana Weinstein and Megan Sumeracki, with Illustrations by Oliver Caviglioli, taken from https://www.learningscientists.org/blog/2020/2/20-1
Designing effective self-explanation is hard!
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Background
Scaffolding self-explanation is a challenging design problem (Bisra et al., 2018)
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Background
Scaffolding self-explanation is a challenging design problem (Bisra et al., 2018)
How to support both learning and problem-solving performance (e.g., error rate, time spent)?
From Long, Y., & Aleven, V. (2017). Enhancing learning outcomes through self-regulated learning support with an open learner model. User Modeling and User-Adapted Interaction, 27(1), 55-88.
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Background
Scaffolding self-explanation is a challenging design problem (Bisra et al., 2018)
How to support both learning and problem-solving performance (e.g., error rate, time spent)?
From Long, Y., & Aleven, V. (2017). Enhancing learning outcomes through self-regulated learning support with an open learner model. User Modeling and User-Adapted Interaction, 27(1), 55-88.
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Design: Intelligent Tutoring System (ITS) for Middle-school Algebra
Anticipatory Diagrammatic Self-explanation: learners “explain” their future problem-solving steps
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Design: Intelligent Tutoring System (ITS) for Middle-school Algebra
Anticipatory Diagrammatic Self-explanation: learners “explain” their future problem-solving steps
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Design: Intelligent Tutoring System (ITS) for Middle-school Algebra
Anticipatory Diagrammatic Self-explanation: learners “explain” their future problem-solving steps
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Design: Intelligent Tutoring System (ITS) for Middle-school Algebra
Anticipatory Diagrammatic Self-explanation: learners “explain” their future problem-solving steps
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Design: Intelligent Tutoring System (ITS) for Middle-school Algebra
Anticipatory Diagrammatic Self-explanation: learners “explain” their future problem-solving steps
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From Long, Y., & Aleven, V. (2017). Enhancing learning outcomes through self-regulated learning support with an open learner model. User Modeling and User-Adapted Interaction, 27(1), 55-88.
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Design: Designing for both Learning and Performance
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Design: Designing for both Learning and Performance
to support conceptual understanding and strategic decision-making
(Booth & Koedinger, 2012; Rau, 2017)
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Design: Designing for both Learning and Performance
to support conceptual understanding and strategic decision-making
(Booth & Koedinger, 2012; Rau, 2017)
Tape diagrams
(Bartel et al., 2021; Murata, 2008;
Nagashima, Yang, et al. 2010)
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Design: Designing for both Learning and Performance
to support conceptual understanding and strategic decision-making
(Booth & Koedinger, 2012; Rau, 2017)
Tape diagrams
(Bartel et al., 2021; Murata, 2008;
Nagashima, Yang, et al. 2010)
2. Contrasting Cases
to support understanding of correct and strategic problem-solving steps through explicit comparisons
(Schwartz et al., 2011)
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Design: Designing for both Learning and Performance
to support conceptual understanding and strategic decision-making
(Booth & Koedinger, 2012; Rau, 2017)
Tape diagrams
(Bartel et al., 2021; Murata, 2008;
Nagashima, Yang, et al. 2010)
2. Contrasting Cases
to support understanding of correct and strategic problem-solving steps through explicit comparisons
(Schwartz et al., 2011)
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Design: Designing for both Learning and Performance
to support conceptual understanding and strategic decision-making
(Booth & Koedinger, 2012; Rau, 2017)
Tape diagrams
(Bartel et al., 2021; Murata, 2008;
Nagashima, Yang, et al. 2010)
2. Contrasting Cases
to support understanding of correct and strategic problem-solving steps through explicit comparisons
(Schwartz et al., 2011)
3. Anticipative Reasoning
to support inference generation about strategic problem-solving steps, which would lead to efficient and effective learning
(Nagashima et al., 2021; Renkl, 1997)
What would be a good next step…?
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Design: Designing for both Learning and Performance
2. Contrasting Cases
3. Anticipative Reasoning
to support conceptual understanding and strategic decision-making
to support understanding of correct and strategic problem-solving steps through explicit comparisons
(Booth & Koedinger, 2012; Rau, 2017)
to support inference generation about strategic problem-solving steps, which would lead to efficient and effective learning
(Renkl, 1997)
What would be a good next step…?
(Schwartz et al., 2011)
Tape diagrams (Bartel et al., 2021; Murata, 2008; Nagashima, Yang, et al. 2010)
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Method: ”In-vivo” Classroom Research
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Method: ”In-vivo” Classroom Research
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Method: ”In-vivo” Classroom Research
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Method: ”In-vivo” Classroom Research
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Method: ”In-vivo” Classroom Research
No-Diagram condition: Tutor with no anticipatory diagrammatic self-explanation
Results: Learning
Did students learn from pretest to posttest?
*
No significant gains between conceptual or procedural knowledge pretest/posttest as a function of condition
No significant overall gain in procedural knowledge from pretest to posttest
Significant overall gain in conceptual knowledge from pretest to posttest
Results (Learning):
Did students learn from pretest to posttest?
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Results (Learning):
What strategies did students use when solving problems?
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Results (Learning):
What strategies did students use when solving problems?
Strategy name | Description |
Algebra | Student uses algebraic manipulations to find an answer |
Unwind | Student works backward using inverse operations to find an answer |
Guess and Check | Student tests potential solutions by substituting different values |
Other | Student uses other non-algebraic strategies |
Answer Only | Student provides an answer without showing any written work |
No Attempt | Student leaves problem blank or explicitly indicates that she/he does not know how to solve the problem |
From Chu et al. (2017) & Koedinger et al. (2008)
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Strategy name | Description |
Algebra | Student uses algebraic manipulations to find an answer |
Unwind | Student works backward using inverse operations to find an answer |
Guess and Check | Student tests potential solutions by substituting different values |
Other | Student uses other non-algebraic strategies |
Answer Only | Student provides an answer without showing any written work |
No Attempt | Student leaves problem blank or explicitly indicates that she/he does not know how to solve the problem |
From Chu et al. (2017) & Koedinger et al. (2008)
Non-Algebra
strategies
Algebra
strategy
Results (Learning):
What strategies did students use when solving problems?
Students with anticipatory diagrammatic self-explanation made a transition to using a formal algebraic problem-solving strategy
(McNemar’s test; p < .01)
No Diagram Condition
Diagram Condition
Results (Learning):
What strategies did students use when solving problems?
Results: Performance
Did students benefit from the intervention during the learning task?
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Results: Performance within the ITS
Students with anticipatory diagrammatic self-explanation showed lower error rate on symbolic steps (only).
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Results: Performance within the ITS
Students with anticipatory diagrammatic self-explanation showed lower error rate on symbolic steps (only).
Diagram
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Results: Performance within the ITS
Students with anticipatory diagrammatic self-explanation showed lower error rate on symbolic steps (only).
Diagram
No-Diagram
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Results: Performance within the ITS
Students with anticipatory diagrammatic self-explanation showed lower error rate on symbolic steps (only).
Diagram
No-Diagram
How did students perform while problem-solving in the ITS?
Students with anticipatory diagrammatic self-explanation showed efficient learning:
Less time per step
Trend toward fewer hints
No difference problems solved
p = .03
p = .07
p = .60
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Discussion
Anticipatory diagrammatic self-explanation embedded in an ITS supported
both learning and performance:
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Discussion
Anticipatory diagrammatic self-explanation embedded in an ITS supported
both learning and performance:
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Discussion
Anticipatory diagrammatic self-explanation embedded in an ITS supported
both learning and performance:
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Contribution
Scaffolding self-explanation is a challenging design problem
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Contribution
Scaffolding self-explanation is a challenging design problem
Anticipatory diagrammatic self-explanation provides an example of how visual representations, contrasting cases, and anticipative reasoning can be integrated into effective scaffolding that helps students learn and perform well.
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Acknowledgements
This research was supported by NSF Award #1760922 and by the Institute of Education Sciences, U.S. Department of Education, through Award #R305B150003 to the University of Wisconsin–Madison. We thank Lauren E. Anthony, Max Benson, Susan Brunner, Octav Popescu, Jonathan Sewall, and all participating teachers and students.
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Thank you!
This research was supported by NSF Award #1760922 and by the Institute of Education Sciences, U.S. Department of Education, through Award #R305B150003 to the University of Wisconsin–Madison. We thank Lauren E. Anthony, Max Benson, Susan Brunner, Octav Popescu, Jonathan Sewall, and all participating teachers and students.
tomonagashima
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Thank you!
This research was supported by NSF Award #1760922 and by the Institute of Education Sciences, U.S. Department of Education, through Award #R305B150003 to the University of Wisconsin–Madison. We thank Lauren E. Anthony, Max Benson, Susan Brunner, Octav Popescu, Jonathan Sewall, and all participating teachers and students.
tomonagashima
(#470) Reasoning about Equations with Tape Diagrams: Insights from Students and Math Teachers
Tomorrow/later today!!
Anna Bartel