Making the Most of Instructional Time: The Benefit of Self-Explanation

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Making the Most of Instructional TimeThe
Benefit of Self-Explanation

• Katie McEldoon, Kelley Durkin
  Bethany Rittle-Johnson

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Instructional Time

• Push to spend more time on topics to increase
  depth of learning (Hu, 2010)
• Instructional time is limited
• Need to utilize this limited time with the most
  effective learning activities
• In math classrooms, students spend a lot of time
  practicing skills (Hiebert et al., 2003)
• How is this instructional time best used?
• Scaffolding the practice with a conceptually
  oriented learning activity
• Completing additional practice

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Conceptually Oriented ActivitySelf-Explanation

• Prompting students to generate explanations to
  themselves in an attempt to make sense of new
  information (Chi, 2000)
• Many domains e.g. Biology, reading, computer
  programming, electrical engineering
• Mathematics (e.g., Atkinson, Renkl, Merrill,
  2003)
• Within mathematics, self-explanation has been
  shown to increase both learning and transfer of
  knowledge to novel tasks (e.g., Rittle-Johnson
  2006 Atkinson, Derry, Renkl Wortham, 2000)

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Conceptually Oriented ActivitySelf-Explanation

• Mechanisms of Self-Explanation
• Integrates new and existing knowledge (Chi et al.
  1994)
• Correction of current mental model (Chi et al.
  1994)
• Inference rules ? proceduralized into usable
  skills (Chi et al. 1989)
• Fosters generalization (Lombrozo 2006
  Rittle-Johnson, 2006)
• Procedural and conceptual knowledge help each
  other grow (Rittle-Johnson Alibali, 1999
  Rittle-Johnson, Siegler, Alibali, 2001)
• Competence in mathematics (Hiebert, 1986)

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Benefit of Extra Practice

• Greater skill at applying initial problem solving
  strategy (Chi, Glaser, Farr 1988 Ericsson,
  Krampe, Tesch-Romer, 1993)
• Strengthen correct strategy application, weaken
  incorrect strategies (Seigler, 2002)
• Problem solving procedure becomes more
  automatized
• Leaving more working memory free to acquire new
  and more efficient strategies (Logan 1990
  Schneider, Shiffrin, 1977 Anderson, 1982, 1983,
  1987 Rosenbloom Newell, 1987)

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Research Questions

1. What is the learning benefit of completing
   self-explanation prompts?
2. What is the learning benefit of solving
   additional practice problems?
3. Which use of this additional instructional time
   is the most beneficial for student learning?

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Hypotheses

• What is the learning benefit of completing
  self-explanation prompts?
• What is the learning benefit of solving
  additional practice problems?
• Which use of this additional instructional time
  is the most beneficial for student learning?

Self-explanation prompts will result in greater
procedural knowledge in familiar and novel
problem types Additional practice problems will
result in greater procedural knowledge in
familiar problem types Self-explanation will be
most beneficial for student learning
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Study Design
Control Self-Explanation Additional Practice
Practice Problem 1 Practice Problem 1 Practice Problem 1
Practice Problem 2 Self-Explain Practice Problem 2
Practice Problem 3 Practice Problem 2 Practice Problem 3
Practice Problem 4 Self-Explain Practice Problem 4
Practice Problem 5 Practice Problem 3 Practice Problem 5
Practice Problem 6 Self-Explain Practice Problem 6
Practice Problem 4 Practice Problem 7
Self-Explain Practice Problem 8
Practice Problem 5 Practice Problem 9
Self-Explain Practice Problem 10
Practice Problem 6 Practice Problem 11
Self-Explain Practice Problem 12
Additional Instructional Time
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Learning Domain Math Equivalence

• The notion that the equal sign means that two
  sides of an equation are equivalent
• 4 2 3 ___ 6
• (McNeil, 2008)
• Many children view the equal sign operationally,
  as a command to carry out arithmetic operations
  (Baroody Ginsburg, 1983 Carpenter, et al.,
  2003 McNeil Alibali, 2005)
• 4 2 3 _9_ 6

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Design

• Participants 75 students in grades 2, 3, and 4
• Procedure
• Pre Test (paper pencil)
• Inclusion Criterion lt80 on pretest
• Intervention (one on one)
• Procedural Instruction
• Practice Problems
• Post Test (immediate)
• Retention Test (two weeks)

? Manipulation Here!
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Assessments

• Pretest, Immediate Posttest, Retention Test
• (Rittle-Johnson, Matthews, Taylor McEldoon,
  2011)
• Procedural Knowledge Section
• Solving Open Equations 2 5 8 ___ 8
• Learning Items 3 4 6 ___
  4
• Transfer Items 8 ___ 8 6 4
• 6 - 4 3 ___ 3
• Conceptual Knowledge Section
• Meaning of the Equal Sign
• Recognizing Valid Equation Structures

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Intervention Procedural Instruction

• 6 4 9 6 __

• Instructed students on Add-Subtract strategy
  (Perry, 1991 Rittle-Johnson, 2006)
• Students asked to solve
• Accuracy Feedback
• Two Instructional Problems

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Intervention Practice Problems

• What number goes in the box?
• 3 4 8 ? 8
• How did you get your answer?
• Right/Actually, 7 is the right answer.

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Study Design
Control Self-Explanation Additional Practice
Practice Problem 1 Practice Problem 1 Practice Problem 1
Practice Problem 2 Self-Explain Practice Problem 2
Practice Problem 3 Practice Problem 2 Practice Problem 3
Practice Problem 4 Self-Explain Practice Problem 4
Practice Problem 5 Practice Problem 3 Practice Problem 5
Practice Problem 6 Self-Explain Practice Problem 6
Practice Problem 4 Practice Problem 7
Self-Explain Practice Problem 8
Practice Problem 5 Practice Problem 9
Self-Explain Practice Problem 10
Practice Problem 6 Practice Problem 11
Self-Explain Practice Problem 12
Additional Instructional Time
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Intervention Self-Explanation Prompts
3 4 8 15 8 Jacob got 15, which is a
wrong answer. 3 4 8 7 8 Hannah got
7, which is the right answer.

• HOW do you think Jacob got 15?
• WHY do you think 15 is a wrong answer?
• HOW do you think Hannah got 7?
• WHY do you think 7 is the right answer?

(Siegler, 2002 Rittle-Johnson 2006)
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Posttest Retention Test

• Immediate Posttest
• Paper pencil
• Approx. 25 minutes
• Retention test
• Average of two weeks after intervention session
• Paper pencil
• Approx. 25 minutes

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Instructional Time

• Intervention Total Problem Solving Time
• Average Problem Solving Time per Problem 26s

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Intervention Accuracy

• No differences by condition
• No gains during additional practice problems
• Low strategy Invention

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Procedural Knowledge Analysis

• Procedural knowledge
• Correct action sequences or strategies for
  solving problems (Rittle-Johnson Alibali, 1999
  Anderson 1993)
• Assessment Procedural Knowledge Section
• Solve equations with operations on both sides
• 4 5 8 ? 8
• Students asked to show their work
• Coded for strategy use

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Coding Examples

• Correct Codes (5)
• Equalizer Sets up the two sides as equal
• 4 5 8 9 8
• 4 5 8 17
• 9 8 17
• Incorrect Codes (3)
• Add to Equal- adds up all numbers before equals
  sign and puts that number in blank
• 4 5 8 17 8
• 4 5 8 17
• Blank 4 5 8 ? 8

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Results Roadmap

• Procedural Knowledge Items
• Learning Items
• Transfer Items
• Student Performance
• Correct Strategy Use
• Incorrect Strategy Use
• Unattempted Items
• Means for post and retention test scores

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Procedural Learning Items

• Same equation structure as the intervention items
• Same learned problem solving strategies can be
  applied to solve
• 7 6 4 7 ___
• 3 6 5 __ 5

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Procedural Learning- Correct
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Procedural Learning- Not Correct
No Significant Differences
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Procedural Learning Summary

• There is a benefit of both self-explanation and
  additional practice
• Increased correct strategy use
• Decreased incorrect strategy use
• No differential performance between additional
  self-explanation and additional practice

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Procedural Transfer Items

• Items that are unlike those in the intervention
  session
• different equation format
• includes subtraction
• Require a modification of the learned strategy in
  order to correctly solve
• 8 __ 8 6 4
• 6 - 4 3 __ 3

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Procedural Transfer- Correct
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Procedural Transfer- Not Correct
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Procedural Transfer Summary

• Self-Explanation benefitted procedural transfer
• Increased correct strategy use
• Decreased incorrect strategy use
• Self-Explanation leave as many items blank as the
  control, but they are getting more of the
  attempted items correct
• Additional Practice increases the number of novel
  problems attempted, even if they may not get them
  correct

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Assessment Results Summary

• Procedural Learning
• Self-explaining and additional practice
  conditions had better performance than control
• More correct, less incorrect strategy use
• Procedural Transfer
• Self-Explanation group had the best performance
• More correct, less incorrect strategy use
• Additional practice students attempted more novel
  items

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Benefits of Additional Instructional Time

• What is the learning benefit of completing
  self-explanation prompts?
• What is the learning benefit of solving
  additional practice problems?
• Which use of this additional instructional time
  is the most beneficial for student learning?

Self-explanation prompts resulted in greater
procedural learning and transfer Additional
practice problems resulted in greater procedural
learning Self-explanation is the most beneficial
for student learning
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Conclusions

• Self-explaining during math learning increases
  both procedural learning and transfer
• This benefit is not just due to the additional
  time on task (Aleven Koedinger, 2002 Matthews
  Rittle-Johnson, 2009)
• Same amount of practice as Control
• Same amount of time as Additional Practice
• Goal of instruction is to allow students to
  transfer their knowledge to novel problems
• Inert Knowledge Problem (Bransford, Brown,
  Cocking, 2001)
• Self-Explanation is a worthwhile use of
  instructional time

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Acknowledgements

• http//peabody.vanderbilt.edu/earlyalgebra.xml
• Laura McLean
• Marci DeCaro
• Kristin Tremblay
• Maryphyllis Crean
• Maddie Feldman
• The Childrens Learning Lab
• The first author is supported by a predoctoral
  training grant provided by the Institute of
  Education Sciences, U.S. Department of Education,
  through Grant R305B040110 to Vanderbilt
  University. The opinions expressed are those of
  the authors and do not represent views of the
  U.S. Department of Education.

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Conceptual Strategy Use

• Perhaps one mechanism is the early adaptation of
  a conceptually oriented problem solving strategy

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Explanation Quality
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All Procedural Items- Correct
No Significant Differences
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All Procedural Items- Not Correct
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All Procedural Items Summary

• No differences in correct strategy use
• However, self-explanation decreased the amount of
  incorrect strategy use
• They were leaving more items unattempted instead

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Conceptual Knowledge
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Compared to What

• Same number of problems, same amount of time
• E.g. Atkinson, Renkl, Merrill, 2003 Hilbert
  Renkl, Kessler Reiss, 2008 de Bruin, Rikers
  Schmidt, 2007 Grosse Renkl, 2003 Mwangi
  Sweller, 1998

Control Self Explain
Practice Problem 1 Practice Problem 1
Self-Explain
Practice Problem 2 Practice Problem 2
Self-Explain
Practice Problem 3 Practice Problem 3
Self-Explain
Practice Problem 4 Practice Problem 4
Self-Explain
Practice Problem 5 Practice Problem 5
Self-Explain
Practice Problem 6 Practice Problem 6
Self-Explain