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Katie McEldoon, Kelley Durkin
& Bethany Rittle-Johnson
1
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 practice2
Conceptually Oriented Activity:Self-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)
3
Conceptually Oriented Activity:Self-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?
6
Hypotheses1. What is the learning benefit of
completing self-explanation prompts?
1. What is the learning benefit of solving additional practice problems?
1. Which use of this additional instructional time is the most beneficial for student learning?
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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
Study Design
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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
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 9
Design Participants: 75 students in grades 2, 3, and 4
Procedure
Pre Test (paper & pencil)
Inclusion Criterion: <80% on pretest
Intervention (one on one)
Procedural Instruction
Practice Problems
Post Test (immediate)
Retention Test (two weeks)
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Manipulation Here!
• Pretest, Immediate Posttest, & Retention Test (Rittle-Johnson, Matthews, Taylor & McEldoon, 2011)
1.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
2.Conceptual Knowledge Section•Meaning of the Equal Sign
•Recognizing Valid Equation Structures
Assessments
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Intervention: Procedural Instruction
6 + 4 + 9 = 6 + __
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• Instructed students on Add-Subtract strategy (Perry, 1991; Rittle-Johnson, 2006)
• Students asked to solve
• Accuracy Feedback
• Two Instructional Problems
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
14
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
Intervention: Self-Explanation Prompts
3 + 4 + 8 = 15 + 8Jacob got 15, which is a wrong answer.
3 + 4 + 8 = 7 + 8Hannah 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?
15(Siegler, 2002; Rittle-Johnson 2006)
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
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No differences by condition
No gains during additional practice problems
Low strategy Invention
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 = + 820
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
21
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
22
Procedural Learning- Correct
23
Procedural Learning- Not Correct
24No Significant Differences
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
25
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 = __ + 326
Procedural Transfer- Correct
27
Procedural Transfer- Not Correct
28
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
29
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
30
Benefits of Additional Instructional Time
1. What is the learning benefit of completing self-explanation prompts?
1. What is the learning benefit of solving additional practice problems?
1. Which use of this additional instructional time is the most beneficial for student learning?
31
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
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 32
http://peabody.vanderbilt.edu/earlyalgebra.xml
Laura McLean
Marci DeCaro
Kristin Tremblay
Maryphyllis Crean
Maddie Feldman
The Children’s 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.
33
Conceptual Strategy Use
Perhaps one mechanism is the early adaptation of a conceptually oriented problem solving strategy
34
Explanation Quality
35
All Procedural Items- Correct
36No Significant Differences
All Procedural Items- Not Correct
37
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
38
Conceptual Knowledge
39
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
40
Control Self ExplainPractice Problem 1 Practice Problem 1
Self-ExplainPractice Problem 2 Practice Problem 2
Self-ExplainPractice Problem 3 Practice Problem 3
Self-ExplainPractice Problem 4 Practice Problem 4
Self-ExplainPractice Problem 5 Practice Problem 5
Self-ExplainPractice Problem 6 Practice Problem 6
Self-Explain