1. Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson
Using Corrective Self-Explanation to Improve Students’ Skill at Solving Algebraic Equations
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson
4/15/2019
Pittsburgh Science of Learning Center

2. Placing Study within Robust Learning Framework
Primary research cluster?
Interactive communication, coordinative learning, refinement & fluency
Independent variable(s)?
IC: Reflective dialog, scripting collaboration, peer tutoring, peer observation of tutoring, …
CL: self-explanation, integrate conceptual & procedural, multi-representations, multi-modal, …
R&F: Feature focusing, example comparison, cognitive mastery, optimal spacing, …
Dependent variables used?
Normal post-test, long term retention, transfer, future learning
4/15/2019
Pittsburgh Science of Learning Center

3. The Educational Problem:
Misconceptions cause learning of incorrect or incomplete knowledge components for solving algebraic equations
The resulting knowledge components are not appropriate or useful for problems with certain features
4/15/2019
Pittsburgh Science of Learning Center

4. Example of Misconception
Does not include negatives as parts of terms
Thinks that negatives can enter and exit a phrase and the phrases can still be equivalent
4/15/2019
Pittsburgh Science of Learning Center

5. Example of resulting overgeneralized knowledge component
May be applying implicit correct knowledge component (with feature validity)
To remove a positive term, subtract it from both sides of the equation
Implicit incorrect knowledge component (missing features):
To remove a term, subtract it from both sides of the equation
4/15/2019
Pittsburgh Science of Learning Center

6. Improving student’s knowledge
Two important steps to improve knowledge (Siegler, 1996):
Weaken the incorrect knowledge component
Construct and strengthen correct knowledge component
Both can be accomplished with self-explanation (Chi, 2000)
4/15/2019
Pittsburgh Science of Learning Center

7. Examining two types of self-explanation
Self-explanation of correct examples
does not highlight situations in which the knowledge components are not applicable
Will not accomplish weakening of incorrect KCs
Self-explanation of incorrect examples (why they’re wrong, e.g., Siegler 2002) can weaken incorrect knowledge components
know that they’re wrong and why they’re wrong
4/15/2019
Pittsburgh Science of Learning Center

8. The educational question:
Will corrective self-explanation produce robust learning when combined with tutored practice in a real-world classroom setting?
4/15/2019
Pittsburgh Science of Learning Center

9. The scientific question:
What is the process of change that leads to robust learning?
Use Siegler’s (1996) dimensions of change (path, rate, source, breadth, and variability of change)
4/15/2019
Pittsburgh Science of Learning Center

10. Pittsburgh Science of Learning Center
Hypothesis
Corrective self-explanation combined with procedural practice will lead to robust learning through two processes:
Weaken low-feature validity knowledge components
Through new explicit knowledge about features and why the features make the KC inappropriate
Facilitate construction of high-feature validity knowledge components
4/15/2019
Pittsburgh Science of Learning Center

11. Corrective self-explanation (explanation of incorrect worked example)
4/15/2019
Pittsburgh Science of Learning Center

12. Pittsburgh Science of Learning Center
Typical self-explanation (explanation of correct worked example)
4/15/2019
Pittsburgh Science of Learning Center

13. Summary of Study design
Independent variable: Self-explanation (of correct or incorrect examples) exercises interspersed with existing Cognitive Tutor Algebra unit
2 x 2 Factorial Design
All treatment groups receive the same number of self-explanation exercises
Control for time between groups (self-explanation groups get less procedural practice)
Self-Explanation of Correct Examples No
Yes
“As-is” Control
Typical
Corrective
Typical + Corrective (half of each)
Self-Explanation of Incorrect Examples
4/15/2019
Pittsburgh Science of Learning Center

14. Pittsburgh Science of Learning Center
Dependent Variables
Paper & pencil posttest
Normal items (procedural)
Transfer items
Procedural format (problems with additional features)
Conceptual format (probing knowledge of features)
Embedded Learnlab-facilitated measures
Long-term retention
Log data from review portion of future unit; Are correct knowledge components applied?
Accelerated future learning
Log data from future unit (no treatment in place); examine learning curves
4/15/2019
Pittsburgh Science of Learning Center

15. Micro-level predictions
Self-Explanation of Correct Examples No
Yes
Increases implicit KCs (correct and incorrect)
Increases implicit and explicit KCs (correct and incorrect)
Increases implicit and explicit correct KCs
**Weakens incorrect KC’s
Self-Explanation of Incorrect Examples
Compared with tutored problem solving and typical self-explanation, corrective self explanation uniquely weakens incorrect KCs, leading to a relative increase in stronger, deeper, correct KCs
Expect strongest results in Corrective only group, due to more exposure to incorrect worked examples
4/15/2019
Pittsburgh Science of Learning Center

16. Which of the 8 main paths probably explain the results?
Compared to regular tutored problem solving and typical self-explanation, self-explanation probably increased the number and strength of correct, deep KCs
These are expected to lead to better scores on normal items as well as robust learning measures.
Sense- making outcomes:
More correct conceptual KCs
Deeper KCs facilitate rederivation
Deeper KCs facilitate adaptation
Deeper KCs  learning by oneself
Foundational skill outcomes:
More correct skill KCs
Stronger KCs
More general KCs
Stronger KCs leave cognitive headroom
Measurable outcomes:
Higher normal test scores
Longer retention
Further transfer
Better future learning
4/15/2019
Pittsburgh Science of Learning Center

17. Macro-Level Explanation
Corrective self-explanation leads to coordination of explicit and implicit knowledge, which supports sense-making; improving foundational skills & robust learning outcomes
Macro-Level Explanation
Robust Learning
Outcomes: Knowledge, reasoning & learning processes
Foundational Skills
Sense-Making
Learning Processes:
Construction, elaboration, discrimination
Refinement of Features
Co-Training
Streng-thening
Instructional Processes: (independent variables or treatments)
Multiple inputs, representations, strategies … Corrective self-explanation
Tutorial dialogue, peer collaboration …
Feedback, example variability, authenticity …
Schedules, part training …

18. Pittsburgh Science of Learning Center
An additional goal:
Examine individual (or group-level) differences in pretest knowledge on the effectiveness of the treatment
Students with good explicit knowledge may not need the treatment
Students with little background knowledge (e.g. not even implicit incorrect) may not be ready to benefit from the treatment (e.g., Renkl’s work)
4/15/2019
Pittsburgh Science of Learning Center