Using Corrective Self-Explanation to Improve Students’ Skill at Solving Algebraic Equations

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

10. 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 Pittsburgh Science of Learning Center

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

12. Typical self-explanation (explanation of correct worked example) 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 Self-Explanation of Incorrect Examples Pittsburgh Science of Learning Center

14. 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 Pittsburgh Science of Learning Center

15. Micro-level predictions Self-Explanation of Correct 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 Self-Explanation of Incorrect Examples 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. Pittsburgh Science of Learning Center

17. 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 Feedback, example variability, authenticity … Tutorial dialogue, peer collaboration … Schedules, part training …

18. 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) Pittsburgh Science of Learning Center