1. Using Mixed-Effects Modeling to Compare Different Grain-Sized Skill Models Mingyu Feng, Worcester Polytechnic Institute Neil T. Heffernan, Worcester Polytechnic Institute Murali Mani, Worcester Polytechnic Institute Cristina Heffernan, Worcester Public Schools

2. July 17th, 2006 AAA’06-W06 2 The “ASSISTment” System An e-assessment and e-learning system that does both ASSISTing of students and assessMENT (movie)movie  Massachusetts Comprehensive Assessment System “MCAS” Web-based system built on Common Tutoring Object Platform (CTOP) [1] [1] Nuzzo-Jones., G. Macasek M.A., Walonoski, J., Rasmussen K. P., Heffernan, N.T., Common Tutor Object Platform, an e-Learning Software Development Strategy, WPI technical report. WPI-CS-TR-06-08. We are giving away accounts !

3. July 17th, 2006 AAA’06-W06 3 ASSISTment We break multi-step problems into “scaffolding questions” “ Hint Messages ” : given on demand that give hints about what step to do next “ Buggy Message ” : a context sensitive feedback message Skills  The state reports to teachers on 5 areas  We seek to report on more and finer grain-sized skills Demo (two triangles problem)two triangles problem (Demo/movie) The original question a. Congruence b. Perimeter c. Equation-Solving The 1 st scaffolding question Congruence The 2 nd scaffolding question Perimeter A buggy message A hint message Geometry

4. July 17th, 2006 AAA’06-W06 4 How was the Skill Models Created

5. July 17th, 2006 AAA’06-W06 5 How was the Skill Models Created [2] Pardos, Z. A., Heffernan, N. T., Anderson, B., & Heffernan C. (2006). Using Fine-Grained Skill Models to Fit Student Performance with Bayesian Networks. Workshop in Educational Data Mining held at the Eight International Conference on Intelligent Tutoring Systems. Taiwan. 2006. Multi-mapped model (WPI-5) vs. single- mapped model (MCAS-5) ?

6. July 17th, 2006 AAA’06-W06 6 Previous Work on Skill Models Fine grained skill models in reporting  Teachers get reports that they think are credible and useful. [3] [3] Feng, M., Heffernan, N.T. (in press). Informing Teachers Live about Student Learning: Reporting in the Assistment System. To be published in Technology, Instruction, Cognition, and Learning Journal Vol. 3. Old City Publishing, Philadelphia, PA. 2006

7. July 17th, 2006 AAA’06-W06 7

8. July 17th, 2006 AAA’06-W06 8

9. July 17th, 2006 AAA’06-W06 9 Previous Work on Skill Models Tracking skill performance over time [4][5] Number Sense [4] Feng, M., Heffernan, N.T., & Koedinger, K.R. (2006). Addressing the Testing Challenge with a Web-Based E-Assessment System that Tutors as it Assesses. Proceedings of the Fifteenth International World Wide Web Conference. pp. 307-316. ACM Press: New York, NY. 2006. [5] Feng, M., Heffernan, N.T., & Koedinger, K.R. (2006). Predicting state test scores better with intelligent tutoring systems: developing metrics to measure assistance required. In Ikeda, Ashley & Chan (Eds.). Proceedings of the Eight International Conference on Intelligent Tutoring Systems. Springer-Verlag: Berlin. pp. 31-40. 2006.

10. July 17th, 2006 AAA’06-W06 10 In this work, we compare different grain-sized skill models  By comparing the accuracy of their prediction of state test score

11. July 17th, 2006 AAA’06-W06 11 Research Questions RQ1: Would adding response data to scaffolding questions help us do a better job of tracking students’ knowledge? RQ2: How does the finer-grained skill model (WPI-78) do on estimating external test scores comparing to the skill model with only 5 categories (WPI-5) and the one even with only one category (WPI-1)? RQ3:Does introducing item difficulty information help to build a better predictive model?

12. July 17th, 2006 AAA’06-W06 12 Data Source 497 students of two middle schools Students used the ASSISTment system every other week from Sep. 2004 to May 2005 Real state test score in May 2005 Item level online data  students’ binary response (1/0) to items that are tagged in different skill models Some statistics  Average usage: 7.3 days, Minimum usage: 6 days  138,000 data points (43,000 original data points)  Average question answered Original: 87, Scaffolding: 189 Online data of 700 8 th grade students available for researchers! If you want access, talk to Neil Heffernan and Kenneth Koedinger.

13. July 17th, 2006 AAA’06-W06 13 How is the Data Organized?

14. July 17th, 2006 AAA’06-W06 14 Approach Fit mixed-effects logistic regression model on the longitudinal online data  using skills as a factor  predicting prob(response=1) on an item tagged with certain skill at certain time  The fitted model gives learning parameters (initial knowledge + learning rate) of each skill of individual student Predict State Test Scores  Identify skills associated with each test item in all skill models  Student full score = item fractional score (prob(response=1)) Compare skill models by Mean Absolute Difference (MAD) and %Err (= MAD/full score)

15. July 17th, 2006 AAA’06-W06 15 Data Preprocessing Strategies Scaffolding Credit  Scaffolding only shows in case of wrong answer to original  We assume correct responses to all scaffolding questions if a student correctly answered the original one Partial Blame  Only blame the skill of the worst performance overall 1 1

16. July 17th, 2006 AAA’06-W06 16 RQ1: Will Scaffolding Response Help?  Why? Using more training data Deal with credit-blame issue better More “identifiability” per skill Scaffolding questions provide valuable information [4][5][6][7] Real MCAS score Assistment Predicted Score (WPI-78) Orig.Orig. + Scaffolds Mary2922.9327.05 Tom2819.3825.35 … Sue2518.5824.10 Dick2216.5721.31 Harry3318.6628.12 [6] Walonoski, J., Heffernan, N.T. (2006). Detection and Analysis of Off-Task Gaming Behavior in Intelligent Tutoring Systems. In Ikeda, Ashley & Chan (Eds.). Proceedings of the Eighth International Conference on Intelligent Tutoring Systems. Springer-Verlag: Berlin. pp. 382-391. 2006 [7] Walonoski, J., Heffernan, N.T. (2006). Prevention of Off-Task Gaming Behavior in Intelligent Tutoring Systems. In Ikeda, Ashley & Chan (Eds.). Proceedings of the Eighth International Conference on Intelligent Tutoring Systems. Springer-Verlag: Berlin. pp. 722-724. 2006. Absolute Difference between Real Score and Assistment Predicted Score Orig.Orig. + Scaffolds 6.061.35 8.621.57 … 6.420.06 5.430.78 14.346.63 MAD6.034.121 %Error 17.75%12.12% Answer: Yes!

17. July 17th, 2006 AAA’06-W06 17 RQ2: Does finer grained model predict better? Real MCAS score Assistment Predicted Score (scaffolding response used) Skill ModelsWPI-1WPI-5WPI-78 Mary2928.5927.6527.05 Tom2827.5826.4325.35 … Sue2526.5624.9424.10 Dick2223.7022.7821.31 Harry3327.5426.3728.12 Absolute Difference between Real Score and Assistment Predicted Score WPI-1WPI-5WPI-78 0.411.351.95 0.421.572.65 … 1.560.060.90 1.700.780.69 5.466.634.88 > > > > P-values of both Paired t-tests are below 0.05 Is 12.12% any good for assessment purpose? MCAS-simulation result: 11.12% MAD4.5524.3434.121 %Error13.39%12.77%12.12%

18. July 17th, 2006 AAA’06-W06 18 Conclusion Recall RQ1, RQ2. Positive answer to both RQ1 and RQ2. RQ3: Item difficulty was introduced as a factor to improve the predictive models. We ended up with better internally fitted models, but surprisingly no significant enhancement on the prediction of state test.

19. Leena RAZZAQ*, Mingyu FENG, Goss NUZZO-JONES, Neil T. HEFFERNAN,* Kenneth KOEDINGER+, Brian JUNKER+, Steven RITTER, Andrea KNIGHT+, Edwin MERCADO*, Terrence E. TURNER, Ruta UPALEKAR, Jason A. WALONOSKI Michael A. MACASEK, Christopher ANISZCZYK, Sanket CHOKSEY, Tom LIVAK, Kai RASMUSSEN Some of the ASSISTMENT TEAM (2004-2005) * This research was made possible by the US Dept of Education, Institute of Education Science, "Effective Mathematics Education Research" program grant #R305K03140, the Office of Naval Research grant # N00014- 03-1-0221, NSF CAREER award to Neil Heffernan, and the Spencer Foundation. Authors Razzaq and Mercado were funded by the National Science Foundation under Grant No. 0231773. All the opinions in this article are those of the authors, and not those of any of the funders. Carnegie Learning