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All Papers for this Session are available at stat.cmu/~brian/NCME07

All Papers for this Session are available at http://www.stat.cmu.edu/~brian/NCME07. Uncertainty, Prediction and Teacher Feedback using an Online System that Teaches as it Assesses. Brian W. Junker.

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All Papers for this Session are available at stat.cmu/~brian/NCME07

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  1. All Papers for this Session are available athttp://www.stat.cmu.edu/~brian/NCME07 2007 NCME Symposium on Learning-Embedded Assessment

  2. Uncertainty, Prediction and Teacher Feedback using an Online Systemthat Teaches as it Assesses Brian W. Junker Thanks to Neil Heffernan, Ken Koedinger, Mingyu Feng, Beth Ayers, Nathaniel Anozie, Zach Pardos, and many others http://www.assistment.org Funding from US Department of Education, National Science Foundation (NSF), Office of Naval Research, Spencer Foundation, and the US Army 2007 NCME Symposium on Learning-Embedded Assessment

  3. The ASSISTments Project • Web-based 8th grade mathematics tutoring system • ASSIST with, and ASSESS, progress toward Massachusetts Comprehensive Assessment System Exam (MCAS) • Guide students through problem solving with MCAS released items • Predict students’ MCAS scores at end of year • Provide feedback to teachers (what to teach next?) • (Generalize to other States…) • Over 50 workers at Carnegie Mellon, Worcester Polytechnic Institute, Carnegie Learning, Worcester Public Schools 2007 NCME Symposium on Learning-Embedded Assessment

  4. The ASSISTment Tutor • Main Items: Released MCAS or “morphs” • Incorrect Main “Scaffold” Items • “One-step” breakdowns of main task • Buggy feedback, hints on request, etc. • All items coded by transfer model (Q-matrix) for knowledge components (KC’s) • Student records contain responses, timing data, bugs/hints, etc. • System tracks students through time, provides teacher reports per student & per class. • Predict MCAS Scores • KC Feedback: learned/not-learned, etc. 2007 NCME Symposium on Learning-Embedded Assessment

  5. This talk draws on two recent reports Predicting MCAS Scores – Summary/Review: Junker, B. W. (2006)."Using on-line tutoring records to predict end-of-year exam scores: experience with the ASSISTments project and MCAS 8th grade mathematics". To appear in Lissitz, R. W. (Ed.), Assessing and modeling cognitive development in school: intellectual growth and standard settings. Maple Grove, MN: JAM Press. KC Feedback – Some Current Progress: Anozie, N. & Junker, B. W. (2007). "Investigating the utility of a conjunctive model in Q matrix assessment using monthly student records in an online tutoring system". Paper to be presented at the Annual Meeting of the National Council on Measurement in Education, April 12, Chicago IL (K4; Thursday 8:15-10:15 Intercontinental Seville East). (These and all papers for this session are available at http://www.stat.cmu.edu/~brian/NCME07) 2007 NCME Symposium on Learning-Embedded Assessment

  6. Challenges: Predicting MCAS • The exact content of the MCAS exam is not known until months after it is given • The ASSISTments themselves are ongoing throughout the school year as students learn (from teachers, from ASSISTment interactions, etc.). 2007 NCME Symposium on Learning-Embedded Assessment

  7. Methods: Predicting MCAS • Regression approaches [Feng et al, 2006; Anozie & Junker, 2006; Ayers & Junker, 2006/2007]: • Percent Correct on Main Questions • Percent Correct on Scaffold Questions • Rasch proficiency on Main Questions • Online metrics (efficiency and help-seeking; e.g. Campione et al., 1985; Grigorenko & Sternberg, 1998) • Both end-of-year and “month-by-month” models • Bayes Net (DINA Model) approaches: • Predicting KC-coded MCAS questions from Bayes Nets (DINA model) applied to ASSISTments [Pardos, et al., 2006]; • Regression on number of KC’s mastered in DINA model [Anozie 2006] • HLM-style growth curve models • At the KC level [Feng, Heffernan & Koedinger, 2006] • At the total score level [Feng, Heffernan, Mani & Heffernan, 2006] 2007 NCME Symposium on Learning-Embedded Assessment

  8. Results: Predicting MCAS • Feng et al. (in press) estimate best-possible (11% of 54pt raw score) from split-half experiments with MCAS • Ayers & Junker (2007) reliability calculation suggests approximate bounds 1.05· MAD · 6.53. 2007 NCME Symposium on Learning-Embedded Assessment

  9. Conclusions: Predicting MCAS • Tradeoff: • Greater model complexity (DINA) can help [Pardos et al, 2006; Anozie, 2006]; • Accounting for question difficulty (Rasch), plus online metrics, does as well [Ayers & Junker, 2007] • Limits of what we can accomplish for prediction • MCAS reliability ¼ 0.91 • Typical ASSISTments ¼ 0.81 • If ASSISTments were perfectly reliable, approx. bound on MAD would be cut in half (3.40) 2007 NCME Symposium on Learning-Embedded Assessment

  10. Goal: KC Feedback • Providing feedback on • individual students • groups of students • Current teacher report: For each skill, report percent correct on all items for which that skill is hardest. • Can we do better? 2007 NCME Symposium on Learning-Embedded Assessment

  11. Challenges: KC Feedback • Different transfer models are used and expected by different stakeholders: • The MCAS itself is scaled using unidimensional IRT / Pct Correct • Description and design of the MCAS is based on • Five-strand model of mathematics (Number & Operations, Algebra, Geometry, Measurement, Data Analysis & Probability) • 39 “learning standards” nested within the five strands. • ASSISTment researchers have developed a transfer model involving up to 106 KC’s (WPI-106, Pardos et al., 2006) nested within the 39 learning standards • Scaffolding can be designed as optimal measures of single KC’s; or as optimal tutoring aids • When more than one transfer model is involved, scaffolds fail to line up with at least one of them! • Different students work through ASSISTments at different rates 2007 NCME Symposium on Learning-Embedded Assessment

  12. Methods: KC Feedback Pardos et al (2006): tend to prefer more KC’s for prediction; Anozie & Junker (2007): inference about KC inference (106 KC’s) Conjunctive binary-skills Bayes Net (Macready & Dayton, 1977; Haertel, 1989; Maris, 1999; Junker & Sijtsma DINA, 2001; etc.) 2007 NCME Symposium on Learning-Embedded Assessment

  13. Results: KC Feedback • Average percent of KC’s mastered: 30-40% • February dip reflects a recording error for main questions • Can also break this down by individual KC (next slide) 2007 NCME Symposium on Learning-Embedded Assessment

  14. Results: KC Feedback 2007 NCME Symposium on Learning-Embedded Assessment

  15. Results: KC Feedback • Prediction based on ‘ideal response’ (P[guess] = P[slip] =0) • Split-half cross-val accuracy 68-73% • Enough to help teachers decide what to teach next. 2007 NCME Symposium on Learning-Embedded Assessment

  16. Digression: Question & Transfer Model Characteristics Main Item: Which graph contains the points in the table? Guess (posterior boxplots) Slip (posterior boxplots) Scaffolds: • Quadrant of (-2,-3)? • Quadrant of (-1,-1)? • Quadrant of (1,3)? • [Repeat main] 2007 NCME Symposium on Learning-Embedded Assessment

  17. Conclusions • Different transfer models for different purposes seem necessary. • For unidimensional prediction, unidimensional IRT, augmented with “assistance metrics”, works well • Account for question difficulty, help-seeking behavior • We are close to best-possible prediction error • A finer grained model like the DINA model is needed for individual and group diagnostics • Individual diagnosis uncertainty can be large • Group diagnosis seems good enough to help teachers decide what to teach next • Scaffold questions: teaching or assessment? 2007 NCME Symposium on Learning-Embedded Assessment

  18. Future Work • Transfer model / KC’s • Discovering and improving the transfer model? • Different transfer models for different purposes – “play together”? • Experimental design to improve KC inferences • Account for learning over time • Prior distributions for skills based on past performance? • Markov Learning Model for each skill? • Compare with crediting/blaming hardest KC • Accuracy of inference? • Speed of computation? 2007 NCME Symposium on Learning-Embedded Assessment

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  20. RMSE and MAD bounds(Ayers & Junker, 2007) • Let • Then • And 2007 NCME Symposium on Learning-Embedded Assessment

  21. Dynamic Models:Anozie and Junker (2006) • More months helps more than more metrics • First 5 online metrics retained for final model(s) 2007 NCME Symposium on Learning-Embedded Assessment

  22. Full Set of Online Metrics 2007 NCME Symposium on Learning-Embedded Assessment

  23. Dynamic Models:Anozie and Junker (2006) • Look at changing influence of online metrics on MCAS prediction over time • Compute monthly summaries of all online metrics (not just %-correct) • Build linear prediction model for each month, using all current and prev. months’ summaries • To enhance interpretation, variable selection • by metric, not by monthly summary • include/exclude metrics simultaneously in all monthly models 2007 NCME Symposium on Learning-Embedded Assessment

  24. KC’s in DINA analysis 2007 NCME Symposium on Learning-Embedded Assessment

  25. Results: KC Feedback • Top shows posterior CI’s for one skill; middle and bottom are ‘sample sizes’ • More data or consistent evidence  smaller CI • Less data, or inconsistent evidence larger CI • Experimental Design? How many questions? Which skills? Etc. 2007 NCME Symposium on Learning-Embedded Assessment

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  27. Methods: KC Feedback • Pardos et al (2006) first tried DINA for MCAS prediction • Compared the 1-KC, 5-KC, 39-KC and 106-KC models • Found 39 KC’s did best; 106 KC’s 2nd best • Anozie & Junker (2007) apply DINA with an eye toward feedback to teachers etc. 2007 NCME Symposium on Learning-Embedded Assessment

  28. Static Prediction Models • Feng et al. (2006 & to appear): • Online testing metrics • Percent correct on main/scaffold/both items • “assistance score” = (errors+hints)/(number of scaffolds) • Time spent on (in-)correct answers • etc. • Compare paper & pencil pre/post benchmark tests • Ayers and Junker (2006): • Rasch & LLTM (linear decomps of item difficulty) • Augmented with online testing metrics • Pardos et al. (2006); Anozie (2006): • Binary-skills conjunctive Bayes nets • DINA models (Junker & Sijtsma, 2001; Maris, 1999; etc.) 2007 NCME Symposium on Learning-Embedded Assessment

  29. The ASSISTment Architectures • Extensible Tutor Architecture • Scalable from simple pseudo-tutors with few users to model-tracing tutors and 1000’s of users • Curriculum Unit • Items organized into multiple curricula • Sections within curriculum: Linear, Random, Experimental, etc. • Problem & Tutoring Strategy Units • Task organization & user interaction (e.g. main item & scaffolds, interface widgets, …) • Task components mapped to multiple transfer models • Logging Unit • Fine-grained human-computer interaction trace • Abstracting/coarsening mechanisms • Web-based Item Builder • Used by classroom teachers to develop content • Support for building curricula, mapping tasks to transfer models, etc. • Relational Database and Network Architecture supports • User Reports (e.g., students, teachers, coaches, administrators) • Research Data Analysis • Razzaq et al. (to appear) overview 2007 NCME Symposium on Learning-Embedded Assessment

  30. Two Assessment Goals • To predict end-of-year MCAS scores • To provide feedback to teachers (what to teach next?) • But there are some complications… 2007 NCME Symposium on Learning-Embedded Assessment

  31. 2004-2005 Data • Tutoring tasks • 493 main items • 1216 scaffold items • Students • 912 eighth-graders in two middle schools • Skills Models (Transfer Models / Q Matrices) • 1 “Proficiency”: Unidimensional IRT • 5 MCAS “strands”: Number/Operations, Algebra, Geometry, Measurement, Data/Probability • 39 MCAS learning standards: nested in the strands • 77 active skills: “WPI April 2005” (106 potential) 2007 NCME Symposium on Learning-Embedded Assessment

  32. Static Models: Feng et al. (2006 & to appear) • What is related to raw MCAS (0-54 pts)? • P&P pre/post benchmark tests • Online metrics: • Pct Correct on Mains • Pct Correct on Scaffolds • Seconds Spent on Incorrect Scaffolds • Avg Number of Scaffolds per Minute • Number of Hints Plus Incorrect Main Items • etc. • All annual summaries 2007 NCME Symposium on Learning-Embedded Assessment

  33. Static Models: Feng et al. (2006 & to appear) • Stepwise linear regression • Mean Abs Deviation • Within-sample MAD = 5.533 • Raw MCAS = 0-54, so Within-sample Pct Err = MAD/54 =10.25% (uses Sept P&P Test) 2007 NCME Symposium on Learning-Embedded Assessment

  34. Static Models:Ayers & Junker (2006) • Compared two IRT models on ASSISTment main questions: • Rasch model for 354 main questions. • LLTM: Constrained Rasch model decompose main question difficulty by skills in the WPI April Transfer Model (77 skills). • Replace “Percent Correct” with IRT proficiency score in linear predictions of MCAS 2007 NCME Symposium on Learning-Embedded Assessment

  35. Static Models:Ayers & Junker (2006) • Rasch fits much better than LLTM • BIC = -3,300 • df = +277 • Attributable to • Transfer model? • Linear decomp of item difficulties? • Residual and difficulty plots suggest transfer model fixes. 2007 NCME Symposium on Learning-Embedded Assessment

  36. Static Models:Ayers & Junker (2006) • Focus on Rasch, predict MCAS with where  = proficiency, Y=online metric • 10-fold cross-validation vs. 54-pt raw MCAS: 2007 NCME Symposium on Learning-Embedded Assessment

  37. Static Models:Pardos et al. (2006) • Compared nested versions of binary skills models (coded both ASSISTments and MCAS): • gi = 0.10, si = 0.05, all items; k = 0.5, all skills • Inferred skills from ASSISTments; computed expected score for 30-item MCAS subset 2007 NCME Symposium on Learning-Embedded Assessment

  38. Static Models: Anozie (2006) • Focused on 77 active skills in WPI April Model • Estimated k’s, gi’s and si’s using flexible priors • Predicted full raw 54-pt MCAS score as linear function of (expected) number of skills learned 2007 NCME Symposium on Learning-Embedded Assessment

  39. Dynamic Prediction Models • Razzaq et al. (to appear): evidence of learning over time • Feng et al. (to appear): student or item covariates plus linear growth curves (a la Singer & Willett, 2003) • Anozie and Junker (2006): changing influence of online metrics over time 2007 NCME Symposium on Learning-Embedded Assessment

  40. Dynamic Models: Razzaq et al. (to appear) • ASSISTment system is sensitive to learning • Not clear what is the source of learning here… 2007 NCME Symposium on Learning-Embedded Assessment

  41. Dynamic Models: Feng et al. (to appear) • Growth-Curve Model I: Overall Learning School was a better predictor (BIC) than Class or Teacher; possibly because School demographics dominate the intercept. • Growth-Curve Model II: Learning in Strands Sept_Test is a good predictor of baseline proficiency. Baseline and learning rates varied by Strand. 2007 NCME Symposium on Learning-Embedded Assessment

  42. Dynamic Models:Anozie and Junker (2006) 2007 NCME Symposium on Learning-Embedded Assessment

  43. Dynamic Models:Anozie and Junker (2006) • Recent main question performance dominates – proficiency? 2007 NCME Symposium on Learning-Embedded Assessment

  44. Dynamic Models:Anozie and Junker (2006) • Older performance on scaffolds similar to recent – learning? 2007 NCME Symposium on Learning-Embedded Assessment

  45. Summary of Prediction Models • Feng et al. (in press) compute the split-half MAD of the MCAS and estimate ideal % Error ~ 11%, or MAD ~ 6 points. • Ayers & Junker (2006) compute reliabilities of the ASSISTment sets seen by all students and estimate upper and lower bounds for optimal MAD: 0.67 MAD 5.21. 2007 NCME Symposium on Learning-Embedded Assessment

  46. New Directions • We have some real evidence of learning • We are not yet modeling individual student learning • Current teacher report: For each skill, report percent correct on all items for which that skill is hardest. • Can we do better? • Approaches now getting underway: • Learning curve models • Knowledge-tracing models 2007 NCME Symposium on Learning-Embedded Assessment

  47. New Directions:Cen, Koedinger & Junker (2005) • Inspired by Draney, Pirolli & Wilson (1995) • Logistic regression for successful skill uses • Random intercept (baseline proficiency) • fixed effects for skill and skill*opportunity • Difficulty factor: skill but not skill*opportunity • Learning factor: skill and skill*opportunity • Part of Data Shop at http://www.learnlab.org • Feng et al. (to appear) fit similar logistic growth curve models to ASSISTment items 2007 NCME Symposium on Learning-Embedded Assessment

  48. New Directions: Knowledge Tracing • Combine knowledge tracing approach of Corbett, Anderson and O’Brien (1995) with DINA model of Junker and Sijtsma (2001) • Each skill represented by a two state (unlearned/learned) Markov process with absorbing state at “learned”. • Can locate time during school year when each skill is learned. • Work just getting underway (Jiang & Junker). 2007 NCME Symposium on Learning-Embedded Assessment

  49. Discussion • ASSISTment system • Great testbed for online cognitive modeling and prediction technologies • Didn’t mention reporting and “gaming detection” technologies • Teachers positive, students impressed • Ready-Fire-Aim • Important! Got system up and running, lots of user feedback & buy-in • But… E.g. lack of control over content and content-rollout (content balance vs MCAS?) • Given this, perhaps only crude methods needed/possible for MCAS prediction? 2007 NCME Symposium on Learning-Embedded Assessment

  50. Discussion • Multiple skill codings for different purposes • Exam prediction vs. teacher feedback; state to state. • Scaffolds • Dependence between scaffolds and main items • Forced-scaffolding: main right  scaffolds right • Content sometimes skills-based, sometimes tutorial • We are now building some true one-skill decomps to investigate stability of skills across items • Student learning over time • Clearly evidence of that! • Some experiments not shown here suggest modest but significant value-added for ASSISTments • Starting to model learning, time-to-mastery, etc. 2007 NCME Symposium on Learning-Embedded Assessment

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