Using On-line Tutoring Records
to Predict End-of-Year Exam
Scores
Experience with the Assistments Project and
MCAS 8th Grade Mathematics
Neil Heffernan, Ken Koedinger, Brian Junker
with 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
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
1
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
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
2
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 source,
teacher-generated “curriculum”,
and transfer model (Q-matrix)
Student records contain
responses, timing data,
bugs/hints, etc.
System tracks students through
time, provides teacher reports per
student & per class.
– MCAS prediction
– Skills learned/not-learned, etc.
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
3
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
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
4
Goals and Complications
• Two Assessment Goals
– To predict end-of-year MCAS scores
– To provide feedback to teachers (what to teach next?)
• Some Complications
– Assessment ongoing throughout the school year as
students learn (from teachers & from ASSISTments!)
– Multiple skills models for different purposes
– Scaffold questions: For tutoring or for measurement?
– Deliberate ready-fire-aim user-assisted development
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
5
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)
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
6
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.)
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
7
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.
Predictor
SEP-TEST
0.75
MARCH-TEST
0.41
MAIN_PERCENT_CORRECT
0.75
MAIN_COUNT
0.47
TOTAL_MINUTES
0.26
PERCENT_CORRECT
0.76
QUESTION_COUNT
0.20
HINT_REQUEST_COUNT
-0.41
AVG_HINT_REQUEST
-0.63
HINT_COUNT
-0.39
AVG_HINT_COUNT
-0.63
BOTTOM_OUT_HINT_COUNT
-0.38
AVG_BOTTOM_HINT
-0.55
ATTEMPT_COUNT
0.08
AVG_ATTEMPT
-0.41
AVG_QUESTION_TIME
-0.12
AVG_ITEM_TIME
-0.39
P & P Tests
ASSISTment
Online Metrics
• All annual summaries
Brian Junker
Carnegie Mellon
Corr
2006 MSDE / MARCES
Conference
8
Static Models:
Feng et al. (2006 & to appear)
• Stepwise linear
regression
• Mean Abs Deviation
Predictor
(Const)
Sept_Test
• Within-sample
MAD = 5.533
• Raw MCAS = 0-54, so
Within-sample Pct Err =
MAD/54 =10.25%
(uses Sept P&P Test)
Brian Junker
Carnegie Mellon
Pct_Correct_All
Avg_Attempts
Avg_Hint_Reqs
2006 MSDE / MARCES
Conference
Coefficient
26.04
0.64
24.21
-10.56
-2.28
9
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
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
10
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.
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
11
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:
Predictors
Variables
CV- MAD
CV % Error
% Corr Main
1
7.18
13.30
 (proficiency)
1
5.90
10.93
 + 5 Online
Metrics
6
5.24
9.70
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
12
Static Models:
Pardos et al. (2006); Anozie (2006)
Conjunctive binary-skills Bayes Net (Maris,
1999; Junker & Sijtsma DINA, 2001; etc.)
P(Congruence)
P(Equation-Solving)
1
P(Perimeter)
2
3
Gate
P(Question)
Gate
P(Question)
G
P(Question)
True
1-s1
True
1-s2
True
1-s3
False
g1
False
g2
False
g3
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
13
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
MODEL
Mean Absolute Deviance (MAD)
% ERROR (30 items)
39 MCAS standards
4.500
15.00
106 skills (WPI Apr)
4.970
16.57
5 MCAS strands
5.295
17.65
1 Binary Skill
7.700
25.67
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
14
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
Months of Data
CV MAD
CV % Err
2
8.11
15.02
3
7.38
13.68
4
6.79
12.58
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
15
Static Models: Anozie (2006)
Main Item:
Which graph
contains the
points in the
table?
Scaffolds:
1.
2.
3.
4.
Brian Junker
Carnegie Mellon
X
Y
-2
-3
-1
-1
1
3
Slip
Guess
Quadrant of (-2,-3)?
Quadrant of (-1,-1)?
Quadrant of (1,3)?
[Repeat main]
2006 MSDE / MARCES
Conference
16
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
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
17
Dynamic Models:
Razzaq et al. (to appear)
% Correct on System per
student
40
35
30
25
20
15
10
5
0
Sep
0
t
•
•
Oct
1
Nov
2
Jan
Dec
3
Jan
4
Feb
5
Mar
6
Time
ASSISTment system is sensitive to learning
Not clear what is the source of learning here…
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
18
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.
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
19
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
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
20
Dynamic Models:
Anozie and Junker (2006)
• More months helps more than more metrics
• First 5 online metrics retained for final model(s)
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
21
Dynamic Models:
Anozie and Junker (2006)
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
22
Dynamic Models:
Anozie and Junker (2006)
• Recent main question performance
dominates – proficiency?
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
23
Dynamic Models:
Anozie and Junker (2006)
• Older performance on scaffolds similar to
recent – learning?
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
24
Summary of Prediction Models
Model
Variables
CV-MAD
CV % Error
CV-RMSE
PctCorrMain
1
7.18
13.30
8.65
#Skills of 77
learned
1?
6.63
12.58
8.62
Rasch
Proficiency
1?
5.90
10.93
7.18
PctCorrMain
+ 4 metrics
35 ( = 5 x 7 )
5.46
10.10
6.56
Rasch Profic
+ 5 metrics
6?
5.24
9.70
6.46
• 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.
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
25
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
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
26
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
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
27
New Directions: Anozie (2006)
• DINA model can be
used to infer skills
directly
• Experimental
posterior intervals
illustrated above right
• When students’ data
contradicts prior or
“borrowed info” from
other students,
intervals widen
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
28
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).
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
29
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 contentrollout (content balance vs MCAS?)
– Given this, perhaps only crude methods
needed/possible for MCAS prediction?
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
30
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.
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
31
References
Anozie, N. (2006). Investigating the utility of a conjunctive model in Q-matrix assessment using monthly student records in an online tutoring
system. Proposal submitted to the National Council on Measurement in Education 2007 Annual Meeting.
Anozie, N.O. & Junker, B. W. (2006). Predicting end-of-year accountability assessment scores from monthly student records in an online
tutoring system. American Association for Artificial Intelligence Workshop on Educational Data Mining (AAAI-06), July 17, 2006, Boston,
MA.
Ayers, E. & Junker, B.W. (2006). Do skills combine additively to predict task difficulty in eighth-grade mathematics? American Association for
Artificial Intelligence Workshop on Educational Data Mining (AAAI-06), July 17, 2006, Boston, MA.
Ayers, E. & Junker, B. W. (2006). IRT modeling of tutor performance to predict end of year exam scores. Working paper.
Corbett, A. T., Anderson, J. R., & O'Brien, A. T. (1995) Student modeling in the ACT programming tutor. Chapter 2 in P. Nichols, S. Chipman, &
R. Brennan, Cognitively Diagnostic Assessment. Hillsdale, NJ: Erlbaum.
Draney, K. L., Pirolli, P., & Wilson, M. (1995). A measurement model for a complex cognitive skill. In P. Nichols, S. Chipman, & R. Brennan,
Cognitively Diagnostic Assessment. Hillsdale, NJ: Erlbaum.
Feng, M., Heffernan, N. T., & Koedinger, K. R. (2006). Predicting state test scores better with intelligent tutoring systems: developing metrocs to
measure assistance required. In Ikeda, Ashley & Chan (Eds.) Proceedings of the Eighth International Conference on Intelligent Tutoring
Systems. Springer-Verlag: Berlin. pp 31-40.
Feng, M., Heffernan, N., Mani, M., & Heffernan, C. (2006). Using mixed effects modeling to compare different grain-sized skill models. AAAI06
Workshop on Educational Data Mining, Boston MA.
Feng, M., Heffernan, N. T., & Koedinger, K. R. (in press). Addressing the testing challenge with a web-based E-assessment system that tutors
as it assesses. Proceedings of the 15th Annual World Wide Web Conference. ACM Press (Anticipated): New York, 2005.
Hao C., Koedinger K., & Junker B. (2005). Automating Cognitive Model Improvement by A*Search and Logistic Regression. In Technical Report
(WS-05-02) of the AAAI-05 Workshop on Educational Data Mining, Pittsburgh, 2005.
Junker, B.W. & Sijtsma K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response
theory. Applied Psychological Measurement 25: 258-272.
Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika 64, 187-212.
Pardos, Z. A., Heffernan, N. T., Anderson, B., & Heffernan, C. L. (2006). Using Fine Grained Skill Models to Fit Student Performance with
Bayesian Networks. Workshop in Educational Data Mining held at the Eighth International Conference on Intelligent Tutoring Systems.
Taiwan. 2006.
Razzaq, L., Feng, M., Nuzzo-Jones, G., Heffernan, N.T., Koedinger, K. R., Junker, B., Ritter, S., Knight, A., Aniszczyk, C., Choksey, S., Livak,
T., Mercado, E., Turner, T.E., Upalekar. R, Walonoski, J.A., Macasek. M.A., & Rasmussen, K.P. (2005). The Assistment Project: Blending
Assessment and Assisting. In C.K. Looi, G. McCalla, B. Bredeweg, & J. Breuker (Eds.) Proceedings of the 12th Artificial Intelligence In
Education. Amsterdam: ISO Press. pp 555-562.
Razzaq, L., Feng, M., Heffernan, N. T., Koedinger, K. R., Junker, B., Nuzzo-Jones, G., Macasek, N., Rasmussen, K. P., Turner, T. E. &
Walonoski, J. (to appear). A web-based authoring tool for intelligent tutors: blending assessment and instructional assistance. In Nedjah,
N., et al. (Eds). Intelligent Educational Machines within the Intelligent Systems Engineering Book Series (see http://isebis.eng.uerj.br).
Singer, J. D. & Willett, J. B. (2003). Applied Longitudinal Data Analysis: Modeling Change and Occurrence. Oxford University Press, New York.
Websites:
http://www.assistment.org
http://www.learnlab.org
http://www.educationaldatamining.org
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
32
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
33
Full Set of Online Metrics
Brian Junker
Carnegie Mellon
2006 MSDE / MARCES
Conference
34