Education

1. 1
Educational data mining in a
computer tutor that listens
Joseph E. Beck
Acknowledgements: NSF, Heinz

2. 2
Take away point
Computer tutors provide gold mine
of fine-grained interaction data
Standardized tests
Creates the ability to assess students and
improve capabilities of computer tutors

3. 3
What is educational data mining?
• Using data to learn about students and
instruction
– E.g. predict student behavior, assess
students, evaluate the tutor’s teaching, etc.
• Motivation: computer tutors provide large
samples of fine-grained, longitudinal data
that are a powerful (unique?) source of
knowledge to improve educational
outcomes

4. 4
Difference between educational
and standard data mining
• Data collected with purpose in mind
– Have control over schema
• Describe more interactive phenomena
• Generally smaller datasets

5. Project LISTEN’s Reading Tutor

6. 6
Data we’ve collected
• Record several items in database
– Student’s speech (as recognized by ASR)
– Student’s help requests
– Tutor’s teaching actions
– (among other things)
• Scale of DB from 2002-2003 school year
– 456 students
– 423,149 student clicks for help
– 4.1 million words heard by speech recognizer

7. 7
Outline
 Predicting student behavior
• E.g. will the student click for help on this
word?
 Inferring student’s skills
• E.g. does the student know “ch” can make a K
sound (e.g. “chaos”)?
 Future work

8. 8
 Predicting student help requests

9. 9
Why predict help requests?
• Goal is to understand the student
– In two senses
• A good model of the student should be able to
predict future actions (e.g. outcome measure)
• Help requests provide window into student’s
reading proficiency (e.g. source of knowledge)
• Non-speech events are less noisy
• Applications of help requests
– Avoid overly complex material
– Provide help ahead of time

10. 10
Learning curves in students’ help
requests (with Peng Jia)
Number of previous encounters
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
.4
.3
.2
.1
0.0
Reading level
Grade 1
Grade 2
Grade 3
Grade 4

11. 11
Region of focus
• “When students need help”
– 1st and 2nd grade ability
– 1-6 prior word encounters
• Selected data
– 53 students
– 175,961 words
– 29,278 help requests
• # of cases per student:
1392 - 7783
• Help rate excluding
common words: 0.54%–
54%
– A few novice readers
requested substantial
amounts of help
Number of previous encounters
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
Mean
help
request
rate
.4
.3
.2
.1
0.0
Reading level
Grade 1
Grade 2
Grade 3
Grade 4

12. 12
How to predict help requests
• Approach: treat as classifier learning problem
– Inputs: features about the word and the student
– Output: whether the student will ask for help
• Need to decide:
– Features describing word and student
– What data to use to train model

13. Abbreviated example of features
(20 features were used)
Word
Student on
this word
Student
overall Requested
help?
Length Frequency
Seen
before?
Helped
before?
Help
rate
Grade
6 1189 Yes No 0.5 1 Yes
11 22255 No No 0.5 1 Yes
3 826 Yes Yes 0.1 3 No
5 1537 No No 0.05 2 No
.
.
.

14. 14
Grouped student prediction
• Predict whether student will request help
by using other students’ data
• Leave one student out cross validation:
– Training data: randomly select 25% of all
other students and pool their data together
• (Using all data crashed the machine.)
– Testing data: student’s data

15. 15
Grouped model prediction results
• Used J48 (version of C4.5) and NBC
• Evaluation criteria: weighted accuracy
– Weigh cases where student asked for help 5 times
more heavily
– Not providing help when needed worse than extra help
• Performance (averaged per-student)
– J48: 71%
– NBC: 75%
• How to (possibly) do better?
– Build individualized models for each student

16. 16
• Incrementally construct models as data are seen
• Same features as grouped student prediction
• Performance (averaged per-student)
– J48: 81%
– NBC: 75%
– Better to use data about individuals than population
• Obvious extension: combine grouped and individual
modeling approaches
Building individual models
All data ordered by time
training testing
Training
testing
beginning
In the
middle

17. 17
Using subword properties to help
predict help requests
(with June Sison)
• If student is predicted to need help on
“chord,” he would probably need help on
“chords” as well
– Word roots?
– But what about “chaos?” “chemical?”
• CH/K/ is common across items
• Model lettersound mappings in words
– Called graphemephoneme (gp) mappings

18. 18
Which gp mappings to use?
• Chemical
– CHK
– EEH
– MM
– IAH
– CK
– AAH
– LL

19. 19
Which gp mappings to use?
• Chemical
– CHK
– EEH
– MM
– IAH
– CK
– AAH
– LL
• First and last parts of a word are most important for
children’s decoding (Perfetti)
– And adults’ decoding (recent email message floating around)
>Aoccdrnig to rsereach at an Elingsh uinervtisy, it deosn't mttaer in waht
>oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht frist and
>lsat ltteres are in the rghit pclae…Tihs is bcuseae we do not raed ervey
>lteter by istlef, but the wrod as a wlohe.

20. 20
Features describing a gp
• P(g): How common is this grapheme?
• P(p|g): How likely is it to generate this
sound given the letters?
• Compute above two features for
– First gp in a word
– Rarest gp in a word
– Average of all gp in a word
• Add to classifier’s set of features

21. 21
Results
• Used individual models with J48
• Improved accuracy by 0.7% absolute (P=0.013)
over not using gp features
– However, already using many features about student
– Suggests students are sensitive to gp properties
• Can we do better?
– These gp properties are static
– Only describe words, not students
– Perhaps modeling a student’s skills would work
better?
• Infer what is in student’s head rather than just predict actions

22. 22
Outline
 Predicting student behavior
• E.g. will the student click for help on this
word?
 Inferring student’s skills
• E.g. does the student know “ch” can make a K
sound (e.g. “chaos”)?
 Future work

23. 23
 Automated assessment
(with Peng Jia and June Sison)
• We gather lots of data; use it to assess students
– “Knowing What Students Know” provides metaphor
• Why perform automated assessment?
– Drawbacks of paper tests:
• Expensive
• Lack of ongoing results
• Costly to report to teachers and computer tutors
• Problem: our data are (literally) noisy
– But we have a lot of it: students attempt over 300 words
per day

24. 24
Converting speech input to usable data
I’LL HAVE TO MOP UP MUTTERED DENNIS…
“I'll have to mop it all up,” muttered Dennis…
Speech input (Sphinx)
Align text
(Multimatch)
Assess subword knowledge

25. 25
Assessing subword knowledge
• Interested in student proficiency in
individual gp mappings
– Maintain knowledge estimate, P(knows), for
each mapping
• “Hidden subskill problem” (latent variable)
– Cannot assess directly
• Credit/blame first and last gp of every
word attempted
– But how?

26. 26
What is knowledge tracing?
(Corbett et al.)
Unlearned
State
Two Learning Parameters
p(L0) Probability the rule is in the learned state at time 0 (prior to the first
opportunity to apply the rule in problem solving).
p(T) Probability the rule will make the transition from the unlearned state to the
learned state at each opportunity to apply the rule
Two Performance Parameters
p(G) Probability the student will guess correctly if the rule is in the unlearned state
p(S) Probability the student will slip (make a mistake) if the rule is in the learned
state
Learned
State
p(T)
correct correct
p(G) 1-p(S)
p(L0)

27. 27
Modifying knowledge tracing
• Problem: noisy speech recognition
• Solution: broaden notion of slip and guess
– P(slip) = chance a skilled student makes a mistake +
chance ASR fails to hear correct reading
– P(guess) = chance a novice pronounces word correctly +
chance ASR incorrectly credits student
• Very different semantics of slip/guess
• Knowledge tracing equations unchanged
• Estimate slip/guess from students working
with Reading Tutor

28. 28
Applying knowledge tracing
• E.g. Student reads “Dennis” correctly
update DD, SS
• Assume student had P(knows) = 0.1 for both
• Update P(knows DD)
– P(guess DD) = 0.81
– P(slip DD) = 0.13
– New P(knows DD) = 0.107
• Update P(knows SS)
– P(guess SS) = 0.80
– P(slip SS) = 0.12
– New P(knows SS) = 0.109
• Slow updates
– A good thing

29. 29
Evaluation of gp mappings
• Data from 2002-2003
• N=259 (1st through 4th graders)
• Goal: predict performance on fluency posttest
– Standardized test is scored by humans
– (Not our final goal)
• Construct 2 linear models for all students
– Mean P(knows) for all gp
• Fluency posttest = 133.3 * mean – 42.8
– Pretest paper-test score
• Fluency posttest = 0.809 * fluency pretest + 20.5

30. 30
Results
• All results are leave-one-out cross validation
– Correlation of 0.862 for P(knows) for all gp
– Correlation of 0.808 for pretests
• Look at within-grade correlation
– Reduce heterogeneity
– E.g. shoe size and spelling ability
Grade Mean Pretest N
1 0.878 0.561 115
2 0.808 0.881 80
3 0.813 0.883 42
4 0.859 0.898 22
Average 0.840 0.806

31. 31
Using mean of P(knows) to predict
GORT posttest
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Predicted GORT posttest score
Actual
GORT
postest
score

32. 32
Outline
 Predicting student behavior
• E.g. will the student click for help on this
word?
 Inferring student’s skills
• E.g. does the student know “ch” can make a K
sound (e.g. “chaos”)?
 Future work

33. 33
Near-term goals
• Construct more general tools
– Crosstabs
– View a student’s growth in reading
• Automated assessment
– Validate gp mappings
– Model latent variables
– Improve ASR

34. 34
Model of student knowledge
Speech
DD ZZZ
DT DDZ
Reading proficiency
…
…
GP knowledge
(371 items!)

35. 35
Model of student knowledge:
adding latent variables
Speech
DD ZZZ
DT DDZ
Reading proficiency
…
…
GP knowledge
“Higher level”
knowledge
e.g. short vowels,
rare use, etc.

36. Improving ASR
• Cannot listen for all mistakes
• Bias ASR based on student proficiencies
• E.g. student encounters “thugs”
– thth, uah, gg, sz
P(say “Thugs”) = 0.90
P(say “Tugs”) = 0.02

37. 37
Improving ASR
• Cannot listen for all mistakes
• Bias ASR based on student proficiencies
• E.g. student encounters “thugs”
– thth, uah, gg, sz
P(say “Thugs”) = 0.90
P(say “Tugs”) = 0.02

38. Improving ASR
• Cannot listen for all mistakes
• Bias ASR based on student proficiencies
• E.g. student encounters “thugs”
– thth, uah, gg, sz
P(say “Thugs”) = 0.90
P(say “Tugs”) = 0.02
Doesn’t know theta
Knows theta
P(say “Thugs”) = 0.95
P(say “Tugs”) = 0.01
P(say “Thugs”) = 0.40
P(say “Tugs”) = 0.40

39. 39
Longer-term goals
• Improving ASR good goal due to ability to
evaluate changes offline
• However, would like to improve educational
outcomes
– Problem: harder to evaluate learning since human
trials are expensive
– Solution: construct a simulation of the student and
tutor and use reinforcement learning (RL)
– Approach used in my dissertation work (at UMass)
on ADVISOR in the AnimalWatch system

40. 40
ADVISOR overview
Predict student
behavior in state s
Pedagogical
Agent
Data from prior
users of tutor
Teaching
goal
Teaching action
“try again”
Result “correct answer,
took 15 sec.”
Teaching policy

41. 41
Why is applying RL harder in the
Reading Tutor than in AnimalWatch?
• Reading Tutor
– Built by others
– Still building student
model
– Domain is reading,
hard to measure
outcomes
– Greater variety of
points to intervene
• AnimalWatch
– I designed
– Started with student
model
– Domain was math,
easy to measure
outcomes
– Built from ground up
with ADVISOR in mind

42. 42
Conclusions
• Can assess students despite noisy data
• For predicting student behavior, data are plentiful
• Can examine models and features
• For predicting student test scores, data are scarce
• Restricted to simple models and need good features
• Educational data mining offers many opportunities
to improve efficacy of teaching
• Big data is a “secret weapon” but…
– We still don’t have enough to do everything we want