QA on “The behavior of tutoring systems”

CPI 494 Feb 3, 2009Kurt VanLehn

What’s a “task domain”?

• Solving linear algebraic equations?• Solving 2x+3=5?• Solving math problems?• Reciting the Gettysburgh Address?• Painting color-by-numbers picture?• Dancing the Macrarena?• Folk dancing.• Writing a funny TV sit-com script

What’s a “task”?

• Writing a hiaku on death of a loved one?• Solving 2x+3=5?• Writing the digit 5?• Reading • Reading an electronic schematic for a 2-

transitor amplifier.

What is a “step”?

• What are the steps in– Solving 2x+5=11? 2x=11-5 2x=6 2x/2=6/2 – Writing the digit “4”– Dividing 10 by 2?– Phonic spelling of the last name of the current US

president?– Writing a hiaku on death of a loved one?– Painting a color-by-numbers picture?

What is a “Knowledge component”?

• Definition (hint: Uses “independently”)?• What are choices of granularity in solving

2x+5=11?

How to use transfer to check if KC’s are defined correctly

• Use KCs to represent task domain, e.g., multi-column addition (496+307) & subtraction

• Determine which KCs must be mastered for one set of tasks, e.g., addition A

• Determine which KCs must be mastered for a second set of tasks, e.g., subtraction S

• Experiment:– Measure time for group S to master subtraction – Measure time for group AS to master subtraction after mastering

addition– Group AS should take less time because some of the subtraction KCs

are also addition KCs, and thus have been mastered already.• |S-A| / |S| ≈ time(AS)/time(S)

– where |X| is the cardinality of set X– Where S-A is the set difference

What is a learning event?

• Definition?• Give example from algebra• Give example from teaching your mom how to

enter a phone number into her cell phone.

Fourth Third Second First Fifth

While studying an example, tries to self-explain; fails; looks in text; succeeds

While solving a problem, looks up example; recalls explanation; maps it to problem

Recalls explanation; slips; corrects

Solves without slips

5 sec.

10 sec.

15 sec.

25 sec.

20 sec.

Du

rati

on

of

the in

stru

ctio

nal even

t

Chronological position of the learning event

Using learning curves to check KCs

• Proper KCs should have smooth learning curves

1 2 3 4 5 6 7 …

Learning event s in chronological order

Dur

ation

of l

earn

ing

even

t

1 2 3 4 5 6 7 …

Learning event s in chronological orderD

urati

on o

f lea

rnin

g ev

ent

How to collect a learning curve

• Track learning of N students• At each of their learning events – Measure time (plot duration on y-axis)– Measure errors (plot error rate on y-axis)– Measure hint requests (plot hints+errors on y-

axis)• Aggregate over the N students– E.g., at the 3rd learning event of all N students,

count number of students who make error & divide by N plot on y-axis, with x=3.

Two nested loops of an immediate feedback step-based tutoring system• Task (outer) loop:– Select task– Do task– Repeat until student has mastered task domain

• Step (inner) loop– Tutor and student do a step, somehow• T:hint; S: trys; T: wrong!; S: trys again; T: Good!

– Repeat until the task is finished

What are the 2 loops for CTAT fraction addition tutor?

• Outer?

• Inner?

What are two loops for Steve?

What are two loops for Andes?

What are two loops for Cognitive Algebra Tutor?

What are two loops for AutoTutor?

What are the two loops for SQL-Tutor?

Main issue for the task (outer) loop?

• How to select the next task?• Where to get tasks to select from?

5 common services for steps

• Minimal feedback• Hints on the next step• Error specific feedback• Assessment of knowledge• Review of solution

Main issues for minimal feedback

• Correctness?• When?

Main issues for next-step hints

• When?• What step to suggest?• How to give hints?

Main issues in error-specific feedback

• How to classify errors?• How to give feedback? Debugging…• When/whether to give feedback?

Main issues in assessment

• What should be assessed?• Grain size of assessment?• How to measure progress, hints & errors?• How to combine progress, hints & errors?

Main issues in reviewing solutions

• Who controls the review?• What depth?• Anything suppressed?• Questions allowed?