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Richard BaraniukMr. Lan, Andrew Waters, Christoph Studer
learning and content analytics
learning analytics
Goal: assess and track student learning progress by analyzing their interactions with content
data (massive, rich, personal)
close the learning
feedback loop
content
learninganalytics assess and track student
learning progress by analyzing their interactions with content
content
learninganalytics assume content
is organized(“knowledge graph”)
http://www.newscientist.com/article/mg21528765.700-the-intelligent-textbook-that-helps-students-learn.html
“While such results are promising, perhaps it's a little soon to crown Inquire the future of textbooks. For starters, after two years of work the system is still only half-finished. The team plan to encode the rest of the 1400-page Campbell Biology by the end of 2013, but they expect a team of 18 biologists will be needed to do so. This raises concerns about whether the project could be expanded to cover other areas of science, let alone other subjects.”
content
learninganalytics content
analytics
standard practice
Johnny
Eve
Patty
Neelsh
Nora
Nicholas
Barbara
Agnes
Vivek
Bob
Fernando
Sarah
Hillary
JudyJanet
standard practice
Johnny
Eve
Patty
Neelsh
Nora
Nicholas
Barbara
Agnes
Vivek
Bob
Fernando
Sarah
Hillary
JudyJanet
Goal: using only “grade book” data, infer:
1. the concepts underlying the questions (content analytics)
2. each student’s “knowledge” of each underlying concept (learning analytics)
from grades to concepts
students
pro
ble
ms
data– graded student responses
to unlabeled questions– large matrix with entries:
white: correct responseblack: incorrect responsegrey: unobserved
standard practice– instructor’s “grade book”
= sum/average over each column
goal– infer underlying concepts and
student understanding without question-level metadata
students
pro
ble
ms
data– graded student responses
to unlabeled questions– large matrix with entries:
white: correct responseblack: incorrect responsegrey: unobserved
goal– infer underlying concepts and
student understanding without question-level metadata
key observation– each question involves only
a small number of “concepts” (low rank)
from grades to concepts
students
pro
ble
ms
~ Ber
statistical model
converts to 0/1(probit or logisticcoin flip transformation)
estimate of each student’s ability to solve each problem(even unsolved problems)
red = strong ability
blue = weak ability
students
pro
ble
ms
+
SPARse Factor Analysis
~ Ber
students
pro
ble
ms
+students
concepts
SPARFA
each problem involves a combination of a small number of key “concepts”
each student’s knowledge of each “concept”
each problem’s intrinsic “difficulty”
~ Ber
students
pro
ble
ms
solving SPARFA
factor analyzing the grade book matrix is a severely ill-posed problem
significant recent progress in relaxation-based optimization for sparse/low-rank problems
– matrix based methods (SPARFA-M)– Bayesian methods (SPARFA-B)
similar to compressive sensing
standard practice
Johnny
Eve
Patty
Neelsh
Nora
Nicholas
Barbara
Agnes
Vivek
Bob
Fernando
Sarah
Hillary
JudyJanet
Grade 8 science
• 80 questions• 145 students• 1353 problems
solved (sparsely) • learned 5 concepts
Grade 8 science
• 80 questions• 145 students• 1353 problems
solved (sparsely) • 5 concepts
questions(w/ estimated inherent difficulty)
concepts
studentknowledge
profile
87
55
23
93
62
summary
scaling up personalized learning requires that we exploit the massive collection of relatively unorganized educational content
can estimate content analytics on this collection as we estimate learning analytics
related work: Rasch model, IRT
integrating SPARFA into
Mr. Lan Andrew Waters Christoph Studer
.com
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