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1
Learning from Meaningful, Purposive Interaction
Fridolin Wild · Medieninformatik · Universität
Regensburg · Knowledge Media Institute · The Open
University
Representing and analysing competence development with network analysis and
natural language processing
2
Outline
Introduction and overview Theoretical foundation Precursor algorithms (SNA + LSA) Algorithm: Meaningful, Purposive Interaction
Analysis• Mathematical foundation• Visual analytics using vector maps as projection
surfaces• Implementation
Application examples for Learning Analytics Evaluation: verification and validation Summary and Outlook
4
Introduction
Fascination with LSA and Matrix Algebra originated in Information Retrieval (UR), then shifted to Technology Enhanced Learning (WU+OU)
Research on Technology Enhanced Learning has its place in the canon of Media & Computing (and Knowledge Media)
It’s a big and growing global Software Market: • Adkins (2011, p.6): 9.2% annual growth till
2015 • Docebo (2014,p.8): 7.9% annual growth till
2016 Drivers of Innovation: open Grand Challenges
to Research and Development in TEL
5
Bridging informal and formalCreate a unified, seamless learning landscape with the help of mobile devices.
learning analyticsautomated feedback using interaction data to predict performance.
#6
fostering engage-mentIncreasing student motivation to learn and engaging the disengaged – using technology.
How can we detect (de-) motivation? How can make use intrinsic/extrinsic reward systems?
#4
New devices for young children’s expression of scientific ideas Mouse and keyboard are a blocker to natural mapping and new modalities of interaction (touch, gestures) can foster a more tactile learning.
#1
Learning to read at home with digital technologies
#2
CSCL in teacher training and professional development
#3
e-assessmentNew forms of assessment of learning in social TEL environments
#5
Understanding how toddler apps can support learning.
early years technology
dataTELUtilising real-time data to improve teaching and learning.
#7#8
networked learning ecologiesInterest-driven lifelong learning in personal learning networks
#9
#10
Fisc
her,
Wild
, Su
therl
and
, Z
irn (
201
4)
#1
6
Objectives for this work (from GC #5,#6,#8)
Represent: to automatically represent conceptual development evident from interaction of learners with more knowledgeable others and resourceful content artefacts; Analyse: to provide the instruments required for further analysis; Visualise: to re-represent this back to the users in order to provide guidance and support decision- making about and during learning.
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Information and Learning
communicatively successful
cooperativelysuccessful
[e]=
PmO
purpose
meaning
(Janich, 1998/2003/2006; Hesse et al., 2009; Hammwoehner, 2005; Wild, 2014, p.27ff)
“learns ‘information’”
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The Foundational Example
Particular unit of company with 9 employees All went through trainings recently Offered by universities (UR, OU), MOOCs,
informal learning (FaceBook, LinkedIn) Now: Christina is off sick HR manager to identify worthy replacement
• SNA• LSA• MPIA
(Wild, 2014, p.60)
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original space
LSA & ‘Similarity’
(Wild, 2014, p.104: cosines)(Wild, 2014, pp.229)
black = 1, white = 0
LSA space
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Shortcomings
Social Network Analysis (SNA)• Blindness to content• Relationship discovery restricted to incidences
captured• Popular for analysis, visualization, simulation,
intervention(Sie et al., 2012)
Latent Semantic Analysis (LSA)• Blindness to purposes & structure (relations, groups,
…)• Lacking instruments for analysis• No clear rule for number of factors to retain• Popular for essay scoring, information retrieval,
dialogue tutoring, recommenders
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Fundamental matrix theorem on orthogonalityCalculating the Nullspace Ker A:Ax = 0 Eq.1
(Wild, 2014, p.131; redrawn from Strang,
1988, p.140)
(Wild, 2014, p.132)
“every matrix transforms its row
space to its column space” (Strang, 1988,
p.140)
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The Eigenvalue Problem & Singular Value Decomposition
(Wild
, 2014,
p.1
43)
For every symmetric, square matrix:(Barth et al., 1998, p.90/E):
Bx = λxn.b.: B = AAT or ATA
Any multiplication of the matrix B with an Eigenvector x yields a constant multiple of the Eigenvector, scaled by the Eigenvalue λ
A = UΣVT
U = Eigenvectors(ATA)
V = Eigenvectors(AAT)Σ = UTAV
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Base transformation (from Term-Doc space to orthogonal Eigenspace)(Wild, 2014, p.144)
Same dims for both Eigenvector types (row and column), same Eigenvalues!
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Prediction of Threshold
Sum of Eigenvalues Σ2 = Sum of trace of matrix A
threshold = 0.8 * sum(A*A)
=> Calculate only the first k Eigendimensions, for which the
sum of Eigenvalues Σ2 does not yet pass the threshold
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Updating using ex post projection
v' = aT Uk Σ k-1
a' = Uk Σk v' T (Wild, 2014, p. 149f; see also Berry et al., 1994, equation 7 and page 16
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Introducing Network Analysis Techniques
Still: result is high-volume, sometimes even big data
Visualisation techniques from (Social) Network Analysis can help!
28
Network Visualisation
Proximity-driven Link
Erosion (Wild, 2014, p.162)
Layout with spring-embedder (Wild, 2014, p.163)
Wireframe Conversion (Wild, 2014, p.167)
Kernel Smoothing (Wild, 2014, p.169)
Hyposometric Tints(Wild, 2014, p.171)
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Class Diagram
(Wild, 2014, p.209)> 10.000 lines of codeR package
MPIATo be: Open Source (GPL-3)
Test-drivendevelopment
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The SNA/LSA example revisited
(Wild, 2014, p.231)
C = computer science
P = pedagogyM = math + stats
41
Evaluations
The role of verification and validation (Schlesinger, 1979, as cited in Oberkampf & Roy, 2010,
p.23)
(Wild, 2014, p.276)
43
Validation Experiments
No standardised test collections for conceptual development
Effectiveness:• Accuracy in application (Essay Scoring)• Convergent and divergent validity• Annotation accuracy• Degree of loss in the visualisation
Efficiency:• Performance gain
44
Evaluation of Scoring
Accuracy
Example of feedback
Using holistic scoring (essay = avg. ~ of 3
model solutions)
45
Performance GainsSavings in calculation time through using the threshold prediction method for SVD calculation truncation (predicted from original doc-term matrix)
47
Innovation in TELThree Grand Challenges (Fischer et al., 2014) addressed:
• “new forms of assessment for social TEL environments” (Whitelock, 2014a)
• “assessment and automated feedback” (Whitelock, 2014b)
• “making use and sense of data for improving teaching and learning” (Plesch et al., 2012)
47
learning analyticsautomated feedback using interaction data to predict performance.
#6
e-assessmentNew forms of assessment of learning in social TEL environments
#5
dataTELUtilising real-time data to improve teaching and learning.
#8