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…in	
  a	
  world	
  of	
  larger	
  and	
  larger	
  data	
  sets,	
  increasing	
  popula4ons	
  of	
  
increasingly	
  diverse	
  learners,	
  constrained	
  educa4on	
  budgets	
  and	
  
greater	
  focus	
  on	
  quality	
  and	
  accountability	
  (Macfadyen	
  &	
  Dawson,	
  
2012),	
  some	
  argue	
  that	
  using	
  analy4cs	
  to	
  op4mize	
  learning	
  
environments	
  is	
  no	
  longer	
  an	
  op4on	
  but	
  an	
  impera4ve…	
  
…Educa4on	
  can	
  no	
  longer	
  afford	
  not	
  to	
  use	
  learning	
  analy4cs.	
  As	
  
Slade	
  and	
  Prinsloo	
  (2013)	
  maintain,	
  “Ignoring	
  informa4on	
  that	
  
might	
  ac4vely	
  help	
  to	
  pursue	
  an	
  ins4tu4on’s	
  goals	
  seems	
  
shortsighted	
  to	
  the	
  extreme”	
  (p.	
  1521).	
  
Macfadyen	
  et	
  al.,	
  2014	
  
What	
  do	
  we	
  mean	
  by	
  	
  
‘learning	
  analy<cs’?	
  
	
  
Leah	
  P.	
  Macfadyen,	
  PhD	
  
Program	
  Director,	
  Evalua<on	
  and	
  Learning	
  Analy<cs	
  
Faculty	
  of	
  Arts,	
  The	
  University	
  of	
  Bri<sh	
  Columbia	
  
Vancouver,	
  Canada	
  
leah.macfadyen@ubc.ca	
  
hNp://www.slideshare.net/leahmac1	
  	
  
hNp://isit.arts.ubc.ca/learning-­‐analy<cs/	
  	
  
	
  
	
  
1.  Learning	
  analy<cs...just	
  another	
  buzzword?	
  
2.  Origins	
  and	
  drivers	
  
3.  Current	
  state	
  of	
  the	
  field:	
  Progress	
  and	
  challenges	
  
4.  Grassroots	
  LA:	
  Mee<ng	
  local	
  needs	
  
5.  ‘Big’	
  learning	
  analy<cs:	
  Ins<tu<onal	
  implementa<ons	
  
6.  Why	
  should	
  you	
  care?	
  
 	
  Learning	
  analy<cs	
  has	
  been	
  defined	
  as	
  
	
  
the	
  process	
  of	
  developing	
  ac#onable	
  insights	
  through	
  problem	
  
defini4on	
  and	
  the	
  applica4on	
  of	
  sta#s#cal	
  models	
  and	
  analysis	
  
against	
  exis4ng	
  and/or	
  simulated	
  future	
  data	
  	
  
	
  
Cooper,	
  2012	
  	
  
The	
  Society	
  for	
  Learning	
  Analy<cs	
  Research	
  (SoLAR)	
  defines	
  
the	
  core	
  ac<vi<es	
  of	
  learning	
  analy<cs	
  as	
  
	
  
the	
  measurement,	
  collec4on,	
  analysis	
  and	
  repor4ng	
  of	
  data	
  
about	
  learners	
  and	
  their	
  contexts	
  for	
  purposes	
  of	
  
understanding	
  and	
  op#mizing	
  learning	
  and	
  the	
  environments	
  
in	
  which	
  learning	
  occurs.	
  
hNp://www.solaresearch.org	
  	
  
	
  
Where	
  has	
  LA	
  come	
  from?	
  
LA	
  draws	
  from,	
  and	
  is	
  closely	
  <ed	
  to,	
  a	
  series	
  of	
  other	
  fields	
  of	
  
study	
  including	
  	
  
	
  
—  Business	
  intelligence	
  
—  Web	
  analy<cs	
  
—  “Academic	
  analy<cs”	
  (2005	
  -­‐	
  )	
  
—  Educa<onal	
  data	
  mining	
  (EDM)(~2000	
  -­‐)	
  
—  “Ac<on	
  analy<cs”	
  (~2008	
  -­‐	
  )	
  
Elias,	
  2011	
  
Drivers	
  
The	
  underpinnings:	
  
	
  
— Socio-­‐poli<cal/economic	
  factors	
  
— Educa<onal	
  factors	
  
— Technological	
  factors	
  
Ferguson,	
  2012	
  
New	
  developments….	
  
1.	
  Converging	
  developments	
  in	
  data	
  science	
  
—  Even	
  bigger	
  “big	
  data”	
  
—  Increasing	
  volumes	
  of	
  teaching-­‐	
  and	
  learning-­‐related	
  data	
  
—  More,	
  and	
  more	
  accessible,	
  data	
  
—  Parallel	
  developments	
  in	
  educa<onal	
  data	
  science	
  
—  Data	
  mining	
  algorithms	
  and	
  predic<ve	
  modelling	
  
—  Approaches	
  to	
  network	
  analysis	
  
—  Approaches	
  to	
  text	
  mining	
  and	
  discourse	
  analysis	
  at	
  scale	
  
—  Increasingly	
  user-­‐friendly	
  sofware	
  
2.	
  Moving	
  beyond	
  number	
  crunching	
  
—  EDM	
  laid	
  groundwork	
  of	
  computa<on	
  and	
  modelling	
  	
  
—  RecogniFon	
  that	
  learning	
  cannot	
  simply	
  be	
  understood	
  by	
  
algorithms,	
  and	
  that	
  social	
  and	
  pedagogical	
  theory,	
  
approaches	
  and	
  insights	
  must	
  also	
  be	
  brought	
  to	
  bear.	
  
—  Technological,	
  ideological,	
  and	
  methodological	
  orienta<ons	
  of	
  
the	
  field	
  of	
  learning	
  analy<cs	
  differen<ate	
  it	
  from	
  EDM	
  	
  
“…technical,	
  pedagogical,	
  and	
  social	
  domains	
  must	
  be	
  brought	
  into	
  
dialogue	
  with	
  each	
  other	
  to	
  ensure	
  that	
  interven4ons	
  and	
  organiza4onal	
  
systems	
  serve	
  the	
  needs	
  of	
  all	
  stakeholders.”	
  
	
  
Siemens	
  &	
  Baker,	
  2012	
  
3.	
  Interdisciplinary	
  collaboraFon	
  	
  
Technical/AnalyFc	
   Social	
  Sciences/EducaFon	
  
•  sta<s<cs	
  
•  data	
  visualiza<on	
  and	
  visual	
  
analy<cs	
  
•  educa<onal	
  data	
  mining	
  
•  computer	
  science	
  
•  machine	
  learning	
  	
  
•  natural	
  language	
  processing	
  
•  human-­‐computer	
  interac<on	
  
•  and	
  others….	
  
	
  
•  social	
  sciences	
  
•  educa<on	
  
•  (educa<onal)	
  psychology	
  
•  psychometrics	
  
•  educa<onal	
  technology	
  
•  art	
  and	
  design	
  
•  and	
  others…	
  
	
  
t 2013
e processing
r interaction
ychology
nology
gher education as a system
social pedagogical
technical/analytic
LA
EDM
Figure 1. The interdisciplinary scope of learning analytics
LA	
  ImplementaFon:	
  Current	
  state	
  of	
  the	
  field	
  
—  Stage	
  1:	
  Extrac<on	
  and	
  repor<ng	
  of	
  transac<on-­‐level	
  data	
  
—  Stage	
  2:	
  Analysis	
  and	
  monitoring	
  of	
  opera<onal	
  performance	
  
—  Stage	
  3:	
  “What-­‐if”	
  decision	
  support	
  (such	
  as	
  scenario	
  building)	
  
—  Stage	
  4:	
  Predic<ve	
  modeling	
  &	
  simula<on	
  
—  Stage	
  5:	
  Automa<c	
  triggers	
  and	
  alerts	
  (interven<ons)	
  
	
  
Goldstein,	
  P.	
  &	
  Katz,	
  R.	
  (2005)	
  
AnalyFcs	
  Panic?	
  
	
  
•  For more on challenges of acting on educational research, see McIntosh, 1979
•  For more on LA strategy and policy, see Ferguson et al., 2014; Macfadyen et al.,
2014
Learning	
  analyFcs	
  goals	
  
—  Learner	
  awareness	
  
—  Monitoring	
  and	
  tracking	
  
—  Reflec<on	
  and	
  research	
  
—  Evalua<on	
  and	
  planning	
  
—  Repor<ng	
  and	
  communica<on	
  
adapted	
  from	
  Kay	
  (2013)	
  
Start	
  where	
  you	
  are:	
  
Clarifying	
  stakeholders,	
  purposes	
  and	
  goals	
  
Discussion Paper, August 2013
Table 2. Purposes and stakeholders in university learning analytics (adapted from Kay (2013))
LA tools or insights can facilitate…
Example
stakeholders?
Learner awareness of own learning strategies and performance to
encourage self-regulated learning and support metacognition
Learners
Monitoring and tracking for immediate decisions
• Identifying problems early enough to intervene
• Distinguishing students who are loafing, gaming the system
Individual educators
Reflection and research for recognizing long term issues
• Insights into learning processes and performance by many
learners
• Education research
o Attrition factors
o Insights into individual performance
Individual educators
Educational researchers
Administrators
Planning
• course design/re-design
• Identifying problems early enough to intervene
• Distinguishing students who are loafing, gaming the system
Individual educators
Reflection and research for recognizing long term issues
• Insights into learning processes and performance by many
learners
• Education research
o Attrition factors
o Insights into individual performance
Individual educators
Educational researchers
Administrators
Planning
• course design/re-design
• curriculum and program planning
• faculty-level planning with regards to course and program
offerings
• teaching assignments
• decision-making with regards to management, staffing, etc.
Individual educators
Administrators
Reporting and communication among and between stakeholder
groups e.g.:
• Educators to learners
• Institution to parents
• Institution to government
• Peer to peer
Learners
Educators
Administrators
Government
In sum, learning analytics as a field spans a wide range of stakeholders, ends and output types. It has at
its core an exploratory and analytic approach to educational research that makes use of large sets of
educational data, with the goal of uncovering new approaches to measuring or monitoring learning or
teaching. Output may include tools, systems or reports for learners and/or educators on their activities
within the teaching and learning system. It may also include automated or non-automated reporting
and/or visualization tools for educators, administrators, governments and policy makers on individual,
unit or institutional performance, with the goal of informing ongoing planning and educational
Big	
  data	
  in	
  UBC	
  Arts…	
  
—  Student	
  informa<on	
  (demographics,	
  origins,	
  academic	
  history…)	
  
—  Enrollment	
  informa<on	
  (enrollments,	
  withdrawals,	
  grades,	
  program	
  
specializa<ons)	
  
—  Course	
  evalua<ons	
  (scores,	
  comments)	
  
—  LMS	
  ac<vity	
  data	
  (‘clickstream’	
  data)	
  
—  MOOC	
  data	
  
—  Ac<vity	
  data	
  from	
  other	
  technologies	
  (lecture	
  annota<on	
  systems,	
  
blogs,	
  wikis)	
  
—  All	
  kinds	
  of	
  student	
  wri<ng	
  (online,	
  offline)	
  
—  Open	
  data	
  (LinkedIn	
  data,	
  geographic	
  data…)	
  
LA	
  quesFons	
  in	
  UBC	
  Arts	
  
—  Do	
  students	
  from	
  different	
  parts	
  of	
  the	
  world	
  show	
  different	
  
ac<vity	
  levels/paNerns	
  in	
  online	
  courses?	
  
—  Which	
  students	
  are	
  more	
  likely	
  to	
  complete	
  course	
  
evalua<ons,	
  and	
  does	
  it	
  maNer?	
  
—  Have	
  average	
  grades	
  changes	
  over	
  <me,	
  and	
  how?	
  
—  Which	
  students	
  are	
  most	
  at	
  risk	
  of	
  failure?	
  (How	
  early	
  can	
  we	
  
iden<fy	
  them	
  and	
  provide	
  beNer	
  support?)	
  
—  Who	
  are	
  our	
  students?	
  Where	
  do	
  they	
  come	
  from	
  and	
  how	
  has	
  
that	
  changed	
  over	
  <me?	
  
—  What	
  can	
  clickstream	
  data	
  tell	
  us	
  about	
  how	
  students	
  
learn?	
  
—  What	
  does	
  ‘learner	
  engagement’	
  look	
  like	
  in	
  a	
  MOOC	
  
and	
  how	
  can	
  we	
  promote	
  it?	
  
—  What	
  are	
  the	
  most	
  common	
  themes	
  in	
  student	
  course	
  
evalua<on	
  comments?	
  
—  What	
  are	
  the	
  most	
  common	
  enrollment	
  choices	
  our	
  
learners	
  make	
  to	
  complete	
  their	
  degrees?	
  Do	
  ‘high	
  
achievers’	
  make	
  different	
  choices	
  than	
  ‘low	
  achievers’?	
  
—  Teaching	
  and	
  learning	
  detec<ve	
  stories	
  of	
  all	
  kinds…..	
  
Author's personal copy
Mining LMS data to develop an ‘‘early warning system” for educators: A proof
of concept
Leah P. Macfadyen a,*, Shane Dawson b
a
Science Centre for Learning and Teaching, The University of British Columbia, 6221 University Boulevard, Vancouver, British Columbia, Canada V6T 1Z1
b
Graduate School of Medicine, University of Wollongong, Wollongong, NSW 2522, Australia
a r t i c l e i n f o
Article history:
Received 21 May 2009
Received in revised form 31 August 2009
Accepted 3 September 2009
Keywords:
Collaborative learning
Evaluation methodologies
Learning communities
Teaching/learning strategies
Post-secondary education
a b s t r a c t
Earlier studies have suggested that higher education institutions could harness the predictive power of
Learning Management System (LMS) data to develop reporting tools that identify at-risk students and
allow for more timely pedagogical interventions. This paper confirms and extends this proposition by
providing data from an international research project investigating which student online activities accu-
rately predict academic achievement. Analysis of LMS tracking data from a Blackboard Vista-supported
course identified 15 variables demonstrating a significant simple correlation with student final grade.
Regression modelling generated a best-fit predictive model for this course which incorporates key vari-
ables such as total number of discussion messages posted, total number of mail messages sent, and total num-
ber of assessments completed and which explains more than 30% of the variation in student final grade.
Logistic modelling demonstrated the predictive power of this model, which correctly identified 81% of
students who achieved a failing grade. Moreover, network analysis of course discussion forums afforded
insight into the development of the student learning community by identifying disconnected students,
patterns of student-to-student communication, and instructor positioning within the network. This study
affirms that pedagogically meaningful information can be extracted from LMS-generated student track-
ing data, and discusses how these findings are informing the development of a customizable dashboard-
like reporting tool for educators that will extract and visualize real-time data on student engagement and
likelihood of success.
Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction
Higher education institutions (HEIs) around the world are undergoing rapid changes as they adapt to the new realities of the knowledge
society. While the development, maintenance and dissemination of knowledge have long been the primary goals of higher education insti-
tutions (Bloland, 1995), recent social and economic changes are forcing universities to adopt new approaches in the way these goals are
achieved. Educators are being asked to demonstrate quality teaching practices with decreasing fiscal and human resources, whilst catering
to the learning needs of a burgeoning student population that is increasingly diverse in many dimensions (Twigg, 1994, 1994a, 1994b).
Student demographics have radically shifted, and student enrollment numbers have dramatically increased (Patrick & Gaële, 2007). The
traditional and idealized experience of higher education as ‘‘academically oriented living and learning communities” where ‘‘full-time stu-
dents receive a good deal of faculty contact and many academic support services in the residential setting” (Volkwein, 1999, p. 14) relies
upon intensive fiscal and labour resources. Unfortunately, the reality is that federal, state and provincial government funding commitments
for higher education have failed to match the escalating sector resourcing requirements (Bates, 2000; Rossner & Stockley, 1997). To sup-
Computers & Education 54 (2010) 588–599
Contents lists available at ScienceDirect
Computers & Education
journal homepage: www.elsevier.com/locate/compedu
Author's personal copy
3.3. Logistic regression
A binary logistic regression analysis was conducted to test the reliability of the model in predicting whether or not an individual student
is considered ‘at risk of failure’. Individual students with course final grade <60% were coded as ‘at risk’ (0), while students with final grade
P60% were coded as ‘performing adequately or better’ (1). In the UBC grading scheme, <60% represents a grade of C- or poorer; <50% is
considered a failing grade (University of British Columbia, 2009). We selected this division point to include students whose final grade indi-
cates that they barely passed the course and may have benefitted from earlier support and intervention.
Details of the regression model are shown in Table 5. For the purposes of this study, the ‘hit rate’ or predictive power of the model is of
greatest significance. Overall, the logistic regression model accurately placed individual students in either the ‘at risk’ or ‘performing ade-
quately’ category 73.7% of the time (Table 6). The model resulted in ‘Type II’ errors (classifying an ‘at risk’ student as ‘performing ade-
quately’) at a rate of only 12.7%: 15 students out of 118 were predicted to be performing adequately, while their final course grade
placed them in the ‘at risk’ category. However, of these 15 students, only four actually failed the course (achieving a final grade of
<50%), representing a ‘predictive failure’ rate of only 3.4% (four students out of 118). The logistic model also resulted in Type I errors
13.6% of the time by placing 16 students in the ‘at risk’ category even though these students eventually passed the course (achieving grades
of >60%). However, given the importance of identifying students at risk of failure early in their course progression, the occurrence of Type I
errors is of less concern. More simply put, it is better to mistakenly identify a student as at risk of failure then to neglect a student requiring
additional learning support. In sum, logistic modelling effectively identified the majority of the students who failed or almost failed this
course and who would have been considered ‘at risk of failure’ by instructors if this data had been accessible earlier in the term.
Table 5
Logistic regression analysis summary for course LMS tracking variables (Nstudents = 118).
Included 95% CI for Exp b
b (SE) Lower Exp b Upper
Constant .46 (.24) 1.58
# Mail messages sent .74*
(.35) 1.05 2.10 4.19
Total # discussion messages posted 1.02*
(.39) 1.30 2.78 5.98
# Assessments finished .66*
(.26) 1.16 1.93 3.22
Note: r2
= .31 (Cox & Snell, 1989), .32 (Nagelkerke, 1991). Model v2
= 9.59.
*
p < .05.
Table 6
‘Risk of failure’ classification results for students in course (Nstudents = 118).
Observed Predicted
At risk Not at risk Percentage correct
At risk 38 15 71.7
Not at risk 16 49 75.4
Overall percentage 73.7
‘At risk’ = final grade <60%; ‘Not at risk’ = final grade >60%.
L.P. Macfadyen, S. Dawson / Computers & Education 54 (2010) 588–599 595
SNAPP http://www.snappvis.org
A ‘Top 10%’ student’s ego network”
A ‘Bottom 10%’ student’s ego network”
Can network analysis help us understand learner
behaviour and persistence in MOOCs?
Change in the
student body
over time?
Who is dropping out?
Finding	
  “Failure	
  Hotspots”	
  
“Student	
  Success”	
  Dashboards	
  
Temporal analysis of enrollment patterns
The	
  Purdue	
  Signals	
  Project	
  	
  
hNp://www.itap.purdue.edu/studio//signals/	
  	
  
“The premise behind CS
is fairly simple: utilize the
wealth of data found at an
educational institution,
including the data
collected by instructional
tools, to determine in real
time which students might
be at risk, partially
indicated by their effort
within a course.”
Arnold & Pistilli, 2012
UMBC’s	
  ‘Check	
  My	
  AcFvity’	
  tool	
  	
  
hNp://www.educause.edu/ero/ar<cle/video-­‐demo-­‐umbcs-­‐check-­‐my-­‐ac<vity-­‐tool-­‐students	
  	
  
UMBC	
  Course	
  AcFvity	
  by	
  Final	
  Grade	
  	
  
Credit: John Fritz, UMBC
CMA	
  Use	
  by	
  Final	
  Grade	
  
Credit: John Fritz, UMBC
PercentGrade
UBC	
  data	
  on	
  ‘self-­‐monitoring’	
  and	
  performance	
  
	
  
Student	
  ApFtude	
  Data	
  	
  
(SATs,	
  current	
  GPA,	
  etc.)	
  
Student	
  Demographic	
  Data	
  
(Age,	
  gender,	
  etc.)	
  
Sakai	
  Event	
  Log	
  Data	
  
Sakai	
  Gradebook	
  Data	
  
PredicFve	
  
Model	
  
Scoring	
  
Iden<fies	
  
students	
  “at	
  
risk”	
  to	
  not	
  
complete	
  
course	
  
SIS	
  Data	
  LMS	
  Data	
  
IntervenFon	
  Deployed	
  
“Awareness”	
  or	
  Online	
  Academic	
  Support	
  
Environment	
  (OASE)	
  
Model	
  Developed	
  
Using	
  Historical	
  Data	
  
Step	
  #1:	
  Developed	
  model	
  
using	
  historical	
  data	
   Academic	
  Alert	
  	
  
Report	
  (AAR)	
  
CreaFng	
  an	
  Open	
  Academic	
  Early	
  Alert	
  System	
  
hbps://confluence.sakaiproject.org/display/LAI/Learning+AnalyFcs+IniFaFve	
  	
  
Research	
  Findings:	
  Final	
  Course	
  Grades	
  
—  Analysis	
  showed	
  a	
  
staFsFcally	
  significant	
  
posi<ve	
  impact	
  on	
  final	
  
course	
  grades	
  
—  No	
  difference	
  between	
  
treatment	
  groups	
  
—  Similar	
  trend	
  among	
  low	
  
income	
  students	
  
50	
  
60	
  
70	
  
80	
  
90	
  
100	
  
Awareness	
   OASE	
   Control	
  
Final	
  Grade	
  (%)	
  
Mean	
  Final	
  Grade	
  for	
  "at	
  Risk"	
  Students	
  	
  
Jayaprakash et al., 2014
Why	
  should	
  you	
  care?	
  
—  Driving	
  and	
  evalua<ng	
  innova<on	
  
—  Support	
  for	
  self-­‐directed	
  learning	
  
—  Provision	
  of	
  informed	
  and	
  targeNed	
  advice	
  and	
  support	
  at	
  all	
  stages	
  of	
  the	
  
learning	
  journey:	
  recruitment,	
  academic	
  advising	
  and	
  recommending,	
  
facilita<on,	
  reten<on	
  
—  Con<nuous	
  assessment	
  of	
  quality	
  of	
  learning	
  materials	
  
—  Development	
  of	
  new	
  (beNer?)	
  educa<onal	
  performance	
  indicators	
  and	
  
modes	
  of	
  assessment	
  
—  Real-­‐<me	
  academic	
  performance	
  monitoring	
  and	
  management	
  for	
  learners	
  
and	
  educators	
  
—  Maintenance	
  of	
  comprehensive	
  	
  
student	
  records	
  
—  Effec<ve	
  repor<ng	
  at	
  mul<ple	
  levels	
  
Learning	
  analy4cs	
  (LA)	
  offers	
  the	
  capacity	
  to	
  inves4gate	
  
the	
  rising	
  4de	
  of	
  learner	
  data	
  with	
  the	
  goal	
  of	
  
understanding	
  the	
  ac4vi4es	
  and	
  behaviors	
  associated	
  
with	
  effec4ve	
  learning,	
  and	
  to	
  leverage	
  this	
  knowledge	
  in	
  
op4mizing	
  our	
  educa4onal	
  systems	
  (Bienkowski,	
  Feng,	
  &	
  
Means,	
  2012;	
  Campbell,	
  DeBlois,	
  &	
  Oblinger,	
  2007).	
  
Macfadyen	
  et	
  al.,	
  2014	
  
leah.macfadyen@ubc.ca
http://www.slideshare.net/leahmac1
Arnold,	
  K.	
  E.	
  &	
  Pis<lli,	
  M.	
  (2012).	
  Course	
  Signals	
  at	
  Purdue:	
  Using	
  Learning	
  Analy<cs	
  To	
  Increase	
  
Student	
  Success.	
  Course	
  Signals	
  at	
  Purdue:	
  Using	
  learning	
  analy<cs	
  to	
  increase	
  student	
  success.	
  
Proceedings	
  of	
  the	
  2nd	
  Interna<onal	
  Conference	
  on	
  Learning	
  Analy<cs	
  &	
  Knowledge.	
  New	
  
York:	
  ACM.	
  
hNps://www.itap.purdue.edu/learning/docs/research/Arnold_Pis<lli-­‐
Purdue_University_Course_Signals-­‐2012.pdf	
  	
  	
  
Bichsel,	
  J.	
  (2012).	
  2012	
  ECAR	
  study	
  of	
  analy4cs	
  in	
  higher	
  educa4on.	
  Retrieved	
  from	
  
hNp://www.educause.edu/library/resources/2012-­‐ecar-­‐study-­‐analy<cs-­‐higher-­‐educa<on	
  	
  
Cooper,	
  (2012).	
  What	
  is	
  Analy<cs?	
  Defini<on	
  and	
  Essen<al	
  Characteris<cs.	
  	
  CETIS	
  Analy4cs	
  
Series,	
  1	
  (5).	
  hNp://publica<ons.ce<s.ac.uk/2012/521	
  	
  
Elias,	
  T.	
  (2011).	
  Learning	
  Analy4cs:	
  Defini4ons,	
  Processes	
  and	
  Poten4al.	
  
hNp://learninganaly<cs.net/LearningAnaly<csDefini<onsProcessesPoten<al.pdf	
  	
  	
  
Ferguson,	
  R.	
  (2012).	
  Learning	
  analy<cs:	
  drivers,	
  developments	
  and	
  challenges.	
  Interna4onal	
  
Journal	
  of	
  Technology	
  Enhanced	
  Learning,	
  4(5/6)	
  pp.	
  304–317.	
  Forrester,	
  J.	
  W.	
  (1961).	
  
Industrial	
  dynamics.	
  Cambridge,	
  MA:	
  MIT	
  Press.	
  
References
Ferguson,	
  R.,	
  Macfadyen,	
  L.	
  P.,	
  Clow,	
  D.,	
  Tynan,	
  B.,	
  Alexander,	
  S.,	
  &	
  Dawson,	
  S.	
  (2014).	
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learning	
  analy<cs	
  in	
  context:	
  Overcoming	
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Goldstein,	
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  Academic	
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technology	
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hNp://www.educause.edu/ECAR/AcademicAnaly<csTheUsesofMana/156526	
  Ison,	
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Systems	
  thinking	
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  prac<ce	
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  ac<on	
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  H.	
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of	
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Jayaprakash,	
  S.	
  M.,	
  Moody,	
  E.	
  W.,	
  Lauría,	
  E.	
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  Regan,	
  J.	
  R.,	
  &	
  Baron,	
  J.	
  D.	
  (2014).	
  Early	
  Alert	
  of	
  
Academically	
  At-­‐Risk	
  Students:	
  An	
  Open	
  Source	
  Analy<cs	
  Ini<a<ve.	
  Journal	
  of	
  Learning	
  
Analy4cs,	
  1(1),	
  6-­‐47.	
  hNp://epress.lib.uts.edu.au/journals/index.php/JLA/ar<cle/view/3249	
  	
  
Kay,	
  J.	
  (2013).	
  Visualiza4on	
  and	
  Data	
  Presenta4on	
  aka	
  Open	
  Learner	
  Modelling	
  (OLM).	
  
Presenta<on	
  at	
  the	
  2013	
  Learning	
  Analy<cs	
  Summer	
  Ins<tute,	
  Stanford,	
  California.	
  Slides	
  
available	
  at:	
  hNp://sydney.edu.au/engineering/it/~judy/Homec/bio.html	
  	
  	
  
	
  
Macfadyen,	
  L.	
  P.,	
  Dawson,	
  S.	
  Pardo,	
  A.,	
  &	
  Gašević,	
  D.	
  (2014).	
  Embracing	
  Big	
  Data	
  in	
  Complex	
  
Educa<onal	
  Systems:	
  The	
  Learning	
  Analy<cs	
  Impera<ve	
  and	
  the	
  Policy	
  Challenge.	
  Research	
  &	
  
Prac<ce	
  in	
  Assessment,	
  9,	
  17-­‐28.	
  
hNp://www.rpajournal.com/dev/wp-­‐content/uploads/2014/10/A2.pdf	
  
Macfadyen,	
  L.	
  P.,	
  &	
  Dawson,	
  S.	
  (2010).	
  Mining	
  LMS	
  data	
  to	
  develop	
  an	
  ‘‘early	
  warning	
  system”	
  
for	
  educators:	
  A	
  proof	
  of	
  concept.	
  Computers	
  &	
  Educa4on,	
  54,588-­‐599.	
  doi:
10.1016/j.compedu.2009.09.008	
  
Macfadyen,	
  L.	
  P.,	
  &	
  Dawson,	
  S.	
  (2012).	
  Numbers	
  Are	
  Not	
  Enough.	
  Why	
  e-­‐Learning	
  Analy<cs	
  
Failed	
  to	
  Inform	
  an	
  Ins<tu<onal	
  Strategic	
  Plan.	
  Educa4onal	
  Technology	
  &	
  Society,	
  15	
  (3),	
  149–
163.	
  
McIntosh,	
  N.	
  E.,.	
  (1979).	
  Barriers	
  to	
  implemen<ng	
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  in	
  Higher	
  Educa<on.	
  Studies	
  in	
  
Higher	
  Educa4on,	
  4(1),	
  77-­‐	
  86.	
  
Méndez,	
  G.,	
  Ochoa,	
  X.,	
  Chiluiza,	
  K.	
  &	
  de	
  Wever,	
  B.	
  (2014)	
  Curricular	
  Design	
  Analysis:	
  A	
  Data-­‐
Driven	
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  Analy4cs,	
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  84–119.	
  
	
  	
  
Norris,	
  D.,	
  Baer,	
  L.,	
  Leonard,	
  J.,	
  Pugliese,	
  L.	
  and	
  Lefrere,	
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  (2008).	
  Framing	
  Ac<on	
  Analy<cs	
  and	
  
Puwng	
  Them	
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  EDUCAUSE	
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from	
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Macfadyen usc tlt keynote 2015.pptx

  • 1. …in  a  world  of  larger  and  larger  data  sets,  increasing  popula4ons  of   increasingly  diverse  learners,  constrained  educa4on  budgets  and   greater  focus  on  quality  and  accountability  (Macfadyen  &  Dawson,   2012),  some  argue  that  using  analy4cs  to  op4mize  learning   environments  is  no  longer  an  op4on  but  an  impera4ve…   …Educa4on  can  no  longer  afford  not  to  use  learning  analy4cs.  As   Slade  and  Prinsloo  (2013)  maintain,  “Ignoring  informa4on  that   might  ac4vely  help  to  pursue  an  ins4tu4on’s  goals  seems   shortsighted  to  the  extreme”  (p.  1521).   Macfadyen  et  al.,  2014  
  • 2. What  do  we  mean  by     ‘learning  analy<cs’?     Leah  P.  Macfadyen,  PhD   Program  Director,  Evalua<on  and  Learning  Analy<cs   Faculty  of  Arts,  The  University  of  Bri<sh  Columbia   Vancouver,  Canada   leah.macfadyen@ubc.ca   hNp://www.slideshare.net/leahmac1     hNp://isit.arts.ubc.ca/learning-­‐analy<cs/        
  • 3. 1.  Learning  analy<cs...just  another  buzzword?   2.  Origins  and  drivers   3.  Current  state  of  the  field:  Progress  and  challenges   4.  Grassroots  LA:  Mee<ng  local  needs   5.  ‘Big’  learning  analy<cs:  Ins<tu<onal  implementa<ons   6.  Why  should  you  care?  
  • 4.    Learning  analy<cs  has  been  defined  as     the  process  of  developing  ac#onable  insights  through  problem   defini4on  and  the  applica4on  of  sta#s#cal  models  and  analysis   against  exis4ng  and/or  simulated  future  data       Cooper,  2012    
  • 5. The  Society  for  Learning  Analy<cs  Research  (SoLAR)  defines   the  core  ac<vi<es  of  learning  analy<cs  as     the  measurement,  collec4on,  analysis  and  repor4ng  of  data   about  learners  and  their  contexts  for  purposes  of   understanding  and  op#mizing  learning  and  the  environments   in  which  learning  occurs.   hNp://www.solaresearch.org      
  • 6. Where  has  LA  come  from?   LA  draws  from,  and  is  closely  <ed  to,  a  series  of  other  fields  of   study  including       —  Business  intelligence   —  Web  analy<cs   —  “Academic  analy<cs”  (2005  -­‐  )   —  Educa<onal  data  mining  (EDM)(~2000  -­‐)   —  “Ac<on  analy<cs”  (~2008  -­‐  )   Elias,  2011  
  • 7. Drivers   The  underpinnings:     — Socio-­‐poli<cal/economic  factors   — Educa<onal  factors   — Technological  factors   Ferguson,  2012  
  • 8. New  developments….   1.  Converging  developments  in  data  science   —  Even  bigger  “big  data”   —  Increasing  volumes  of  teaching-­‐  and  learning-­‐related  data   —  More,  and  more  accessible,  data   —  Parallel  developments  in  educa<onal  data  science   —  Data  mining  algorithms  and  predic<ve  modelling   —  Approaches  to  network  analysis   —  Approaches  to  text  mining  and  discourse  analysis  at  scale   —  Increasingly  user-­‐friendly  sofware  
  • 9. 2.  Moving  beyond  number  crunching   —  EDM  laid  groundwork  of  computa<on  and  modelling     —  RecogniFon  that  learning  cannot  simply  be  understood  by   algorithms,  and  that  social  and  pedagogical  theory,   approaches  and  insights  must  also  be  brought  to  bear.   —  Technological,  ideological,  and  methodological  orienta<ons  of   the  field  of  learning  analy<cs  differen<ate  it  from  EDM     “…technical,  pedagogical,  and  social  domains  must  be  brought  into   dialogue  with  each  other  to  ensure  that  interven4ons  and  organiza4onal   systems  serve  the  needs  of  all  stakeholders.”     Siemens  &  Baker,  2012  
  • 10. 3.  Interdisciplinary  collaboraFon     Technical/AnalyFc   Social  Sciences/EducaFon   •  sta<s<cs   •  data  visualiza<on  and  visual   analy<cs   •  educa<onal  data  mining   •  computer  science   •  machine  learning     •  natural  language  processing   •  human-­‐computer  interac<on   •  and  others….     •  social  sciences   •  educa<on   •  (educa<onal)  psychology   •  psychometrics   •  educa<onal  technology   •  art  and  design   •  and  others…    
  • 11. t 2013 e processing r interaction ychology nology gher education as a system social pedagogical technical/analytic LA EDM Figure 1. The interdisciplinary scope of learning analytics
  • 12. LA  ImplementaFon:  Current  state  of  the  field   —  Stage  1:  Extrac<on  and  repor<ng  of  transac<on-­‐level  data   —  Stage  2:  Analysis  and  monitoring  of  opera<onal  performance   —  Stage  3:  “What-­‐if”  decision  support  (such  as  scenario  building)   —  Stage  4:  Predic<ve  modeling  &  simula<on   —  Stage  5:  Automa<c  triggers  and  alerts  (interven<ons)     Goldstein,  P.  &  Katz,  R.  (2005)  
  • 13. AnalyFcs  Panic?     •  For more on challenges of acting on educational research, see McIntosh, 1979 •  For more on LA strategy and policy, see Ferguson et al., 2014; Macfadyen et al., 2014
  • 14. Learning  analyFcs  goals   —  Learner  awareness   —  Monitoring  and  tracking   —  Reflec<on  and  research   —  Evalua<on  and  planning   —  Repor<ng  and  communica<on   adapted  from  Kay  (2013)  
  • 15. Start  where  you  are:   Clarifying  stakeholders,  purposes  and  goals   Discussion Paper, August 2013 Table 2. Purposes and stakeholders in university learning analytics (adapted from Kay (2013)) LA tools or insights can facilitate… Example stakeholders? Learner awareness of own learning strategies and performance to encourage self-regulated learning and support metacognition Learners Monitoring and tracking for immediate decisions • Identifying problems early enough to intervene • Distinguishing students who are loafing, gaming the system Individual educators Reflection and research for recognizing long term issues • Insights into learning processes and performance by many learners • Education research o Attrition factors o Insights into individual performance Individual educators Educational researchers Administrators Planning • course design/re-design
  • 16. • Identifying problems early enough to intervene • Distinguishing students who are loafing, gaming the system Individual educators Reflection and research for recognizing long term issues • Insights into learning processes and performance by many learners • Education research o Attrition factors o Insights into individual performance Individual educators Educational researchers Administrators Planning • course design/re-design • curriculum and program planning • faculty-level planning with regards to course and program offerings • teaching assignments • decision-making with regards to management, staffing, etc. Individual educators Administrators Reporting and communication among and between stakeholder groups e.g.: • Educators to learners • Institution to parents • Institution to government • Peer to peer Learners Educators Administrators Government In sum, learning analytics as a field spans a wide range of stakeholders, ends and output types. It has at its core an exploratory and analytic approach to educational research that makes use of large sets of educational data, with the goal of uncovering new approaches to measuring or monitoring learning or teaching. Output may include tools, systems or reports for learners and/or educators on their activities within the teaching and learning system. It may also include automated or non-automated reporting and/or visualization tools for educators, administrators, governments and policy makers on individual, unit or institutional performance, with the goal of informing ongoing planning and educational
  • 17. Big  data  in  UBC  Arts…   —  Student  informa<on  (demographics,  origins,  academic  history…)   —  Enrollment  informa<on  (enrollments,  withdrawals,  grades,  program   specializa<ons)   —  Course  evalua<ons  (scores,  comments)   —  LMS  ac<vity  data  (‘clickstream’  data)   —  MOOC  data   —  Ac<vity  data  from  other  technologies  (lecture  annota<on  systems,   blogs,  wikis)   —  All  kinds  of  student  wri<ng  (online,  offline)   —  Open  data  (LinkedIn  data,  geographic  data…)  
  • 18. LA  quesFons  in  UBC  Arts   —  Do  students  from  different  parts  of  the  world  show  different   ac<vity  levels/paNerns  in  online  courses?   —  Which  students  are  more  likely  to  complete  course   evalua<ons,  and  does  it  maNer?   —  Have  average  grades  changes  over  <me,  and  how?   —  Which  students  are  most  at  risk  of  failure?  (How  early  can  we   iden<fy  them  and  provide  beNer  support?)   —  Who  are  our  students?  Where  do  they  come  from  and  how  has   that  changed  over  <me?  
  • 19. —  What  can  clickstream  data  tell  us  about  how  students   learn?   —  What  does  ‘learner  engagement’  look  like  in  a  MOOC   and  how  can  we  promote  it?   —  What  are  the  most  common  themes  in  student  course   evalua<on  comments?   —  What  are  the  most  common  enrollment  choices  our   learners  make  to  complete  their  degrees?  Do  ‘high   achievers’  make  different  choices  than  ‘low  achievers’?   —  Teaching  and  learning  detec<ve  stories  of  all  kinds…..  
  • 20. Author's personal copy Mining LMS data to develop an ‘‘early warning system” for educators: A proof of concept Leah P. Macfadyen a,*, Shane Dawson b a Science Centre for Learning and Teaching, The University of British Columbia, 6221 University Boulevard, Vancouver, British Columbia, Canada V6T 1Z1 b Graduate School of Medicine, University of Wollongong, Wollongong, NSW 2522, Australia a r t i c l e i n f o Article history: Received 21 May 2009 Received in revised form 31 August 2009 Accepted 3 September 2009 Keywords: Collaborative learning Evaluation methodologies Learning communities Teaching/learning strategies Post-secondary education a b s t r a c t Earlier studies have suggested that higher education institutions could harness the predictive power of Learning Management System (LMS) data to develop reporting tools that identify at-risk students and allow for more timely pedagogical interventions. This paper confirms and extends this proposition by providing data from an international research project investigating which student online activities accu- rately predict academic achievement. Analysis of LMS tracking data from a Blackboard Vista-supported course identified 15 variables demonstrating a significant simple correlation with student final grade. Regression modelling generated a best-fit predictive model for this course which incorporates key vari- ables such as total number of discussion messages posted, total number of mail messages sent, and total num- ber of assessments completed and which explains more than 30% of the variation in student final grade. Logistic modelling demonstrated the predictive power of this model, which correctly identified 81% of students who achieved a failing grade. Moreover, network analysis of course discussion forums afforded insight into the development of the student learning community by identifying disconnected students, patterns of student-to-student communication, and instructor positioning within the network. This study affirms that pedagogically meaningful information can be extracted from LMS-generated student track- ing data, and discusses how these findings are informing the development of a customizable dashboard- like reporting tool for educators that will extract and visualize real-time data on student engagement and likelihood of success. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Higher education institutions (HEIs) around the world are undergoing rapid changes as they adapt to the new realities of the knowledge society. While the development, maintenance and dissemination of knowledge have long been the primary goals of higher education insti- tutions (Bloland, 1995), recent social and economic changes are forcing universities to adopt new approaches in the way these goals are achieved. Educators are being asked to demonstrate quality teaching practices with decreasing fiscal and human resources, whilst catering to the learning needs of a burgeoning student population that is increasingly diverse in many dimensions (Twigg, 1994, 1994a, 1994b). Student demographics have radically shifted, and student enrollment numbers have dramatically increased (Patrick & Gaële, 2007). The traditional and idealized experience of higher education as ‘‘academically oriented living and learning communities” where ‘‘full-time stu- dents receive a good deal of faculty contact and many academic support services in the residential setting” (Volkwein, 1999, p. 14) relies upon intensive fiscal and labour resources. Unfortunately, the reality is that federal, state and provincial government funding commitments for higher education have failed to match the escalating sector resourcing requirements (Bates, 2000; Rossner & Stockley, 1997). To sup- Computers & Education 54 (2010) 588–599 Contents lists available at ScienceDirect Computers & Education journal homepage: www.elsevier.com/locate/compedu Author's personal copy 3.3. Logistic regression A binary logistic regression analysis was conducted to test the reliability of the model in predicting whether or not an individual student is considered ‘at risk of failure’. Individual students with course final grade <60% were coded as ‘at risk’ (0), while students with final grade P60% were coded as ‘performing adequately or better’ (1). In the UBC grading scheme, <60% represents a grade of C- or poorer; <50% is considered a failing grade (University of British Columbia, 2009). We selected this division point to include students whose final grade indi- cates that they barely passed the course and may have benefitted from earlier support and intervention. Details of the regression model are shown in Table 5. For the purposes of this study, the ‘hit rate’ or predictive power of the model is of greatest significance. Overall, the logistic regression model accurately placed individual students in either the ‘at risk’ or ‘performing ade- quately’ category 73.7% of the time (Table 6). The model resulted in ‘Type II’ errors (classifying an ‘at risk’ student as ‘performing ade- quately’) at a rate of only 12.7%: 15 students out of 118 were predicted to be performing adequately, while their final course grade placed them in the ‘at risk’ category. However, of these 15 students, only four actually failed the course (achieving a final grade of <50%), representing a ‘predictive failure’ rate of only 3.4% (four students out of 118). The logistic model also resulted in Type I errors 13.6% of the time by placing 16 students in the ‘at risk’ category even though these students eventually passed the course (achieving grades of >60%). However, given the importance of identifying students at risk of failure early in their course progression, the occurrence of Type I errors is of less concern. More simply put, it is better to mistakenly identify a student as at risk of failure then to neglect a student requiring additional learning support. In sum, logistic modelling effectively identified the majority of the students who failed or almost failed this course and who would have been considered ‘at risk of failure’ by instructors if this data had been accessible earlier in the term. Table 5 Logistic regression analysis summary for course LMS tracking variables (Nstudents = 118). Included 95% CI for Exp b b (SE) Lower Exp b Upper Constant .46 (.24) 1.58 # Mail messages sent .74* (.35) 1.05 2.10 4.19 Total # discussion messages posted 1.02* (.39) 1.30 2.78 5.98 # Assessments finished .66* (.26) 1.16 1.93 3.22 Note: r2 = .31 (Cox & Snell, 1989), .32 (Nagelkerke, 1991). Model v2 = 9.59. * p < .05. Table 6 ‘Risk of failure’ classification results for students in course (Nstudents = 118). Observed Predicted At risk Not at risk Percentage correct At risk 38 15 71.7 Not at risk 16 49 75.4 Overall percentage 73.7 ‘At risk’ = final grade <60%; ‘Not at risk’ = final grade >60%. L.P. Macfadyen, S. Dawson / Computers & Education 54 (2010) 588–599 595
  • 22.
  • 23. A ‘Top 10%’ student’s ego network”
  • 24. A ‘Bottom 10%’ student’s ego network”
  • 25. Can network analysis help us understand learner behaviour and persistence in MOOCs?
  • 26. Change in the student body over time?
  • 30. Temporal analysis of enrollment patterns
  • 31.
  • 32. The  Purdue  Signals  Project     hNp://www.itap.purdue.edu/studio//signals/     “The premise behind CS is fairly simple: utilize the wealth of data found at an educational institution, including the data collected by instructional tools, to determine in real time which students might be at risk, partially indicated by their effort within a course.” Arnold & Pistilli, 2012
  • 33.
  • 34. UMBC’s  ‘Check  My  AcFvity’  tool     hNp://www.educause.edu/ero/ar<cle/video-­‐demo-­‐umbcs-­‐check-­‐my-­‐ac<vity-­‐tool-­‐students    
  • 35. UMBC  Course  AcFvity  by  Final  Grade     Credit: John Fritz, UMBC
  • 36. CMA  Use  by  Final  Grade   Credit: John Fritz, UMBC
  • 37. PercentGrade UBC  data  on  ‘self-­‐monitoring’  and  performance    
  • 38. Student  ApFtude  Data     (SATs,  current  GPA,  etc.)   Student  Demographic  Data   (Age,  gender,  etc.)   Sakai  Event  Log  Data   Sakai  Gradebook  Data   PredicFve   Model   Scoring   Iden<fies   students  “at   risk”  to  not   complete   course   SIS  Data  LMS  Data   IntervenFon  Deployed   “Awareness”  or  Online  Academic  Support   Environment  (OASE)   Model  Developed   Using  Historical  Data   Step  #1:  Developed  model   using  historical  data   Academic  Alert     Report  (AAR)   CreaFng  an  Open  Academic  Early  Alert  System   hbps://confluence.sakaiproject.org/display/LAI/Learning+AnalyFcs+IniFaFve    
  • 39. Research  Findings:  Final  Course  Grades   —  Analysis  showed  a   staFsFcally  significant   posi<ve  impact  on  final   course  grades   —  No  difference  between   treatment  groups   —  Similar  trend  among  low   income  students   50   60   70   80   90   100   Awareness   OASE   Control   Final  Grade  (%)   Mean  Final  Grade  for  "at  Risk"  Students     Jayaprakash et al., 2014
  • 40. Why  should  you  care?   —  Driving  and  evalua<ng  innova<on   —  Support  for  self-­‐directed  learning   —  Provision  of  informed  and  targeNed  advice  and  support  at  all  stages  of  the   learning  journey:  recruitment,  academic  advising  and  recommending,   facilita<on,  reten<on   —  Con<nuous  assessment  of  quality  of  learning  materials   —  Development  of  new  (beNer?)  educa<onal  performance  indicators  and   modes  of  assessment   —  Real-­‐<me  academic  performance  monitoring  and  management  for  learners   and  educators   —  Maintenance  of  comprehensive     student  records   —  Effec<ve  repor<ng  at  mul<ple  levels  
  • 41. Learning  analy4cs  (LA)  offers  the  capacity  to  inves4gate   the  rising  4de  of  learner  data  with  the  goal  of   understanding  the  ac4vi4es  and  behaviors  associated   with  effec4ve  learning,  and  to  leverage  this  knowledge  in   op4mizing  our  educa4onal  systems  (Bienkowski,  Feng,  &   Means,  2012;  Campbell,  DeBlois,  &  Oblinger,  2007).   Macfadyen  et  al.,  2014   leah.macfadyen@ubc.ca http://www.slideshare.net/leahmac1
  • 42. Arnold,  K.  E.  &  Pis<lli,  M.  (2012).  Course  Signals  at  Purdue:  Using  Learning  Analy<cs  To  Increase   Student  Success.  Course  Signals  at  Purdue:  Using  learning  analy<cs  to  increase  student  success.   Proceedings  of  the  2nd  Interna<onal  Conference  on  Learning  Analy<cs  &  Knowledge.  New   York:  ACM.   hNps://www.itap.purdue.edu/learning/docs/research/Arnold_Pis<lli-­‐ Purdue_University_Course_Signals-­‐2012.pdf       Bichsel,  J.  (2012).  2012  ECAR  study  of  analy4cs  in  higher  educa4on.  Retrieved  from   hNp://www.educause.edu/library/resources/2012-­‐ecar-­‐study-­‐analy<cs-­‐higher-­‐educa<on     Cooper,  (2012).  What  is  Analy<cs?  Defini<on  and  Essen<al  Characteris<cs.    CETIS  Analy4cs   Series,  1  (5).  hNp://publica<ons.ce<s.ac.uk/2012/521     Elias,  T.  (2011).  Learning  Analy4cs:  Defini4ons,  Processes  and  Poten4al.   hNp://learninganaly<cs.net/LearningAnaly<csDefini<onsProcessesPoten<al.pdf       Ferguson,  R.  (2012).  Learning  analy<cs:  drivers,  developments  and  challenges.  Interna4onal   Journal  of  Technology  Enhanced  Learning,  4(5/6)  pp.  304–317.  Forrester,  J.  W.  (1961).   Industrial  dynamics.  Cambridge,  MA:  MIT  Press.   References
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