VLE: Virtual Learning Environment for Statistics

VLE: Virtual Learning Environment for Statistics Sergei Zuyev and Mikael Enelund Department of Mathematical Sciences and Department of Applied Mechanics, Chalmers University of Technology, Sweden

Abstract The VLE developed at the Department of Statistics and Modelling Science of the University of Strathclyde, UK, and at Chalmers University, Sweden, provides students with a unified teaching environment containing randomly generated questions (quizzes) on every subject of the course syllabus, extensive system of hints and answers, links to the class text and other support materials: statistical tables, demonstrations, help files. Since it is web-based, the VLE is accessible from anywhere anytime, it does not depend on the operating system used, it has infinite number of variations of the study questions, so it provides students with valuable resource to practise beyond the assisted lab times. The VLE also provides class organises with extensive tools for monitoring each student’s activity on the VLE allowing for immediate intervention with individualised help should there be a need. It is also used for tests and examination: the students by the end of the course become very familiar with its environment and this helps to ease the examination stress. Since marking is done automatically, VLE saves a huge amount of staff time leaving them to scrutinise only boundary case submissions and appeals.

Introduction Chalmers
University
of
Technology
is
reputed
for
the
level
of
its
graduates
in
 Engineering.
However,
modern
technological
challenges
and
ubiquitous
use
of
 computers
call
for
changes
in
the
way
Probability
and
Statistics

(and
in
fact
most
 subjects
in
engineering
educations)
are
taught
at
the
university.

Scientists
working
 in
Cognitive
Psychology
recently
noted
that
modern
students
learn
much
 differently
than
it
used
to
be
a
few
decades
ago,
see,
e.g.
Sinclair
et
al.
(2006).
A
 term
`Nintendo
Syndrome’
has
been
dubbed
to
describe
the
approach
typical
for
 video‐games
generation:
do
not
read
manuals,
but
go
and
try.
If
”killed”,
try
 something
else
until
you
get
to
the
next
level.
This
attitude
now
clearly
shows
in
 studying:
it
becomes
increasingly
hard
to
make
students
read
books.
At
the
same
 time
providing
them
with
ways
to
try
before
reading
proves
educationally
 rewarding:
after
being
”killed”
a
few
times
most
of
the
students
unavoidably
come
 to
a
book
and
actually
learn
deeper.

 The
Mechanical
engineering
program
at
Chalmers
has
long
standing
record
of
 program
and
course
developments
as
well
as
pedagogical
innovations.

The
 program
played
a
leading
role
in
the
development
of
the
CDIO
(conceive–design
–
 implement
‐operate)
initiative
for
engineering
equation,
see
Crawley
et
al.
(2007).
 The
aim
of
the
CDIO‐model
is
to
strengthen
engineering
fundamentals
and
 engineering
practice
with
focus
on
integration,
entirety
and
systems
thinking.

 Further,
focus
is
transferred
from
solving
special
problems
with
solutions
that
are
 known
in
beforehand
to
more
open
general
problems
without
closed
form
 solutions.

In
the
Mechanical
engineering
program
at
Chalmers
itself
the
CDIO‐ approach
is
manifest
in
the
number
realistic
engineering
projects,
in
integrating


2

ways
of
teaching
programming,
communication,
team
work
and
project
work,
in
a
 reformed
integrated
mathematics
education
and
in
the
construction
of
new
 learning
environments,
notably
a
prototyping
lab
and
workshop.

 Cornerstones
in
the
reformed
mathematics
education
are,
see
also
Enelund
and
 Larsson
(2006),

 •
Full
integration
of
computational
aspects
(including
programming)
and
symbolic
 aspects
of
mathematics
 •
Emphasis
on
the
full
view
of
problem
solving,
i.e.,
set
up
the
mathematical
model,
 formulate
the
equations,
solve
the
equations
and
visualize
the
solution
to
asses
the
 correctness
of
the
model
and
the
solution
 •
Computer
assignments
and
exercises
from
engineering
and
physics
 •
Joint
computer
assignments
between
math
courses
and
mechanics
courses
 taught
in
parallel
 The
Virtual
Learning
Environment
(VLE)
for
Probability
and
Statistics
perfectly
fits
 this
paradigm
providing
students
with
a
unified
web‐based
framework

for
self‐ teaching.
It
has
being
developed
since
2005
at
the
Statistics
and
Modelling
Science
 department
of
the
University
of
Strathclyde,
UK
and
since
2009
also
at
Chalmers
 University
of
Technology.
At
Chalmers,
the
entire
course
of
Probability
and
 Statistics
for
3rd
year
Mechanical
Engineer
students
was
ported
to
use
VLE

and
 the
performance
results
of
208
students

as
well
as
the
students
evaluations
are
 very
promising.

The
students
strongly
believe
that
it
is
natural
to
use
the
 computer
to
solve
probability
and
statistics
problem.


Moreover,
they
sincerely
 appreciate
to
work
in
the
VLE
and
think
that
it
facilitates
their
learning
process.

 


VLE Approach The novel approach consists in shifting the weight from formal lectures and towards self-practise and self-studying with the help of the VLE also aided with statistical routines of Matlab computer package (or of Excel or Minitab). The VLE teaching environment contains randomly generated questions (quizzes) on every subject of the course curriculum. Currently, over 700 quizzes to be used with randomly generated data are programmed and their number is growing. They cover a wide range of themes including elementary probability: events and operations on these, Full Probability and Bayes formulae, random variables and their characteristics, standard distributions and limit theorems. Basic statistics covers graphical analysis and main numeric characteristics of data, sampling, estimates: point and interval, confidence intervals, hypotheses testing (Z-, t-, F- for means and variance), two-sample tests, regression for bi-variate and multivariate data. The VLE provides an extensive system of hints and answers to each study question, direct links to the course Study Guide and other support materials: statistical tables,

2

3

demonstrations, help files. A snapshot of a web-browser running VLE is shown in Figure 1 below.

Figure 1. Student study session. Since it is web-based, the VLE is accessible from anywhere anytime, it does not depend on the operating system used, it has infinite number of variations of the study questions, so it provides students with valuable resource to practise beyond the assisted session times.

Structure of a Typical VLE-based Course Currently the VLE provides easy ways to set up a new course with the following components. Methods is the main study session where students find questions categorised by themes and corresponding weeks. Each call to a question generates a new instance with new data, so that a student can try a question as many times as necessary to get consistently correct answers. Each question contains a hint with a direct link to the corresponding chapter of the Study Guide covering the theory and also a possibility to see the answers as the last resort. To provide students with assistance, Study sessions are usually organized with the teaching staff available to answer all possible problems. By our experience, a class of 20-30 students is usually well covered by just one demonstrator.

3

4

Projects is a specific task for students to work in a small group on a real world engineering problem, e.g., prediction of probability for crack growth and failure of a railway structure. It usually assumes writing a report which is then assessed by teaching staff. The VLE provides means to assign students to a group automatically as well as reshuffling and moving students between the groups later. Test sessions are usually organised during the teaching period and represents the same type of questions but carrying a weight in the total test mark and deprived of hints and other help systems. The marking is done by the system with the answers’ accuracy predefined. No staff intervention is necessary apart from the overall surveyance on the test environment: no noise, no talking, etc. The system can be set in such a way that only users of the computers installed in a certain location in a certain time can access the test. Examination is basically the same as a test session above with additional control on the timing: a test can be opened to the students for the whole week, for example, while examination session has much stricted time frame. Help system provides students with various support materials: the Study Guide available as a whole or by chapters, electronic statistical tables, statistical demos, links to external data sets, computer software help. Administrative tools. A great feature of the VLE is that it also provides the class organises with extensive tools for monitoring each student's activity on the VLE. Each question tried can be examined for an error which allows for immediate intervention with individualised help should there be a need, see an activity log on Figure 2.

Figure 2. VLE administrator view. 4

5

Apart from monitoring tools including mass email posting, various diagnostic views and building of surveys, the VLE contains tools for setting a new course: extensive timetabling capabilities, flexible structure and, most important, a new question builder. A new question can be added by copying and updating similar existing ones (context and keyword searches are provided for selecting questions from the bank) or by programming a completely new question from scratch using a standard template. Basically, when building a new question one has to figure out the range of plausible values for its data so that the question is meaningful whatever realisation of random data is generated.

VLE Internals The VLE and WWW systems are hosted at Chalmers by a virtual machine running Enterprise Linux system on the university mainframe. It provides the Apache web server, the PHP server-side scripting language, MySQL database and Statistical Computing System R, see R Development Core Team (2010). In addition, various database administration tasks are accomplished using the phpMyAdmin utility. Minimal requirements are not high: 2.4Ghz processor, 1GB RAM and 12 Gb of disk space (RAID-1 preferably for production system). The VLE is written in php which provides the web-interface and interconnection with the class data organised as a MySQL database. Many study questions are also realised in php for which an extensive library of basic statistics functions and graphics was written. Lately, the VLE has an integral support of R Statistical package so now Rroutines can be directly included in the question code including graphics produced by R. This opens widest possibilities for developing even advanced statistical courses: almost any numeric procedure that R is capable of can now be put in a form of a VLE question for students to practise. The latest example is multiple regression questions that the students at Chalmers learn with the help of Matlab. These questions are actually programmed with R which mimicks the corresponding Matlab’s procedures: regress and stepwise. Rserve package is used for interaction between php and R.

Learning with the VLE Six years of experience of using VLE at Strathclyde and lately at Chalmers University of Technology proves great potential of the VLE for teaching Statistics. First and foremost, it meets the challenges with changing learning attitudes outlined above by providing the students with a great tool to learn by practise. It gives them ways to practise as much as they feel like to become confident with the topic. As results show, a typical student at Chalmers during 7 weeks of the classes answered on average 150-200 questions! It is hardly possible to achieve in a Statistics class run in a traditional way. No wonder the results shown by the students are much higher than expected from previous years. Since the VLE uses web-interface, it is available to the registered students 24 hours from anywhere. This is not only a great helper to special needs students who now have

5

6

all the time to quietly learn at their own pace, but also for ordinary students when they cannot attend assisted classes due to illness or other reasons. The students also enjoyed the timely help and attention when the class organiser emailed some students about their alarming performance: this is certainly not what they usually expect in a big class of over 200 students. Here is just a few quotes from emails of students who took Statistics VLE course at Chalmers this year: On 22 Apr 2010, at 18:31, a male student wrote: First of all I'd like to say that I really like the VLE-system, I am retaking this year's course since I failed it last year, and I must say that this year's course is multiple times better than last year's in every single way, partially due to the VLE-system but not only, I also think that the study guide is very good! On 22 Apr 2010, at 14:05, a male student wrote: We students love your humble approach and everyone I've spoken with is more than positive to the course as a whole in your regime. I am engaged in education questions in the local student union at mechanical engineering and I don't think that I've ever heard so many positive reviews when introducing a new concept. Keep up the good work! On 22 Apr 2010, at 10:22, a male student wrote: First and foremost, thank you for a good course-layout! I really like VLE and how it eases the studying of this subject which was previously known to be pretty hard.

On 20 May 2010, at 12:09, a female student wrote: Even if we are test pilots for this course I must say it's one of the most well-organized courses I've attended at Chalmers! Well done Sergei! On 30 May 2010, at 12:11, a male student wrote: Thank you for a great course! This has been a great way of learning statistics.

Future Prospects Although the VLE can already be considered a solid mature system, there is still a numerous ways to develop it further. First of all, making it more modular will ease its installation at other universities and adaptation to their specific environment. Reshaping the VLE development as an open source project will also necessitate modular approach and would provide a new huge step. Rather challenging task is internationalisation and the next year or two we should be able to see its first results.

6

7

References Sinclair, G., McClaren, M. and Griffin, M.J. (2006) “E-learning and beyond. A discussion paper.” Campus 2020 process for the British Columbia Ministry of Advanced Education. http://www.aved.gov.bc.ca/campus2020/documents/elearning.pdf Crawley, E. F., Malmqvist, J., Brodeur, D. R. and Östlund, S. (2007) ‘’Rethinking Engineering Education – The CDIO Approach’’, Springer-Verlag, New York. Enelund, M. and Larsson S. (2006), “A Computational Mathematics Education for Students of Mechanical Engineering”, World Transactions on Engineering and Technology Education, Vol. 5, No. 2, pp 329-332, 2006. R Development Core Team (2010) “R: A Language and Environment for Statistical Computing”, Vienna, Austria, http://www.R-project.org

7