EFFECTIVENESS OF USING
E-LEARNING IN UNDERGRADUATE
MATHEMATICS COURSES
LS Abraham
Department of Mathematics
School of Mathematical &
Computational Sciences
Walter Sisulu University
P. Bag X1, Mthatha, 5117
South Africa
E-mail: lsabraham@wsu.ac.za
W Sinkala
Department of Applied
Mathematics
School of Mathematical &
Computational Sciences
Walter Sisulu University
P. Bag X1, Mthatha, 5117
South Africa
E-mail: wsinkala@wsu.ac.za
L Abraham, W Sinkala: e-learning conference
2011
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I.

BACKGROUND
Students admitted to do undergraduate mathematics courses are
not equipped with the skills or knowledge to pursue them.
Marks at SATAP Maths test taken by applicants to 1st yr BSC Extended Programme
at WSU, who obtained at least 40% marks for matric maths:
Year
No. who took
the maths test
No
passed
(at least 40%
mark)
% pass
2010
175
35
20
2011
142
39
27
L Abraham, W Sinkala: e-learning conference
2011
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….(contd.)

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There is low motivation among students.
Students are not often sure of their learning outcomes.
Students don’t try to access material required for
meeting the outcomes.
Performance statistics in level I BSc Maths modules from 2008 to 2010 at WSU
Year
Average % of pass from both
semesters
(Pass = Score at least 50%)
in the Regular stream
Average % of pass from both
semesters
(Pass = Score at least 50%)
in the Extended stream
2008
33
42
2009
35
66
2010
28
49
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The Case for e-Learning...



Young people are enthusiastic about using
electronic gadgets whether they are used for
play or for learning.
Computers are used only in a very limited
and domesticated way.
Students have no opportunities to learn
mathematics with the computer because this
is not part of mathematical contents.
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Conservatism among lecturers




The perception that mathematics is a conceptual
subject and the common opinion is that face-to-face
contact is necessary for conveying these concepts.
The ‘conceived’ huge amount of work involved in the
preparation of material that has to be compatible with
the web technology used in their LMS.
For an effective delivery, information has to be
presented differently for the computer screen than for
the printed page. So a new way to present content
needs to be developed.
There are problems surrounding symbol presentation
in the Hypertext Markup Language (HTML), the
language commonly used for internet presentation.
L Abraham, W Sinkala: e-learning conference
2011
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II.
A.
B.
C.
D.
E.
E-LEARNING EXPERIENCES OF THE
MATHEMATICAL FRATERNITY ON
DIFFERENT PARTS OF THE GLOBE
Parallel web-course to traditional mathematics course in
Università Bocconi in Milan
Jorge A Perez enhancing calculus learning through
Blackboard’s Discussion Board
Embracing On-line learning in the University of Florida and in
the University of Helsinki
On-line assessment in Mathematics and Anti-semester course
in the University of Pretoria
E-learning at Walter Sisulu University
L Abraham, W Sinkala: e-learning conference
2011
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A.
Parallel web-course to traditional mathematics course
in Università Bocconi in Milan
Project:
Università Bocconi developed since 1999/2000 a project which foresaw that for each
traditional course a parallel web-course be developed. Learning Space (in the 3.5
version) is made up of four main environments: Schedule, Media Center, Course Room,
Assessment Manager.
One aspect of the project was a complete e-learning course dedicated to students with
poor performances in mathematics ( all students registered at Università Bocconi since
more than three years, who have not succeeded in giving the first-year mathematics
exam); this course concerns approximately 100 students.
Observations after the start of the project:
 The quality of the teaching offer had sharply and undoubtedly improved.
Students considered the material in the Media Center very helpful, but its preparation
had taken a lot of time.
The Course Room had been lively, although mainly centered on teachers’
communications and students’ questions; it was not the place in which to pose or
discuss interesting additional mathematical problems. The students with particularly poor
performances in mathematics for whom the course was intended were much more
interested in ‘finally passing this exam’ than in ‘exploring the infinite beauty of
mathematics.’
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2011
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B.
Jorge A Perez enhancing calculus learning through
Blackboard’s Discussion Board
.Project:
The main goal was to help students with their efforts to learn
Calculus by encouraging them to participate in the Discussion
Board.
Once or twice a week, depending on the complexity of the topics
introduced, a thread was started in the Discussion Board. The
prompt asked students to explain in their own words the math
concepts presented to them that particular day or week.
Observations of the Instructor :
The use of the Discussion Board helped students in many ways:
1.It facilitated student interaction beyond the classroom;
2.It gave more advanced students opportunities to improve their
own understanding by explaining concepts to classmates;
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2011
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C.
Embracing on-line learning in the University of Florida and in
the University of Helsinki
1.Using
Web Technologies to Teach Mathematics at Florida State
University
The On-Line Single Variable Calculus was used to teach calculus at Florida
State University in 2004. Students were told that they need to have the
textbook, Stewart’s Early Transcendentals. An anonymous study about
studying habits was conducted during weeks 10 – 12 of classes.
In spite of having the book, most students (76.2%) responding to the survey
told that on-line materials are their primary source for the course.
When studying calculus what materials you are using?
%
Only Stewart’s book
9.5
Mainly Stewart’s book accompanied by the on-line
0
Mainly the on-line lecture notes accompanied by Stewart’s
book
14.3
On-line materials are my primary source for the course
76.2
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2011
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2.
On-line Lectures vs. Traditional Instruction at the University of
Helsinki
The basic course in calculus based at the University of Helsinki was
offered both as a traditional course and as a fully on-line course.
The traditional course consisted of lectures in large sections, problems
sessions in small sections and examinations.
Students of the on-line course did all of their studying over the web.
Examinations for the on-line students were the same as the
examinations for the traditional course.
Traditional class
Online class
Retention of students
62
66
1st test average
results (out of 24)
11.74
12.74
L Abraham, W Sinkala: e-learning conference
2011
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D.
Web-based courses at University of Pretoria
On-line assessment in Mathematics
Investigation:
At the University of Pretoria, web-based courses in Mathematics have
been running using WebCT. Johann Engelbrecht and Ansie
Harding has made an investigation into performance differences in
Constructed Response Questions (CRQ)s and Provided Response
Questions (PRQs) based on calculus courses taught in the first
two semesters of study.
Observation:
They conclude that students perform better in online PRQs than in
online CRQs, on average, and better in paper CRQs than in online
CRQs. It is therefore important to use a combination of question
types when setting an online paper.
1.
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2011
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Anti-semester course
About the course:
The majority of students who entered the anti-semester course are repeaters. They are
reluctant to attend class since, from their perspective; they’ve “heard it all before”.
A web-based course was developed with continuous guidance and support from the
lecturers. The lecturers tried to guide the student through the subject content by
providing
Detailed learning objectives for every section;
Guiding notes linking the textbook to the learning objectives;
Dynamic scheduling by daily communication;
Prescribed and pre-scheduled problems;
Complete and/or partial solutions to assigned problems (after time);
Communication facilities through a discussion forum and e-mail facility;
Weekly online self-testing;
Group activities such as projects and assignments;
An administrative notice board;
Weekly meetings.
Finding:
From 2000 to 2003 the pass rates of the web-presented courses were consistently
higher than those of the preceding four years of live classroom instruction. The needs
of the students who had to repeat the Calculus course and did not want to attend
classes were met in a highly successful manner.
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2011
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E.
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E-Learning in the Maths department at WSU with
the experiences of the authors
Used in the delivery of the module, Quantitative Techniques for
self-assessment tests, for uploading question papers of previous
years, memorandums and statistical tables. The instructor, L
Bester admits that her job is now easier as students get the
material they want without the lecturer having to do the task of
photocopying for 150 students.
Used in the delivery of the EP module, Integrated Mathematics II
for providing module information, announcements, practice
questions and for assessment purposes. The instructor L
Abraham sees the LMS as a medium to explain mathematical
concepts
Students doing Mathematics / Applied Mathematics at level 3 are
trained on MATLAB (essentially for numerical methods) & EXCEL
(for solving Operations Research problems such as the
Transportation Problem). Dr W Sinkala has been passionate about
applying and sharing his knowledge of mathematical software with
staff and students.
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2011
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III.
OBSERVATIONS FROM OWN EXPERIENCES
Unpleasant:
 Supervising eight 20-minute test sessions in the lab was timeconsuming.
 Students did not regularly log onto their Wiseup accounts and
take full advantage of the provided materials. .
 Students complained that they failed to access their accounts
from computers in the labs, often, due to computer faults or
networking problems.
Pleasant:
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Students got individual feedback immediately after their test.
Most of those who attempted the test a 2nd time performed better
than the 1st time.
The grades of the students were available without having to do
any marking.
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2011
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IV.
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RECOMMENDATIONS
. Lecturers who are still finding their feet in the using of
technology can take small steps like using CDs that
accompanies text books as with Stewart Calculus for projecting
in the classroom. The use of multimedia interactive courseware
with its ability to visualize concepts can be used to explain
calculus concepts.
Students are advantaged when given opportunities to work on
Mathematical software and Math type-setting programmes which
they will be using in their future research activities.
An introduction before a Mathematics lecture, module outcomes,
an archive of the mathematical progress of the class, discussion
forums, practice questions, links to resources all put on the LMS
are contributions.
Test containing PRQs with feedbacks serve as a preparation tool
for a more weighted assessment.
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2011
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V.
FUTURE OF E-LEARNING IN MATHEMATICS
This rapid transformation of mode of working has changed the nature
of doing mathematics in a fundamental way. Mathematics done with
the aid of a computer is qualitatively different from mathematics done
with paper and pencil alone. The computer does not simply ‘assist’
the mathematician in doing business as usual; rather, it changes the
nature of what is done - Devlin
The wealthiest and farthest-seeing Universities are today eager to
invest energies and resources on the use of technological
innovations in education. Presumably some of these investments will
turn out to be unproductive, but the idea that in the future the issue of
education will not do without a deep technological involvement
appears strong and widely shared. – G Osimo
Whether paper activities in mathematics will ever be completely
replaced by online activities is highly unlikely. But that online
mathematics has come to stay is beyond doubt. –
Engelbrecht/Harding
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THE END
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