L Abraham, W Sinkala: e-learning conference 2011 1 EFFECTIVENESS OF USING E-LEARNING IN UNDERGRADUATE MATHEMATICS COURSES LS Abraham Department of Mathematics

L Abraham, W Sinkala: e-learning conference 2011

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EFFECTIVENESS OF USING E-LEARNING IN UNDERGRADUATE MATHEMATICS COURSES

LS Abraham Department of Mathematics School of Mathematical & Computational SciencesWalter Sisulu UniversityP. Bag X1, Mthatha, 5117South AfricaE-mail: [email protected]

W SinkalaDepartment of Applied MathematicsSchool of Mathematical & Computational SciencesWalter Sisulu UniversityP. Bag X1, Mthatha, 5117South AfricaE-mail: [email protected]


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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


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….(contd.)

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.


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II. E-LEARNING EXPERIENCES OF THE MATHEMATICAL FRATERNITY ON DIFFERENT PARTS OF THE GLOBE

A. Parallel web-course to traditional mathematics course in Università Bocconi in Milan

B. Jorge A Perez enhancing calculus learning through Blackboard’s Discussion Board

C. Embracing On-line learning in the University of Florida and in the University of Helsinki

D. On-line assessment in Mathematics and Anti-semester course in the University of Pretoria

E. E-learning at Walter Sisulu University


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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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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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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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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


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D. Web-based courses at University of Pretoria

1. 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.


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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 providingDetailed 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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E. 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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III. OBSERVATIONS FROM OWN EXPERIENCES

Unpleasant: Supervising eight 20-minute test sessions in the lab was time-

consuming. 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:

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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IV. 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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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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L Abraham, W Sinkala: e-learning conference 2011 1 EFFECTIVENESS OF USING E-LEARNING IN UNDERGRADUATE MATHEMATICS COURSES LS Abraham Department of Mathematics