Using technology in the teaching of mathematics at the National University of Lesotho Moneoang Leshota National University of Lesotho, Lesotho, mjmakoele@nul.ls Introduction In 1993 while I was studying for my Masters degree in the UK, I came across the book Computers in the Mathematics Curriculum by the Mathematical Association. After reading through this book, I felt an uplifting in spirits which had not happened in a long time. How wonderful it would be to get into my Pre-entry programme class back in Lesotho and draw all these different graphs (linear, quadratic) using excel spreadsheet instead of pencil and a graph sheet. I recalled how it used to be: The pencil should have a very sharp tip, and should actually be HP so that it does not a make a mess on the graph sheet when one rubs it off. To draw the quadratic graph, one should not move their hand as the graph might have bumps. This happened around the time when I was about to finish my dissertation Discontinuities in Mathematics Education between High School and University in Lesotho: Bridging the Gap. I had learned most profoundly how technologies could aid in the teaching and learning of mathematics, and had experimented with Derive and Cabri-Geometre. My view was that, the usage of computers and other technologies was quite a breakthrough in my teaching of mathematics, and for my students as, whom the biggest concern at the time for them was their poor and seemingly deteriorating performance in mathematics at o level and beyond. I returned home in 1993 and was about to experiment with my new-found knowledge on using technology to teach the Pre-Entry Science class just about to enter into first year of their BSc degree. Then reality hit home. Socio-Economic factors in Lesotho Lesotho is a country of approximately 30000 km 2 in area, with a population of just over two million people. According to the Human Development Report 2005, Lesotho is ranked 149 th out of 177 countries on the Human Development Index with a HDI value of 0.497. It is one of the low human development countries with GNP
per capita (PPP US$) of 2561, and 49.2% of the population living below the income poverty line, therefore, quite a poor country. In terms of technology and technology development, Lesotho has 16 telephone mainlines per 1000 people, 47 cellular subscribers per 1000 people, 14 internet users per 1000 people, and 42 researchers per 1000 000 people (HDR, 2005). Therefore, for most of the population of Lesotho acquiring a computer would be quite impossible, so that the usage of computers is done mostly from the work-place by adults instead of school children. Political factors At the National University of Lesotho (NUL), in 1993 when I got back from my studies, there were about one hundred and twenty students joining the faculty of science and technology at first year level. The computer laboratories available in the university were stocked with about fifty (50) machines which were used exclusively by students at second year level and above, who measured in computer science. In recent years, the university has introduced a computer literacy course for all students of the university making it compulsory for each student to have done at least this computer literacy course by the time they graduate. To this effect, the university introduced a few computer laboratories stocked with computers to serve this purpose. All first year students in all faculties of the university excluding the faculty of science do the computer literacy course. The faculty of science and technology has two streams of first year students. The first stream, the specialized programme has about one hundred and twenty students majoring in Computer Science, Information Technology and Statistics. The second stream is the BSc general stream of some four hundred students following common first year programme. Both streams follow a similar curriculum for mathematics in the first year, namely, M1501 Algebra, Trigonometry and Analytical Geometry, and M1502 Calculus I. The implications here are that for the specialized programme, one can introduce the usage of computers in the teaching, but not for the general stream, as this stream would only have access to computers in their second year. The National University of Lesotho is mostly funded by government for its activities. At present, top on government agenda are issues of HIV and AIDS which is 30% prevalent in Lesotho, and issues of poverty reduction. Hence, the need for acquisition of more computers would have to be prioritised with all these other national programmes. Since the acquisition would be just for supplementing the teaching of
mathematics there would have to be a major political support on the side of the university to place its demand on computer acquisition to government. Lesotho and the Republic of South Africa Lesotho has an unusually distinct feature of being completely landlocked by another country, the Republic of South Africa. This makes South Africa Lesotho s immediate neighbour at all points. This is one rich neighbour ranking 120 th on HDI scale, with GNP per capita (PPP US$) of 10346 and 192 researchers per 1million people, features which cannot be compared at all with those of Lesotho. Due to this proximity and South Africa s international position academically, most of the students from Lesotho attend school in South Africa, from primary level up to university level. It is obvious that those students who start schooling in South Africa and are able to continue throughout university there would have better access to computers. On the other hand, most of the students only manage to get to South Africa at tertiary level. These students would have to work extremely hard to compete with the best of South African students who have had access to computers from early schooling. Mathematics education in Lesotho It is my opinion that mathematics education in Lesotho has not transformed in any major way in the last two decades or so. Factors affecting student performance in mathematics at high school and university were grouped into three categories way back in 1993 (Makoele: M.Sc Dissertation), namely: Teaching Methods used in the schools There was evident lack of teaching approaches such as investigation and problemsolving. It was believed by both students and lecturers interviewed at the time that the teaching was not geared to understanding due to pressures of examinations at the end of three years and five years respectively for the Lesotho schools, so that the teaching was seen to encourage rote learning. I have not found reason to believe that things have changed for the better in recent years as I teach more new students at university coming directly from the schools.
Mathematics at University On this particular issue, important factors were: i. The method of lecturing, which is traditionally followed at university requires some adjustment in the learning habits of students. ii. iii. Big classes at university of about 400 students taught together as opposed to classes of 40 to 50 students at school. The syllabus which in other countries would be covered over a period of two years at A level, is done over nine months at the NUL. Textbooks. Due to foreign exchange rates, the cost of textbooks is very high, hence there would be not much variety in the books for reference purposes. It has been the case that at NUL for some years there had not been prescribed books and students depend entirely on lecture notes. Research. In my opinion, research in mathematics education is virtually non-existent. Where there has been some research done, it would be uncoordinated, and hence unavailable to the public. In particular, at NUL, the departments of mathematics education and mathematics fall under two different faculties, their only interaction being of students in mathematics education taking mathematics courses in the department of mathematics. The department of mathematics education main focus is on the teaching of mathematics at school level, so that it does not work on research issues in undergraduate teaching of mathematics. On the other hand, there is a feeling among the members of the department of mathematics that issues of undergraduate teaching of mathematics fall under education and therefore have no place really in the department of mathematics. This has caused a major neglect of this important sector in the teaching of mathematics, so that at NUL there is no study or research whatsoever about the teaching of mathematics at undergraduate level, let alone the usage of digital technologies in the teaching of undergraduate mathematics. Mathematics Education in the World The Lecturers at NUL are expected to be conversant with the stuff that they teach to students like everyone else. In the light of unavailability of textbooks as mentioned earlier, they depend largely on the wide world web for reference. Here one finds lecture notes of other lecturers teaching the same subject in their own universities, research on current issues on specific subject matters, and innovations in the development of mathematics teaching. In as much as the stuff from the internet is fascinating, it is also very intimidating to some extent. For example, in teaching a topic in complex functions, I was distraught when introducing the concept of
complex maps, until I discovered a web page where someone did the very mapping using computer technology. This was so helpful to me that I conducted the next lecture to some 30 students in my office showing them how the functions map. And the next thought was, if only I could do that for all the courses and to all students that I teach. The possibilities created by technology in the teaching of undergraduate mathematics cannot be overemphasized, but the challenges posed by inaccessibility to these technologies and to be part of the global village that researches first hand on issues of using these technologies in the teaching of mathematics are similarly devastating to those interested in the technologies. Conclusion I believe that for many of us in the developing countries, the possibility of using digital technologies in the teaching of mathematics would be a great advantage. It is true that these technologies do not come cheap, but if they could be available, then a lot of work done in specialised programmes such as bridging and remedial programmes instituted for the science students entering tertiary education would be minimised, and there would be better results from these remedial and bridging programmes observed than without the technologies. Despite all these, I agree with Harold Wenglinsky who says that Computers can raise student achievement and even improve a school's climate. But they have to be placed in the right hands and used in the right ways.(education Week). What is needed is research on the aspects of the teaching of mathematics at all sectors of education, that is, from primary throughout to tertiary level so that individual efforts made could be adequately monitored and publicised. The research would help in giving guidance for educators to know exactly where and how to use the digital technologies. References Makoele, M. (1993). Discontinuities in Mathematics Education Between High School and University in Lesotho: Bridging the Gap. M.Sc. Dissertation, University of Reading, UK. Mann, W.J. & Tall, D. (1992). Computers in the Mathematics Curriculum. A Report of the Mathematical Association. Archer, J. (n.d.). The Link to Higher Scores http://counts.edweek.org/sreports/tc98/ets/ets-n.htm