Mathematics in Rwanda

		Mathematics Education in Rwanda	In January 2007 my wife Susan Taylor and I started our five month sabbatical stay in Rwanda. Also with us were Prof. Carol Shubin (on a Fulbright Scholarship) and her family and graduate student Jennifer Wright. We taught at different Universities in the capital Kigali and learned to love this beautiful, but troubled country. This page contains my personal observations of the education system in Rwanda.
Introduction		Introduction Rwanda is a very small country in central Africa, about 3 degrees south of the equator and 1000 km west of the Indian Ocean. It has a population of just under 9 million people. It is among the 20 least developed nations in the world with a per capita income of about $250 per year. Unlike many other African countries, Rwanda has a single language - Kinyarwanda - spoken by all its residents. The population of Rwanda consists of three "ethnic" groups; the great majority are the Bahutu, a sizeable Batutsi minority, and a tiny number of Batwa. Rwanda was a country in the modern sense long before the colonial times. A feudal kingdom with a ruling class consisting mainly of Batutsi. In 1888 it became a German colony, as one of the last regions in Africa to be colonized, but no European set foot in the country until the mid 1890s. After World War I, Belgium took over the colonial rule and governed the country largely by taking ruthless advantage of the "ethnic" stratification of the society. They favored the Batutsi, which still has ramifications today. French became the language of business and government. With independence in 1961 the long supressed Bahutu majority took over the government, and for the following 30 years there were wide spread pogroms against the Batutsi. After an invasion by largely Batutsi exiles in 1990, Rwanda was devastated by a genocide in spring of 1994. Almost 1 million people were killed in 100 days, mostly members of the Batutsi minority. The Bahutu led government, which was responsible for the genocide was overthrown, and a new government led by the exile forces took over. The government has made a concerted effort to eradicate the tensions between the different groups, and Rwanda is currently a relatively stable and peaceful country. The government also made large investments in education. I visited the country on a sabbatical leave from January to May 2007, and taught at the Kigali institute of Science and Technology. top of page	Map of Rwanda Young Mountain Gorilla in Volcanoes National Park
Elementary Education
Secondary Education
Higher Education
Challenges
Advantages
Remarks
References

		Elementary Education In a society as poor as Rwanda, elementary education plays the most important role of the entire education system. Literacy in itself is more important than preparing students for professional jobs. After the genocide, elementary education became free and therefore accessible to all school age children. Elementary school is for six years and children are instructed in the basics, Kinyarwanda, Arithmetics, and at least one foreign language French or English. Despite it being free, sending a child to school carries expenses for a family; there are school uniforms to be bought and other supplies, and the child is not able to help the family in farming. Nevertheless, almost 95% of school aged children start elementary school. Around 15% drop out before finishing in sixth grade. top of page
		Secondary Education Only 35% of the graduates of elementary school continue on to secondary school for six more years of education. Students from rural areas often attend boarding schools in one of the larger cities. Instruction in secondary schools is in Kinyarwanda or a second language, traditionally in French, but recently English became more common. Students will learn a second foreign language besides the language of instruction. The goal is that all students are proficient in Kinyarwanda, English and French. The mathematics curriculum consists of algebra, geometry, trigonometry and calculus and is as such very similar to the curriculum the very best US students take. However, all secondary students take all these subjects. Teachers in secondary school receive significantly more training than in the US. Typically, a teacher is trained in two subjects. And the content taught in each of these subjects is broader than the content taught for a single subject undergraduate degree in the US. For example, prospective teachers in the combination Biology-Chemistry will take a considerable amount of mathematics coursework including a course in ordinary and partial differential equations! Prospective mathematics teachers will typically study subjects such as number theory, complex analysis, functional analysis, and similarly high level coursework in their second subject. All prospective teachers are also trained in pedagogy. Secondary school ends with a national exam. The mathematics portion of this exam has two levels. At the advanced A-level, students need to be proficient in all subjects including calculus. At the lower B-level of the exams, proficiency in the pre-calculus subjects is tested. top of page	Elementary School Students in Kinigi Village near Volcanoes NP Future Secondary School Teachers at the Kigali Institute of Education
		Higher Education This is the area where I have most experience. The national exam determines whether or not a graduate from secondary school can attend a university or not. Moreover, it will determine whether the student gets financial support in form of an interest free loan of 1,000,000 Rwandan Francs (about $1,800 called a bursary) or not. Finally, the government will also determine a students major depending on the outcome of the exam. The bursary (the FRw 1,000,000) will cover the entire cost of the four year program, including room and board for the 10 month academic year. All students take about 40 hours worth of classes every week during the semester. All first year mathematics students take all their courses together, and stay in a cohort for the entire four years. Mathematics students are expected to have passed the A-level mathematics exam. The curriculum at the Kigali Institute of Technology for a BS in Applied Mathematics was as follows(only the Math courses are listed, and the list is incomplete): Year 1: Analysis I: (6 hours of lecture, 2 hours tutorial, this course is a rigorous calculus course, like Apostol's book) Algebra I: (6 h lecture, 2 h tutorial)(Linear Algebra) Analysis II: (6+2, Continuation of Analysis I) Algebra II: (6+2, Abstract Algebra) Year 2: Analysis III: (6+2, Multivariable Analysis) Analysis IV: (6+2, ODE and PDE) Statistics: (6+2) Numerical Analysis: (6+2) Year 3: Functional Analysis: (6+2) Complex Analysis: (6+2) Algebra III: (6+2) Linear Programming: (6+2) Mathematical Modelling I&II (6+2, each) Year 4: Seminar Research/Thesis Mathematical Modelling III Besides these courses, students take Physics and Foreign Language courses in their first two years. One can see that this program is very ambitious. Students must pass finals in each of those courses. However, passing means achieving 50% or more of the possible marks. Unfortunately, much of the program consists of wishful thinking. The lack of resources severly impedes the program. There are too few computer labs and no text books. At KIST blackboards were a limited resource as were desks for students and light bulbs. Internet access is slow if it is available. Finally there is a severe shortage of qualified teaching personnel. At KIST there are currently only two faculty members with doctorate degrees. Much of the teaching is done by faculty with MS degrees or even BS degrees. I taught Analysis IV to 60 second year students. Their preparation was similar to a junior or senior at CSUN. Some of the students were incredibly good, and most were extremely well motivated. As one can see the content of the four year BS degree is significantly more than here, almost what we require for an MS in Applied Mathematics. top of page	Building on the Campus of the Kigali Institute of Science and Technology Students of my Analysis IV Class at KIST Class room at the National University in Butare with Real Analysis in French. The black boards at KIST were not nearly as nice.
		Challenges Resources for education are the biggest challenges. As mentioned above, we lacked books, black boards, computers, desks and many more of the things we take for granted here. It is difficult and expensive to attract faculty to the universities in Rwanda. There is only a handful of Rwandans who ever got a Doctorate in Mathematics. There are few post-graduate degrees offered in the country, and graduates will go to neighboring African countries, South Africa, Europe or North America for MS and Ph.D. degrees. Most will never come back after having experienced life in prosperity. Secondary teachers in the capital Kigali earn approximately $85 per month,which is a lot compared to the per capita income. Nevertheless it is not enough to live in Kigali and pay back your bursary. The government has started a push to become an anglophone country (instead of a francophone one). This has to do with the uneasy relationship between France, who was a major supporter of the previous regime (and therefore bears some responsibility for the genocide) and the current Rwandan leadership (most of whom grew up in anglophone Uganda). In the long run the switch to English will make it easier to attract qualified faculty and other professionals from other more developed countries (such as India and South Africa). In the short term this created a shortage of qualified teachers in secondary schools, since most of the existing teachers were trained in the existing francophone environment. top of page	Typical country side in Rwanda, hills with small farms, red clay, and banana trees
		Advantages The Rwandan Education System has some advantages from which we in the US can learn. One would be that Secondary School has truly world class standards in mathematics and an enforcement mechanism which goes beyond the standardized assessments we use here. The national exam, coupled with minimum entrance requirements for universities plays an important role here. The preparedness of entering students is more uniform than here which allows for a more advanced undergraduate curriculum and a cohort structure of the undergraduate program. Besides the practical advantages of a cohort structure (easier scheduling etc.) it also has tangible pedagogical advantages. Cohorts form a structured environment in which students can learn from each other. Finally each cohort elected a representative (the chef); the chef was responsible for distributing course materials and collecting homework assignments. The chef even selected dates for exams, which made it easy for faculty to avoid conflicts etc. . Class representatives are an institution which we could easily make use of in the United States as well. top of page	Farm near Volcanoes National Park
		Remarks In the introduction I write about the "ethnic" groups as Bahutu and Batutsi. In the western media these group were called "Hutus" and "Tutsis", I used the correct Kinyarwanda terms. Much nonsense was and still is written about the "ethnic" differences between these groups. The origin of this nonsense is an English missionary, Jonathan Speke, who visited the great lakes region in the 1840s (not Rwanda itself) and claimed that the ruling group was taller and of lighter complexion than the toiling masses. He immediately found a "racial" difference between the groups and claimed that the ruling group (the Batutsi in Rwanda, but similar structures existed in many small kingdoms, which now make up Uganda) must be the lost tribe of Israel. If there was such a difference in physical appearance it may well have been due to the simple fact that the ruling group were cattle owners and had for generations been subject to a diet rich in meat and dairy products compared to the rather protein poor diet of the toiling masses. In fact, when the Belgians issued racial identity cards in the 1930s, the criteria to be Batutsi was to own at least seven cows, and not whether your parents were Batutsi or not. Rwandans come in all shapes and sizes, just like Bavarians do. So in my humble opinion the "ethnic" division between the two groups was artificially constructed by the Europeans. top of page
		References For more information about Rwanda I list some references. However, the best way to learn more about Rwanda is to join one of many volunteer organizations like Doctors without Borders, Engineers without Borders, or the Peace Corps and go there and stay for a few months. Short of this you can also visit Rwanda as a tourist, view the mountain gorillas and have some of the best goat brochettes in the world. Books about Rwanda: Rose Carr, The Land of a Thousand Hills: This is the autobiography of the American Rose Carr, who lived in Rwanda from 1949 to 2006. It is a nice read to get an introduction into Rwanda's history, but read my remarks above first. Gerard Prunier, The Rwanda Crisis: History of a Genocide: Probably the most comprehensive work on the Rwandan genocide. Gil Courtemanche, A Sunday Afternoon at the Pool in Kigali: This is a novel set against the background of the genocide. Well written, but some readers may find it difficult, due to its graphic content. Romeo Dallaire, Shaking Hands with the Devil: A personal account of the commander of the UN peace keeping mission in Rwanda during the genocide. Movies: Hotel Rwanda, unfortunately this movie was not shot in Rwanda, but in South Africa, otherwise it gives a good introduction to the genocide. I saw it after I had been at the scene - the Hotel Mille Collines - several times and found that the town in the movie didn't look like Kigali at all. However, if you watch the opening credits you can see Rwanda's country side in the background behind Don Sheadle. Un Dimanche a Kigali, this Canadian production is the movie to the above mentioned book and was shot on location. It is difficult to get in the United States. I saw parts of it (the last 45 min or so) at the Rwanda Film festival in Kigali. Shooting Dogs, a Portugese movie about the UN peace keeping mission in Rwanda. You will understand the meaning of the title after reading about the genocide. Gorillas in the Mist: The life and death of Dian Fossey, the famed mountain gorilla researcher. It is shot on location in Volcanoes National Park and portraits the beauty of the country very well.